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Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī)^[1] (Template:Lang-fa Ghiyās-ud-dīn Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician.

Biography

Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380, in Kashan, in central Iran. This region was controlled by Tamurlane, better known as Timur. Al-Kashi lived in poverty during his childhood and the beginning years of his adulthood.

The situation changed for the better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and his wife, Goharshad, a Persian princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world’s greatest mathematicians.

Eight years after he came into power in 1409, their son, Ulugh Beg, founded an institute in Samarkand which soon became a prominent university. Students from all over the Middle East, and beyond, flocked to this academy in the capital city of Ulugh Beg’s empire. Consequently, Ulugh Beg harvested many great mathematicians and scientists of the Muslim world. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg, and it is said that he was the king’s favourite student.

Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on the Chord and Sine”, when he died in 1429. Some scholars believe that Ulugh Beg may have ordered his murder, while others say he died a natural death. The details are unclear.

Astronomy

Khaqani Zij

Al-Kashi produced a Zij entitled the Khaqani Zij, which was based on Nasir al-Din al-Tusi's earlier Zij-i Ilkhani. In his Khaqani Zij, al-Kashi thanks the Timurid sultan and mathematician-astronomer Ulugh Beg, who invited al-Kashi to work at his observatory (see Islamic astronomy) and his university (see Madrasah) which taught Islamic theology as well as Islamic science. Al-Kashi produced sine tables to four sexagesimal digits (equivalent to eight decimal places) of accuracy for each degree and includes differences for each minute. He also produced tables dealing with transformations between coordinate systems on the celestial sphere, such as the transformation from the ecliptic coordinate system to the equatorial coordinate system.^[2]

Astronomical Treatise on the size and distance of heavenly bodies

He wrote the book Sullam al-Sama on the resolution of difficulties met by predecessors in the determination of distances and sizes of heavenly bodies such as the Earth, the Moon, the Sun and the Stars.

Treatise on Astronomical Observational Instruments

In 1416, al-Kashi wrote the Treatise on Astronomical Observational Instruments, which described a variety of different instruments, including the triquetrum and armillary sphere, the equinoctial armillary and solsticial armillary of Mo'ayyeduddin Urdi, the sine and versine instrument of Urdi, the sextant of al-Khujandi, the Fakhri sextant at the Samarqand observatory, a double quadrant Azimuth-altitude instrument he invented, and a small armillary sphere incorporating an alhidade which he invented.^[3]

Plate of Conjunctions

Al-Kashi invented the Plate of Conjunctions, an analog computing instrument used to determine the time of day at which planetary conjunctions will occur,^[4] and for performing linear interpolation.^[5]

Planetary computer

Al-Kashi also invented a mechanical planetary computer which he called the Plate of Zones, which could graphically solve a number of planetary problems, including the prediction of the true positions in longitude of the Sun and Moon,^[5] and the planets in terms of elliptical orbits;^[6] the latitudes of the Sun, Moon, and planets; and the ecliptic of the Sun. The instrument also incorporated an alhidade and ruler.^[7]

Mathematics

Law of cosines

In French, the law of cosines is named Théorème d'Al-Kashi (Theorem of Al-Kashi), as al-Kashi was the first to provide an explicit statement of the law of cosines in a form suitable for triangulation.

The Treatise on the Chord and Sine

In The Treatise on the Chord and Sine, al-Kashi computed sin 1° to nearly as much accuracy as his value for π, which was the most accurate approximation of sin 1° in his time and was not surpassed until Taqi al-Din in the 16th century. In algebra and numerical analysis, he developed an iterative method for solving cubic equations, which was not discovered in Europe until centuries later.^[2]

A method algebraically equivalent to Newton's method was known to his predecessor Sharaf al-Dīn al-Tūsī. Al-Kāshī improved on this by using a form of Newton's method to solve $x^{P} - N = 0$ to find roots of N. In western Europe, a similar method was later described by Henry Biggs in his Trigonometria Britannica, published in 1633.^[8]

In order to determine sin 1°, al-Kashi discovered the following formula often attributed to François Viète in the 16th century:^[9]

