formulasearchengine - User contributions [en]

Force between magnets

2015-01-05T20:57:16Z

50.47.60.86: /* Force between two cylindrical magnets */

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The body lock functions just like the liner lock nevertheless, instead of utilizing a separate lock bar, it makes use of the actual frame which can also be spring loaded to hold the blade in place. He decided to name in “integral lock”. The mid lock is actually a back lock positioned on the center of the knife spine as a substitute of the back. This gives added energy for the blade lock and allows the blade to face up to more strain than the again lock. Chilly Metal is an avid proponent of the mid lock. Lock Again (Again Lock) In a big signal of this rising reputation, Benchmade Knives , an organization not often related to bushcrafting, decided to pick up on the pattern. In March of 2012, they called on their gifted in-house knife designer, outdoor enthusiast Shane Sibert , to assist create Benchmade's first ever bushcraft knife - the 162 Bushcrafter. Determined not to repeat this painful piece of historical past, Benchmade took particular care in constructing the Bushcrafter to make it face up to heavy use. Their main goal was to make sure that the S30V Stainless used on the Bushcrafter would not solely have excellent edge-retention, but additionally be extremely tough, easy to sharpen and chip resistant. The SRK comes with a black blade so the very first thing I did was remove the paint. I intended to make use of the SRK for meat slicing and searching, so the painted blade seemed bizarre and Rambo-like. Apart from, I hunt with a number of former navy sorts, and they'd have laughed a "tactical" or survival knife out of camp! The primary fixed that it's best to look for is a fixed blade knife , all good survival knives ought to have a set blade. Most of these knives can deal with way more punishment and hard use than a [http://dallaskoreans.com/index.php?document_srl=404980&mid=Test folding knife] and might be a significantly better device for chopping and cutting. The Whiskey Folding KnifeThey’ve taken the basic French Opinel chrome steel blade pocket knife, and added the Son of a Sailor contact with sign [http://wiki.Paconun.eu/index.php/Old_Timer_Knife_Values flag-impressed colorblocking]. This walnut model, the No. 6, is named the Whiskey, and is available in woodland Inexperienced & Neon Coral or Cobalt & Seafoam. Every knife is hand-painted and will differ a bit from the picture. No two are precisely alike, but all are made with care!These knives are made with heavy-duty paint and polish. This can be a software supposed for rugged use, and a rough patina might be earned on the complete finish of the knife, over time. Green & Neon Coral Cobalt & Seafoam

Sextupole magnet

2013-11-12T18:06:50Z

50.47.59.86: /* Sextupoles in particle accelerators */

{{Use dmy dates|date=September 2010}}
A [[timeline]] of '''[[algebra]]''' and '''[[geometry]]'''

==Before 1000 BC==
* ca. 2000 BC — [[Scotland]], [[Carved Stone Balls]] exhibit a variety of symmetries including all of the symmetries of [[Platonic solid]]s.
* 1800 BC — [[Moscow Mathematical Papyrus]], findings volume of a frustum
* 1650 BC — [[Rhind Mathematical Papyrus]], copy of a lost scroll from around 1850 BC, the scribe [[Ahmes]] presents one of the first known approximate values of [[pi|π]] at 3.16, the first attempt at [[squaring the circle]], earliest known use of a sort of [[cotangent]], and knowledge of solving first order linear equations

