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| In ancient [[Indian mathematics]], a '''[[Vedic]] square''' is a variation on a typical 9 × 9 [[multiplication table]]. The entry in each cell is the [[digital root]] of the product of the column and row headings i.e. the [[remainder]] when the product of the row and column headings is divided by 9 (with remainder 0 represented by 9).
| | It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. You can either install Word - Press yourself or use free services offered on the web today. The effect is to promote older posts by moving them back onto the front page and into the rss feed. Hosted by Your Domain on Another Web Host - In this model, you first purchase multiple-domain webhosting, and then you can build free Wordpress websites on your own domains, taking advantage of the full power of Wordpress. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it. <br><br>These websites can be easily customized and can appear in the top rankings of the major search engines. When you write a new post, you'll see a small bar that goes across the text input area. Which is perfect for building a mobile site for business use. You can add new functionalities and edit the existing ones to suit your changing business needs. For a Wordpress website, you don't need a powerful web hosting account to host your site. <br><br>Saying that, despite the launch of Wordpress Express many months ago, there has still been no sign of a Wordpress video tutorial on offer UNTIL NOW. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. This platform can be customizedaccording to the requirements of the business. These frequent updates have created menace in the task of optimization. After that the developer adds the unordered list for navigations. <br><br>The next thing I did after installing Wordpress was to find myself a free good-looking Wordpress-theme offering the functionality I was after. And, make no mistake,India's Fertility Clinics and IVF specialists are amongst the best in the world,and have been for some time. To do this, you should link your posts to other relevant posts that you've created. If you just want to share some picture and want to use it as a dairy, that you want to share with your friends and family members, then blogger would be an excellent choice. If your site does well you can get paid professional designer to create a unique Word - Press theme. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. Here is more info about [http://nsaksi.com/main/index.php?qa=1040&qa_1=easy-plans-in-worpress-examined wordpress backup plugin] take a look at our own web-page. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. Useful Plugins Uber - Menu Top Megamenu Now it is the time of sticky Top navbar. Word - Press is an open source content management system which is easy to use and offers many user friendly features. Article Source: Hostgator discount coupons for your Wordpress site here. |
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| <div align="center">
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| {|class="wikitable" style="text-align:center; width:270px; height:270px" border="1"
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| ! !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
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| |-
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| ! 1
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| |1||2||3||4||5||6||7||8||9
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| |-
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| !2
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| |2||4||6||8||1||3||5||7||9
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| |-
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| !3
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| |3||6||9||3||6||9||3||6||9
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| |-
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| !4
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| |4||8||3||7||2||6||1||5||9
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| |-
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| !5
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| |5||1||6||2||7||3||8||4||9
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| |-
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| !6
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| |6||3||9||6||3||9||6||3||9
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| |-
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| !7
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| |7||5||3||1||8||6||4||2||9
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| |-
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| !8
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| |8||7||6||5||4||3||2||1||9
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| |-
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| !9
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| |9||9||9||9||9||9||9||9||9
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| |}
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| </div>
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| [[File:Shapes in the Vedic Square.png|thumb|Highlighting specific numbers within the Vedic square reveals distinct shapes each with some form of [[reflection symmetry]]. ]]