$\sin 3 ϕ = 3 \sin ϕ - 4 \sin^{3} ϕ$

The Key to Arithmetic

Computation of 2π

In his numerical approximation, he correctly computed 2π (or $τ$ ) to 9 sexagesimal digits^[10] in 1424,^[2] and he converted this approximation of 2π to 17 decimal places of accuracy.^[11] This was far more accurate than the estimates earlier given in Greek mathematics (3 decimal places by Archimedes), Chinese mathematics (7 decimal places by Zu Chongzhi) or Indian mathematics (11 decimal places by Madhava of Sangamagrama). The accuracy of al-Kashi's estimate was not surpassed until Ludolph van Ceulen computed 20 decimal places of π nearly 200 years later.^[2] It should be noted that al-Kashi's goal was not to compute the circle constant with as many digits as possible but to compute it so precisely that the circumference of the largest possible circle (ecliptica) could be computed with highest desirable precision (the diameter of a hair).

Decimal fractions

In discussing decimal fractions, Struik states that (p. 7):^[12]

"The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphlet De Thiende, published at Leyden in 1585, together with a French translation, La Disme, by the Flemish mathematician Simon Stevin (1548-1620), then settled in the Northern Netherlands. It is true that decimal fractions were used by the Chinese many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and sexagesimal fractions with great ease in his Key to arithmetic (Samarkand, early fifteenth century).^[13]"

Khayyam's triangle

In considering Pascal's triangle, known in Persia as "Khayyam's triangle" (named after Omar Khayyám), Struik notes that (p. 21):^[12]

"The Pascal triangle appears for the first time (so far as we know at present) in a book of 1261 written by Yang Hui, one of the mathematicians of the Sung dynasty in China.^[14] The properties of binomial coefficients were discussed by the Persian mathematician Jamshid Al-Kāshī in his Key to arithmetic of c. 1425.^[15] Both in China and Persia the knowledge of these properties may be much older. This knowledge was shared by some of the Renaissance mathematicians, and we see Pascal's triangle on the title page of Peter Apian's German arithmetic of 1527. After this we find the triangle and the properties of binomial coefficients in several other authors.^[16]"

Biographical film

In 2009 IRIB produced and broadcast (through Channel 1 of IRIB) a biographical-historical film series on the life and times of Jamshid Al-Kāshi, with the title The Ladder of the Sky ^[17]^[18] (Nardebām-e Āsmān ^[19]). The series, which consists of 15 parts of each 45 minutes duration, is directed by Mohammad-Hossein Latifi and produced by Mohsen Ali-Akbari. In this production, the role of the adult Jamshid Al-Kāshi is played by Vahid Jalilvand.^[20]^[21]^[22]

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.

Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.

One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London

Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property

All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004

It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.

Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines

External links

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A summary of "Miftah al-Hisab"
About Jamshid Kashani

Template:Islamic astronomy Template:Islamic mathematics

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↑ A. P. Youschkevitch and B. A. Rosenfeld. "al-Kāshī (al-Kāshānī), Ghiyāth al-Dīn Jamshīd Masʿūd" Dictionary of Scientific Biography.
↑ ^2.0 ^2.1 ^2.2 ^2.3 Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.

Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.

One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London

Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property

All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004

It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.

Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines
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↑ Template:Harv
↑ Template:Harv
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256
↑ The statement that a quantity is calculated to $n$ sexagesimal digits implies that the maximal inaccuracy in the calculated value is less than $59 / 6 0^{n + 1} + 59 / 6 0^{n + 2} + \dots = 1 / 6 0^{n}$ in the decimal system. With $n = 9$ , Al-Kashi has thus calculated $2 π$ with a maximal error less than $1 / 6 0^{9} \approx 9.92 \times 1 0^{- 17} < 1 0^{- 16}$ . That is to say, Al-Kashi has calculated $2 π$ exactly up to and including the 16th place after the decimal separator. For $2 π$ expressed exactly up to and including the 18th place after the decimal separator one has: $6.283 185 307 179 586 476$ .
↑ ^12.0 ^12.1 D.J. Struik, A Source Book in Mathematics 1200-1800 (Princeton University Press, New Jersey, 1986). ISBN 0-691-02397-2
↑ P. Luckey, Die Rechenkunst bei Ğamšīd b. Mas'ūd al-Kāšī (Steiner, Wiesbaden, 1951).
↑ J. Needham, Science and civilisation in China, III (Cambridge University Press, New York, 1959), 135.
↑ Russian translation by B.A. Rozenfel'd (Gos. Izdat, Moscow, 1956); see also Selection I.3, footnote 1.
↑ Smith, History of mathematics, II, 508-512. See also our Selection II.9 (Girard).
↑ The narrative by Latifi of the life of the celebrated Iranian astronomer in 'The Ladder of the Sky' , in Persian, Āftāb, Sunday, 28 December 2008, [1].
↑ IRIB to spice up Ramadan evenings with special series, Tehran Times, 22 August 2009, [2].
↑ The name Nardebām-e Āsmān coincides with the Persian translation of the title Soll'am-os-Samā' (سُلّمُ السَماء) of a scientific work by Jamshid Kashani written in Arabic. In this work, which is also known as Resāleh-ye Kamālieh (رسالهٌ كماليه), Jamshid Kashani discusses such matters as the diameters of Earth, the Sun, the Moon, and of the stars, as well as the distances of these to Earth. He completed this work on 1 March 1407 CE in Kashan.
↑ The programmes of the Holy month of Ramadan, Channel 1, in Persian, 19 August 2009, [3]. Here the name "Latifi" is incorrectly written as "Seifi".
↑ Dr Velāyati: 'The Ladder of the Sky' is faithful to history, in Persian, Āftāb, Tuesday, 1 September 2009, [4].
↑ Fatemeh Udbashi, Latifi's narrative of the life of the renowned Persian astronomer in 'The Ladder of the Sky' , in Persian, Mehr News Agency, 29 December 2008, [5].

[1] A. P. Youschkevitch and B. A. Rosenfeld. "al-Kāshī (al-Kāshānī), Ghiyāth al-Dīn Jamshīd Masʿūd" Dictionary of Scientific Biography.

[MacTutor-2] 2.0 ^2.1 ^2.2 ^2.3 Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.

Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.

One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London

Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property

All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004

It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.

Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines

[3] Template:Harv

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[Kennedy-5] 5.0 ^5.1 Template:Harv

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[8] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[9] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[10] Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256

[11] The statement that a quantity is calculated to $n$ sexagesimal digits implies that the maximal inaccuracy in the calculated value is less than $59 / 6 0^{n + 1} + 59 / 6 0^{n + 2} + \dots = 1 / 6 0^{n}$ in the decimal system. With $n = 9$ , Al-Kashi has thus calculated $2 π$ with a maximal error less than $1 / 6 0^{9} \approx 9.92 \times 1 0^{- 17} < 1 0^{- 16}$ . That is to say, Al-Kashi has calculated $2 π$ exactly up to and including the 16th place after the decimal separator. For $2 π$ expressed exactly up to and including the 18th place after the decimal separator one has: $6.283 185 307 179 586 476$ .

[Struik1986-12] 12.0 ^12.1 D.J. Struik, A Source Book in Mathematics 1200-1800 (Princeton University Press, New Jersey, 1986). ISBN 0-691-02397-2

[13] P. Luckey, Die Rechenkunst bei Ğamšīd b. Mas'ūd al-Kāšī (Steiner, Wiesbaden, 1951).

[14] J. Needham, Science and civilisation in China, III (Cambridge University Press, New York, 1959), 135.

[15] Russian translation by B.A. Rozenfel'd (Gos. Izdat, Moscow, 1956); see also Selection I.3, footnote 1.

[16] Smith, History of mathematics, II, 508-512. See also our Selection II.9 (Girard).

[17] The narrative by Latifi of the life of the celebrated Iranian astronomer in 'The Ladder of the Sky' , in Persian, Āftāb, Sunday, 28 December 2008, [1].

[18] IRIB to spice up Ramadan evenings with special series, Tehran Times, 22 August 2009, [2].

[19] The name Nardebām-e Āsmān coincides with the Persian translation of the title Soll'am-os-Samā' (سُلّمُ السَماء) of a scientific work by Jamshid Kashani written in Arabic. In this work, which is also known as Resāleh-ye Kamālieh (رسالهٌ كماليه), Jamshid Kashani discusses such matters as the diameters of Earth, the Sun, the Moon, and of the stars, as well as the distances of these to Earth. He completed this work on 1 March 1407 CE in Kashan.