==1st millennium BC==
* 800 BC — [[Baudhayana]], author of the Baudhayana [[Sulba Sutras|Sulba Sutra]], a [[Vedic Sanskrit]] geometric text, contains [[quadratic equations]], and calculates the [[square root]] of 2 correct to five decimal places
* ca. 600 BC — the other [[Vedic civilization|Vedic]] “[[Sulba Sutras]]” (“rule of chords” in [[Sanskrit]]) use [[Pythagorean triples]], contain of a number of geometrical proofs, and approximate [[pi|π]] at 3.16
* 5th century BC — [[Hippocrates of Chios]] utilizes [[Lune (mathematics)|lunes]] in an attempt to [[squaring the circle|square the circle]]
* 5th century BC — [[Apastamba]], author of the Apastamba [[Sulba Sutras|Sulba Sutra]], another [[Vedic Sanskrit]] geometric text, makes an attempt at [[squaring the circle]] and also calculates the [[square root]] of 2 correct to five decimal places
* 530 BC — [[Pythagoras]] studies propositional [[geometry]] and vibrating lyre strings; his group also discover the [[irrational number|irrationality]] of the [[square root]] of [[two]],
* 370 BC — [[Eudoxus of Cnidus|Eudoxus]] states the [[method of exhaustion]] for [[area]] determination
* 300 BC — [[Euclid]] in his ''[[Euclid's Elements|Elements]]'' studies [[geometry]] as an [[axiomatic system]], proves the [[Infinite set|infinitude]] of [[prime number]]s and presents the [[Euclidean algorithm]]; he states the law of reflection in ''Catoptrics'', and he proves the [[fundamental theorem of arithmetic]]
* 260 BC — [[Archimedes]] [[method of exhaustion|proved]] that the value of [[pi|π]] lies between 3 + 1/7 (approx. 3.1429) and 3 + 10/71 (approx. 3.1408), that the area of a circle was equal to π multiplied by the square of the radius of the circle and that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He also gave a very accurate estimate of the value of the square root of 3.
* 225 BC — [[Apollonius of Perga]] writes ''On [[Conic section|Conic Sections]]'' and names the [[ellipse]], [[parabola]], and [[hyperbola]],
* 150 BC — [[Jainism|Jain]] mathematicians in [[History of India|India]] write the “Sthananga Sutra”, which contains work on the theory of numbers, arithmetical operations, [[geometry]], operations with [[fractions]], simple equations, [[cubic equations]], quartic equations, and [[permutations]] and [[combinations]]
* 140 BC — [[Hipparchus]] develops the bases of [[trigonometry]].

==1st millennium==
* ca. 340 — [[Pappus of Alexandria]] states his [[Pappus's hexagon theorem|hexagon theorem]] and his [[Pappus's centroid theorem|centroid theorem]]
* 500 — [[Aryabhata]] writes the “Aryabhata-Siddhanta”, which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of [[sine]] and [[cosine]], and also contains the [[Aryabhata's sine table|earliest tables of sine]] and cosine values (in 3.75-degree intervals from 0 to 90 degrees)
* 600s — [[Bhaskara I]] gives a rational approximation of the sine function
* 700s — [[Virasena]] gives explicit rules for the [[Fibonacci sequence]], gives the derivation of the [[volume]] of a [[frustum]] using an [[Infinity|infinite]] procedure, and also deals with the [[logarithm]] to [[base 2]] and knows its laws
* 700s — [[Shridhara]] gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations
* 820 — [[Al-Mahani]] conceived the idea of reducing [[Geometry|geometrical]] problems such as [[doubling the cube]] to problems in algebra.
* ca. 900 — [[Abu Kamil]] of Egypt had begun to understand what we would write in symbols as <math>x^n \cdot x^m = x^{m+n}</math>
* 975 — [[Al-Batani]] — Extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions. Derived the formula: <math> \sin \alpha = \tan \alpha / \sqrt{1+\tan^2 \alpha} </math> and <math> \cos \alpha = 1 / \sqrt{1 + \tan^2 \alpha}</math>.

==1000–1500==
*ca. 1000 — [[Law of sines]] is discovered by [[Islamic mathematics|Muslim mathematicians]], but it is uncertain who discovers it first between [[Abu-Mahmud al-Khujandi]], [[Abu Nasr Mansur]], and [[Abū al-Wafā' al-Būzjānī|Abu al-Wafa]].
* ca. 1100 — [[Omar Khayyám]] “gave a complete classification of [[cubic equation]]s with geometric solutions found by means of intersecting [[conic section]]s.” He became the first to find general [[geometry|geometric]] solutions of [[cubic equation]]s and laid the foundations for the development of [[analytic geometry]] and [[non-Euclidean geometry]]. He also extracted [[root of a function|roots]] using the [[decimal]] system ([[Hindu-Arabic numeral system]]).
* 1135 — [[Sharafeddin Tusi]] followed al-Khayyam's application of algebra to geometry, and wrote a treatise on [[cubic equation]]s which “represents an essential contribution to another [[algebra]] which aimed to study [[curve]]s by means of [[equation]]s, thus inaugurating the beginning of [[algebraic geometry]].”<ref name=MacTutor>[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html Arabic mathematics], ''[[MacTutor History of Mathematics archive]]'', [[University of St Andrews]], Scotland</ref>
* ca. 1250 — [[Nasir Al-Din Al-Tusi]] attempts to develop a form of [[non-Euclidean geometry]].
* 15th century — [[Nilakantha Somayaji]], a [[Kerala school of astronomy and mathematics|Kerala school]] mathematician, writes the “Aryabhatiya Bhasya”, which contains work on infinite-series expansions, problems of algebra, and spherical geometry

==17th century==
* 1600s – Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series
* 1619 – [[Johannes Kepler]] discovers two of the [[Kepler-Poinsot polyhedra]].