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| Numerous [[geometric]] [[patterns]] and [[symmetries]] can be observed in a Vedic square some of which can be found in traditional [[Islamic art]].{{Harv|Pritchard|2003|pp=119–122}}
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| <div align="center"> | |
| {|class="wikitable" style="text-align:center; width:270px; height:270px" border="1"
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| ! !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
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| |-
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| ! 1
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| |style="background-color:red"|1||style="background-color:orange"|2||style="background-color:yellow"|3||style="background-color:lime"|4||style="background-color:green"|5||style="background-color:blue"|6||style="background-color:aqua"|7||style="background-color:purple"|8||style="background-color:fuchsia"|9
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| |-
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| !2
| |
| |style="background-color:orange"|2||style="background-color:lime"|4||style="background-color:blue"|6||style="background-color:purple"|8||style="background-color:red"|1||style="background-color:yellow"|3||style="background-color:green"|5||style="background-color:aqua"|7||style="background-color:fuchsia"|9
| |
| |-
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| !3
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| |style="background-color:yellow"|3||style="background-color:blue"|6||style="background-color:fuchsia"|9||style="background-color:yellow"|3||style="background-color:blue"|6||style="background-color:fuchsia"|9||style="background-color:yellow"|3||style="background-color:blue"|6||style="background-color:fuchsia"|9
| |
| |-
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| !4
| |
| |style="background-color:lime"|4||style="background-color:purple"|8||style="background-color:yellow"|3||style="background-color:aqua"|7||style="background-color:orange"|2||style="background-color:blue"|6||style="background-color:red"|1||style="background-color:green"|5||style="background-color:fuchsia"|9
| |
| |-
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| !5
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| |style="background-color:green"|5||style="background-color:red"|1||style="background-color:blue"|6||style="background-color:orange"|2||style="background-color:aqua"|7||style="background-color:yellow"|3||style="background-color:purple"|8||style="background-color:lime"|4||style="background-color:fuchsia"|9
| |
| |-
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| !6
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| |style="background-color:blue"|6||style="background-color:yellow"|3||style="background-color:fuchsia"|9||style="background-color:blue"|6||style="background-color:yellow"|3||style="background-color:fuchsia"|9||style="background-color:blue"|6||style="background-color:yellow"|3||style="background-color:fuchsia"|9
| |
| |-
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| !7
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| |style="background-color:aqua"|7||style="background-color:green"|5||style="background-color:yellow"|3||style="background-color:red"|1||style="background-color:purple"|8||style="background-color:blue"|6||style="background-color:lime"|4||style="background-color:orange"|2||style="background-color:fuchsia"|9
| |
| |-
| |
| !8
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| |style="background-color:purple"|8||style="background-color:aqua"|7||style="background-color:blue"|6||style="background-color:green"|5||style="background-color:lime"|4||style="background-color:yellow"|3||style="background-color:orange"|2||style="background-color:red"|1||style="background-color:fuchsia"|9
| |
| |-
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| !9
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| |style="background-color:fuchsia"|9||style="background-color:fuchsia"|9||style="background-color:fuchsia"|9||style="background-color:fuchsia"|9||style="background-color:fuchsia"|9||style="background-color:fuchsia"|9||style="background-color:fuchsia"|9||style="background-color:fuchsia"|9||style="background-color:fuchsia"|9
| |
| |}
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| </div> | |
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| ==Algebraic Properties==
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| This table can be viewed as the multiplication table of the [[monoid]] <math>((\mathbb{Z}/9\mathbb{Z})^{\times}, \{1, \circ\})</math> where <math>\mathbb{Z}/9\mathbb{Z}</math> is the set of positive integers partitioned by the [[residue class]]es [[Modular arithmetic|modulo]] nine. Also, the operator ''<math>\circ</math>'' means the abstract "multiplication" between the elements of this monoid. If <math>a,b</math> are elements of <math>((\mathbb{Z}/9\mathbb{Z})^{\times}, \{1, \circ\})</math> then <math>a \circ b</math> can be defined as <math>(a \times b) \mod{9}</math> by using the [[Modulo operation|modulus operator mod]], where we take the element 9 as the representative of the residue class of 0 rather than the traditional choice of 0.
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| This does not form a [[Group (mathematics)|group]] not every non-zero element has a corresponding [[inverse element]], for example <math>6\circ 3 = 9</math> but there is no <math>a \in \{ 1,\cdots,9 \}</math> such that <math>9\circ a = 6.</math>.