[20] The programmes of the Holy month of Ramadan, Channel 1, in Persian, 19 August 2009, [3]. Here the name "Latifi" is incorrectly written as "Seifi".

[21] Dr Velāyati: 'The Ladder of the Sky' is faithful to history, in Persian, Āftāb, Tuesday, 1 September 2009, [4].

[22] Fatemeh Udbashi, Latifi's narrative of the life of the renowned Persian astronomer in 'The Ladder of the Sky' , in Persian, Mehr News Agency, 29 December 2008, [5].

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-Hi there, I am Alyson Boon although it is not the title on  clairvoyant [http://www.zavodpm.ru/blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going cheap psychic readings] - [http://bigpolis.com/blogs/post/6503 bigpolis.com] - my birth certificate. Office supervising is exactly where her primary income arrives from. The favorite pastime for him and his children is to perform lacross and he would never give it up. Alaska is the only location I've been residing in but now I'm considering other options.<br><br>Look at my web page [http://www.prograd.uff.br/novo/facts-about-growing-greater-organic-garden clairvoyants]
+{{Peacock|date=October 2009}}
+{{Infobox Muslim scholar |
+ <!-- Astronomer Category -->
+ notability = [[Persian peoples|Persian]] [[Muslim]] [[scholar]]|
+ era = [[Islamic Golden Age]]|
+ image =|
+ caption = |
+ name = '''Ghiyāth al-Dīn Jamshīd Kāshānī''' |
+ title= al-Kashi|
+ birth_date = 1380|
+ death_date = 22 June 1429 |
+ ethnicity = [[Persian people|Persian]]|
+ region = [[Iran]]|
+ Maddhab = |
+ school_tradition|= |
+ main_interests = [[Islamic astronomy|Astronomy]], [[Islamic mathematics|Mathematics]]|
+ notable_ideas= Pi decimal determination to the 16th place|
+  works = [[Sullam al-Sama]]|
+ influences =|
+ influenced =
+}}
+'''Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī''' (or '''al-Kāshānī''')<ref>[[A. P. Youschkevitch]] and [[B. A. Rosenfeld]]. "[http://www.encyclopedia.com/doc/1G2-2830902260.html al-Kāshī (al-Kāshānī), Ghiyāth al-Dīn Jamshīd Masʿūd]" ''[[Dictionary of Scientific Biography]]''.</ref> ({{lang-fa|غیاث‌الدین جمشید کاشانی}} ''Ghiyās-ud-dīn Jamshīd Kāshānī'') (c. 1380 [[Kashan]], [[Iran]] &ndash; 22 June 1429 [[Samarkand]], [[Transoxania]]) was a [[Persian people|Persian]] [[Islamic astronomy|astronomer]] and [[Islamic mathematics|mathematician]].
+==Biography==
+Al-Kashi was one of the best mathematicians in the [[Islamic world]]. He was born in 1380, in [[Kashan]], in central Iran. This region was controlled by [[Timur|Tamurlane]], better known as Timur. Al-Kashi lived in poverty during his childhood and the beginning years of his adulthood.
+The situation changed for the better when Timur died in 1405, and his son, [[Shah Rukh (Timurid dynasty)|Shah Rokh]], ascended into power. Shah Rokh and his wife, [[Goharshad]], a Persian princess, were very interested in the [[sciences]], and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world’s greatest mathematicians.
+Eight years after he came into power in 1409, their son, Ulugh Beg, founded an institute in [[Samarkand]] which soon became a prominent university. Students from all over the [[Middle East]], and beyond, flocked to this academy in the capital city of Ulugh Beg’s empire. Consequently, Ulugh Beg harvested many great mathematicians and scientists of the [[Muslim world]]. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg, and it is said that he was the king’s favourite student.
+Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on the Chord and Sine”, when he died in 1429. Some scholars believe that Ulugh Beg may have ordered his murder, while others say he died a natural death. The details are unclear.
+==Astronomy==
+===''Khaqani Zij''===