==18th century==
* 1722 – [[Abraham de Moivre]] states [[de Moivre's formula]] connecting [[trigonometric function]]s and [[complex number]]s,
* 1733 – [[Giovanni Gerolamo Saccheri]] studies what geometry would be like if [[parallel postulate|Euclid's fifth postulate]] were false,
* 1796 – [[Carl Friedrich Gauss]] proves that the [[heptadecagon|regular 17-gon]] can be constructed using only a [[compass and straightedge]]
* 1797 – [[Caspar Wessel]] associates vectors with [[complex number]]s and studies complex number operations in geometrical terms,

==19th century==
* 1806 – [[Louis Poinsot]] discovers the two remaining [[Kepler-Poinsot polyhedra]].
* 1829 – [[Bolyai]], [[Carl Friedrich Gauss|Gauss]], and [[Nikolai Ivanovich Lobachevsky|Lobachevsky]] invent hyperbolic [[non-Euclidean geometry]],
* 1837 – [[Pierre Wanzel]] proves that doubling the cube and [[trisecting the angle]] are impossible with only a compass and straightedge, as well as the full completion of the problem of [[Constructible polygon|constructibility]] of regular polygons
* 1843 – [[William Rowan Hamilton|William Hamilton]] discovers the calculus of [[quaternion]]s and deduces that they are non-commutative,
* 1854 – [[Bernhard Riemann]] introduces [[Riemannian geometry]],
* 1854 – [[Arthur Cayley]] shows that [[quaternion]]s can be used to represent rotations in four-dimensional [[space]],
* 1858 – [[August Ferdinand Möbius]] invents the [[Möbius strip]],
* 1870 – [[Felix Klein]] constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate,
* 1873 – [[Charles Hermite]] proves that [[e (mathematical constant)|e]] is transcendental,
* 1878 – Charles Hermite solves the general quintic equation by means of elliptic and modular functions
* 1882 – [[Ferdinand von Lindemann]] proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,
* 1882 – Felix Klein invents the [[Klein bottle]],
* 1899 – [[David Hilbert]] presents a set of self-consistent geometric axioms in ''Foundations of Geometry''

==20th century==
* 1901 – [[Élie Cartan]] develops the [[exterior derivative]],
* 1905 – [[Albert Einstein|Einstein's]] theory of [[special relativity]].
* 1912 – [[Luitzen Egbertus Jan Brouwer]] presents the [[Brouwer fixed-point theorem]],
* 1916 – [[Albert Einstein|Einstein's]] theory of [[general relativity]].
* 1930 – [[Casimir Kuratowski]] shows that the [[three-cottage problem]] has no solution,
* 1931 – [[Georges de Rham]] develops theorems in [[cohomology]] and [[characteristic class]]es,
* 1933 – [[Karol Borsuk]] and [[Stanislaw Ulam]] present the [[Borsuk-Ulam Theorem|Borsuk-Ulam antipodal-point theorem]],
* 1955 – [[H. S. M. Coxeter]] et al. publish the complete list of [[uniform polyhedron]],
* 1975 – [[Benoit Mandelbrot]], [[fractal]]s theory,
* 1981 – [[Mikhail Gromov (mathematician)|Mikhail Gromov]] develops the theory of [[hyperbolic group]]s, revolutionizing both infinite group theory and global differential geometry,
* 1983 – the [[classification of finite simple groups]], a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,
* 1991 – [[Alain Connes]] and [[John Lott (mathematician)|John Lott]] develop [[non-commutative geometry]],
* 1998 – [[Thomas Callister Hales]] (almost certainly) proves the [[Kepler conjecture]],

==21st century==
* 2003 – [[Grigori Perelman]] proves the [[Poincaré conjecture]],
* 2007 – a team of researches throughout North America and Europe used networks of computers to map [[E8 (mathematics)]].<ref>Elizabeth A. Thompson, MIT News Office, ''Math research team maps E8'' http://www.huliq.com/15695/mathematicians-map-e8</ref>

==References==
{{Reflist}}

{{DEFAULTSORT:Timeline Of Algebra And Geometry}}
[[Category:Mathematics timelines|Algebra and geometry]]
[[Category:Algebra| Timeline]]
[[Category:Geometry| ]]

Digital biquad filter

2012-07-24T20:30:55Z

50.47.193.134: /* References */ Updated broken link

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