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| If we consider the subset <math>\{1,2,4,5,7,8\}</math>, however, this does form a group. It forms a [[cyclic group]] with 2 as one choice of [[Generating set of a group|generator]]. In fact, this is just the group of multiplicative [[Unit (ring theory)|units]] in the [[Ring (mathematics)|ring]] <math>\mathbb{Z}/9\mathbb{Z}</math>.
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| <div align="center"> | |
| {|class="wikitable" style="text-align:center; width:270px; height:270px" border="1"
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| ! <math>\circ</math> !! 1 !! 2 !! 4 !! 5 !! 7 !! 8
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| |-
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| ! 1
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| |1||2||4||5||7||8
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| |-
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| !2
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| |2||4||8||1||5||7
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| |-
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| !4
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| |4||8||7||2||1||5
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| |-
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| !5
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| |5||1||2||7||8||4
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| |-
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| !7
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| |7||5||1||8||4||2
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| |-
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| !8
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| |8||7||5||4||2||1
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| |}
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| </div>
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| We can see the every columns and rows has all six cells. It shows that <math>\{1, 2, 4, 5, 7, 8\}</math> forms a [[Latin square]].
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| <div align="center"> | |
| {|class="wikitable" style="text-align:center; width:270px; height:270px" border="1"
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| ! <math>\circ</math> !! 1 !! 2 !! 4 !! 5 !! 7 !! 8
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| |-
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| ! 1
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| |style="background-color:red"|1||style="background-color:orange"|2||style="background-color:lime"|4||style="background-color:green"|5||style="background-color:aqua"|7||style="background-color:purple"|8
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| |-
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| !2
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| |style="background-color:orange"|2||style="background-color:lime"|4||style="background-color:purple"|8||style="background-color:red"|1||style="background-color:green"|5||style="background-color:aqua"|7
| |
| |-
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| !4
| |
| |style="background-color:lime"|4||style="background-color:purple"|8||style="background-color:aqua"|7||style="background-color:orange"|2||style="background-color:red"|1||style="background-color:green"|5
| |
| |-
| |
| !5
| |
| |style="background-color:green"|5||style="background-color:red"|1||style="background-color:orange"|2||style="background-color:aqua"|7||style="background-color:purple"|8||style="background-color:lime"|4
| |
| |-
| |
| !7
| |
| |style="background-color:aqua"|7||style="background-color:green"|5||style="background-color:red"|1||style="background-color:purple"|8||style="background-color:lime"|4||style="background-color:orange"|2
| |
| |-
| |
| !8
| |
| |style="background-color:purple"|8||style="background-color:aqua"|7||style="background-color:green"|5||style="background-color:lime"|4||style="background-color:orange"|2||style="background-color:red"|1
| |
| |}
| |
| </div>
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| | |
| ==See also==
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| *[[Latin square]]
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| *[[Modular arithmetic]]
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| *[[Monoid]]
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| ==References==
| |
| *{{cite book|last=Deskins|first=W.E.|title=Abstract Algebra|publisher=Dover|location=New York|pages=162–167|isbn=0-486-68888-7|year=1996|ref=harv}}
| |
| *{{cite book|last=Pritchard|first=Chris|title=The Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry Teaching|publisher=Cambridge University Press|location=Great Britain|pages=119–122|isbn=0-521-53162-4|year=2003|ref=harv}}
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| *Talal Ghannam: ''The Mystery of Numbers: Revealed Through Their Digital Root''. CreateSpace Publications 2012, ISBN 978-1477678411, pp. 68–73
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| == External links ==
| |
| *[http://mathormagic.com/vedic_square Vedic Square] - MATH or MAGIC!
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| *[http://people.revoledu.com/kardi/tutorial/DigitSum/Vedic-square.html Digital Root: Vedic Square]
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| *{{YouTube|id=Zx-vnMXS3-E|title="Magic Maths - In a minute - Vedic Square"}}
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| | |
| [[Category:Asian mathematics]]
| |
| [[Category:Modular arithmetic]]
| |
| | |
| | |
| {{algebra-stub}}
| |
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