+Al-Kashi produced a ''[[Zij]]'' entitled the ''Khaqani Zij'', which was based on [[Nasir al-Din al-Tusi]]'s earlier ''[[Zij-i Ilkhani]]''. In his ''Khaqani Zij'', al-Kashi thanks the [[Timurid dynasty|Timurid]] sultan and mathematician-astronomer [[Ulugh Beg]], who invited al-Kashi to work at his [[observatory]] (see [[Islamic astronomy]]) and his [[university]] (see [[Madrasah]]) which taught [[Kalam|Islamic theology]] as well as [[Islamic science]]. Al-Kashi produced [[Trigonometric functions|sine]] tables to four [[sexagesimal]] digits (equivalent to eight [[decimal]] places) of accuracy for each degree and includes differences for each minute. He also produced tables dealing with transformations between [[coordinate system]]s on the [[celestial sphere]], such as the transformation from the [[ecliptic coordinate system]] to the [[equatorial coordinate system]].<ref name=MacTutor/>
+===''Astronomical Treatise on the size and distance of heavenly bodies''===
+He wrote the book [[Sullam al-Sama]] on the resolution of difficulties met by predecessors in the determination of distances and sizes of [[Astronomical object|heavenly bodies]] such as the [[Earth]], the [[Moon]], the [[Sun]] and the [[Stars]].
+===''Treatise on Astronomical Observational Instruments''===
+In 1416, [[al-Kashi]] wrote the ''Treatise on Astronomical Observational Instruments'', which described a variety of different instruments, including the [[Triquetrum (astronomy)|triquetrum]] and [[armillary sphere]],  the [[Equinox|equinoctial]] armillary and [[Solstice|solsticial]] armillary of [[Mo'ayyeduddin Urdi]], the [[sine]] and [[versine]] instrument of Urdi, the [[Sextant (astronomical)|sextant]] of [[al-Khujandi]], the Fakhri sextant at the [[Samarqand]] observatory, a double quadrant [[Azimuth]]-[[altitude]] instrument he invented, and a small armillary sphere incorporating an [[alhidade]] which he invented.<ref>{{Harv|Kennedy|1961|pp=104–107}}</ref>
+====Plate of Conjunctions====
+Al-Kashi invented the Plate of Conjunctions, an [[Analog computer|analog computing]] instrument used to determine the time of day at which [[planetary conjunction]]s will occur,<ref>{{Harv|Kennedy|1947|p=56}}</ref> and for performing [[linear interpolation]].<ref name=Kennedy/>
+====Planetary computer====
+Al-Kashi also invented a mechanical planetary [[Analog computer|computer]] which he called the Plate of Zones, which could graphically solve a number of planetary problems, including the prediction of the true positions in [[longitude]] of the [[Sun]] and [[Moon]],<ref name=Kennedy>{{Harv|Kennedy|1950}}</ref> and the [[planet]]s in terms of [[elliptical orbit]]s;<ref>{{Harv|Kennedy|1952}}</ref> the [[latitude]]s of the Sun, Moon, and planets; and the [[ecliptic]] of the Sun. The instrument also incorporated an [[alhidade]] and [[ruler]].<ref>{{Harv|Kennedy|1951}}</ref>
+==Mathematics==
+===Law of cosines===
+In [[French language|French]], the [[law of cosines]] is named ''[[:fr:Théorème d'Al-Kashi|Théorème d'Al-Kashi]]'' (Theorem of Al-Kashi), as al-Kashi was the first to provide an explicit statement of the law of cosines in a form suitable for [[triangulation]].
+===''The Treatise on the Chord and Sine''===
+In ''The Treatise on the Chord and Sine'', al-Kashi computed sin 1° to nearly as much accuracy as his value for π, which was the most accurate approximation of sin 1° in his time and was not surpassed until [[Taqi al-Din Muhammad ibn Ma'ruf|Taqi al-Din]] in the 16th century. In [[algebra]] and [[numerical analysis]], he developed an [[iterative method]] for solving [[cubic equation]]s, which was not discovered in Europe until centuries later.<ref name=MacTutor/>
+A method algebraically equivalent to [[Newton's method]] was known to his predecessor [[Sharaf al-Dīn al-Tūsī]]. Al-Kāshī improved on this by using a form of Newton's method to solve <math>x^P - N = 0</math> to find roots of ''N''. In [[western Europe]], a similar method was later described by Henry Biggs in his ''Trigonometria Britannica'', published in 1633.<ref>{{citation|title=Historical Development of the Newton-Raphson Method|first=Tjalling J.|last=Ypma|journal=SIAM Review|volume=37|issue=4|date=December 1995|publisher=Society for Industrial and Applied Mathematics|pages=531–551 [539]|doi=10.1137/1037125}}</ref>
+In order to determine sin 1°, al-Kashi discovered the following formula often attributed to [[François Viète]] in the 16th century:<ref>{{citation|title=Sherlock Holmes in Babylon and Other Tales of Mathematical History|last=Marlow Anderson, Victor J. Katz|first=Robin J. Wilson|publisher=[[Mathematical Association of America]]|year=2004|isbn=0-88385-546-1|page=139}}</ref>
+<math>\sin 3 \phi = 3 \sin \phi - 4 \sin^3 \phi\,\!</math>
+===''The Key to Arithmetic''===
+====Computation of 2π====
+In his [[numerical approximations of π|numerical approximation]], he correctly computed 2π (or [[Tau (2π)|<math>\tau</math>]]) to 9 [[sexagesimal]] digits<ref>''Al-Kashi'', author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256</ref> in 1424,<ref name=MacTutor/> and he converted this approximation of 2π to 17 [[decimal]] places of accuracy.<ref>The statement that a quantity is calculated to <math>\scriptstyle n</math> sexagesimal digits implies that the maximal ''inaccuracy'' in the calculated value is less than  <math>\scriptstyle 59/60^{n+1} + 59/60^{n+2} + \dots = 1/60^n</math> in the [[decimal]] system. With <math>\scriptstyle n=9</math>, Al-Kashi has thus calculated <math>\scriptstyle 2\pi</math> with a maximal ''error'' less than <math>\scriptstyle 1/60^{9}\approx 9.92\times 10^{-17} < 10^{-16}\,</math>. That is to say, Al-Kashi has calculated <math>\scriptstyle 2\pi</math> exactly up to and including the 16th place after the [[decimal separator]]. For <math>\scriptstyle 2\pi</math> expressed exactly up to and including the 18th place after the decimal separator one has: <math>\scriptstyle 6.283\,185\,307\,179\,586\,476</math>.</ref> This was far more accurate than the estimates earlier given in [[Greek mathematics]] (3 decimal places by [[Archimedes]]), [[Chinese mathematics]] (7 decimal places by [[Zu Chongzhi]]) or [[Indian mathematics]] (11 decimal places by [[Madhava of Sangamagrama]]). The accuracy of al-Kashi's estimate was not surpassed until [[Ludolph van Ceulen]] computed 20 decimal places of π nearly 200 years later.<ref name=MacTutor>{{MacTutor|id=Al-Kashi|title=Ghiyath al-Din Jamshid Mas'ud al-Kashi}}</ref> It should be noted that al-Kashi's goal was not to compute the circle constant with as many digits as possible but to compute it so precisely that the circumference of the largest possible circle (ecliptica) could be computed with highest desirable precision (the diameter of a hair).
+====Decimal fractions====
+In discussing [[decimal fractions]], [[Dirk Jan Struik|Struik]] states that (p.&nbsp;7):<ref name="Struik1986">D.J. Struik, ''A Source Book in Mathematics 1200-1800'' (Princeton University Press, New Jersey, 1986). ISBN 0-691-02397-2</ref>
+<blockquote>
+"The introduction of decimal fractions as a common computational practice can be dated back to the [[Flemish Region|Flemish]] pamphlet ''De Thiende'', published at [[Leiden|Leyden]] in 1585, together with a French translation, ''La Disme'', by the Flemish mathematician [[Simon Stevin]] (1548-1620), then settled in the Northern [[Netherlands]]. It is true that decimal fractions were used by the [[Chinese mathematics|Chinese]] many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and [[sexagesimal]] fractions with great ease in his ''Key to arithmetic'' (Samarkand, early fifteenth century).<ref>P. Luckey, ''Die Rechenkunst bei Ğamšīd b. Mas'ūd al-Kāšī'' (Steiner, Wiesbaden, 1951).</ref>"
+</blockquote>
+====Khayyam's triangle====
+In considering [[Pascal's triangle]], known in Persia as "Khayyam's triangle" (named after [[Omar Khayyám]]), Struik notes that (p.&nbsp;21):<ref name="Struik1986"/>
+<blockquote>
+"The Pascal triangle appears for the first time (so far as we know at present) in a book of 1261 written by [[Yang Hui]], one of the mathematicians of the [[Sung dynasty]] in [[China]].<ref>J. Needham, ''Science and civilisation in China'', III (Cambridge University Press, New York, 1959), 135.</ref> The properties of [[binomial coefficient]]s were discussed by the Persian mathematician Jamshid Al-Kāshī in his ''Key to arithmetic'' of c. 1425.<ref>Russian translation by B.A. Rozenfel'd (Gos. Izdat, Moscow, 1956); see also Selection '''I.3''', footnote '''1'''.</ref> Both in China and Persia the knowledge of these properties may be much older. This knowledge was shared by some of the [[Renaissance]] mathematicians, and we see [[Blaise Pascal|Pascal]]'s triangle on the title page of [[Peter Apian]]'s [[German language|German]] arithmetic of 1527. After this we find the triangle and the properties of binomial coefficients in several other authors.<ref>Smith, ''History of mathematics'', II, 508-512. See also our Selection '''II.9''' (Girard).</ref>"
+</blockquote>
+== Biographical film ==
+In 2009 [[IRIB]] produced and broadcast (through Channel 1 of IRIB) a biographical-historical film series on the life and times of Jamshid Al-Kāshi, with the title ''[[The Ladder of the Sky]]'' <ref>''The narrative by Latifi of the life of the celebrated Iranian astronomer in 'The Ladder of the Sky' '', in Persian, Āftāb, Sunday, 28 December 2008, [http://www.aftab.ir/news/2008/dec/28/c5c1230463130_art_culture_media_serial.php].</ref><ref>''IRIB to spice up Ramadan evenings with special series'', Tehran Times, 22 August 2009, [http://www.tehrantimes.com/index_View.asp?code=201568].</ref> (''Nardebām-e Āsmān'' <ref>The name ''Nardebām-e Āsmān'' coincides with the [[Persian language|Persian]] translation of the title ''Soll'am-os-Samā' '' (سُلّمُ السَماء) of a scientific work by Jamshid Kashani written in [[Arabic language|Arabic]]. In this work, which is also known as ''Resāleh-ye Kamālieh'' (رسالهٌ كماليه), Jamshid Kashani discusses such matters as the diameters of [[Earth]], the [[Sun]], the [[Moon]], and of the [[stars]], as well as the distances of these to Earth. He completed this work on 1 March 1407 CE in Kashan.</ref>). The series, which consists of 15 parts of each 45 minutes duration, is directed by Mohammad-Hossein Latifi and produced by Mohsen Ali-Akbari. In this production, the role of the adult Jamshid Al-Kāshi is played by Vahid Jalilvand.<ref>''The programmes of the Holy month of Ramadan, Channel 1'', in Persian, 19 August 2009, [http://ch1.iribtv.ir/index.php?option=com_content&task=view&id=5246&Itemid=265]. Here the name "Latifi" is incorrectly written as "Seifi".</ref><ref>''Dr Velāyati: 'The Ladder of the Sky' is faithful to history'', in Persian, Āftāb, Tuesday, 1 September 2009, [http://www.aftab.ir/news/2009/sep/01/c5c1251816526_art_culture_media_serial.php].</ref><ref>Fatemeh Udbashi, ''Latifi's narrative of the life of the renowned Persian astronomer in 'The Ladder of the Sky' '', in Persian, Mehr News Agency, 29 December 2008, [http://www.mehrnews.ir/NewsPrint.aspx?NewsID=808056].</ref>
+==Notes==
+{{reflist|2}}
+==See also==
+*[[History of numerical approximations of π]]
+== References ==
+*{{Citation
+ |last=Kennedy
+ |first=Edward S.
+ |year=1947
+ |title=Al-Kashi's Plate of Conjunctions
+ |journal=[[Isis (journal)|Isis]]
+ |volume=38
+ |issue=1–2
+ |pages=56–59
+ |doi=10.1086/348036
+ }}
+*{{Citation
+ |last=Kennedy
+ |first=Edward S.
+ |year=1950
+ |title=A Fifteenth-Century Planetary Computer: al-Kashi's "Tabaq al-Manateq" I. Motion of the Sun and Moon in Longitude
+ |journal=[[Isis (journal)|Isis]]
+ |volume=41
+ |issue=2
+ |pages=180–183
+ |doi=10.1086/349146
+ }}
+*{{Citation
+ |last=Kennedy
+ |first=Edward S.
+ |year=1951
+ |title=An Islamic Computer for Planetary Latitudes
+ |journal=[[Journal of the American Oriental Society]]
+ |volume=71
+ |issue=1
+ |pages=13–21
+ |doi=10.2307/595221
+ |publisher=American Oriental Society
+ |jstor=595221
+ }}
+*{{Citation
+ |last=Kennedy
+ |first=Edward S.
+ |year=1952
+ |title=A Fifteenth-Century Planetary Computer: al-Kashi's "Tabaq al-Maneteq" II: Longitudes, Distances, and Equations of the Planets
+ |journal=[[Isis (journal)|Isis]]
+ |volume=43
+ |issue=1
+ |pages=42–50
+ |doi=10.1086/349363
+ }}
+*{{MacTutor|id=Al-Kashi|title=Ghiyath al-Din Jamshid Mas'ud al-Kashi}}
+==External links==
+* {{cite encyclopedia | editor = Thomas Hockey et al | last = Schmidl | first = Petra G. | title=Kāshī: Ghiyāth (al‐Milla wa‐) al‐Dīn Jamshīd ibn Masʿūd ibn Maḥmūd al‐Kāshī &#91;al‐Kāshānī&#93; | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | year = 2007 | location = New York | pages = 613–5 | url=http://islamsci.mcgill.ca/RASI/BEA/Kashi_BEA.htm | isbn=978-0-387-31022-0}} ([http://islamsci.mcgill.ca/RASI/BEA/Kashi_BEA.pdf PDF version])
+*[http://www.math-cs.cmsu.edu/~mjms/2000.2/azar5.ps A summary of "Miftah al-Hisab"]
+*[http://www.iranchamber.com/personalities/jkashani/jamshid_kashani.php About Jamshid Kashani]
+{{Islamic astronomy}}
+{{Islamic mathematics}}
+{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
+| NAME              = Kashi, Jamshid
+| ALTERNATIVE NAMES =
+| SHORT DESCRIPTION = Persian mathematician and astronomer
+| DATE OF BIRTH     = 1380
+| PLACE OF BIRTH    =
+| DATE OF DEATH     = 1429
+| PLACE OF DEATH    =
+}}
+{{DEFAULTSORT:Kashi, Jamshid}}
+[[Category:1380 births]]
+[[Category:1429 deaths]]
+[[Category:People from Kashan]]
+[[Category:Astronomers of medieval Islam]]
+[[Category:Persian astronomers]]
+[[Category:Mathematicians of medieval Islam]]
+[[Category:14th-century mathematicians]]
+[[Category:15th-century mathematicians]]
+[[Category:Medieval Persian mathematicians]]
+[[Category:Medieval Persian astrologers]]
+[[Category:15th-century astronomers]]
+[[Category:15th-century Iranian people]]

Monodromy theorem: Difference between revisions

Revision as of 22:56, 16 March 2013

Contents

Biography

Astronomy

Khaqani Zij

Astronomical Treatise on the size and distance of heavenly bodies

Treatise on Astronomical Observational Instruments

Plate of Conjunctions

Planetary computer

Mathematics

Law of cosines

The Treatise on the Chord and Sine

The Key to Arithmetic

Computation of 2π

Decimal fractions

Khayyam's triangle

Biographical film

Notes

See also

References

External links

Navigation menu

Monodromy theorem: Difference between revisions

Revision as of 22:56, 16 March 2013

Biography

Astronomy

Khaqani Zij

Astronomical Treatise on the size and distance of heavenly bodies

Treatise on Astronomical Observational Instruments

Plate of Conjunctions

Planetary computer

Mathematics

Law of cosines

The Treatise on the Chord and Sine

The Key to Arithmetic

Computation of 2π

Decimal fractions

Khayyam's triangle

Biographical film

Notes

See also

References

External links

Navigation menu

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