{"id":96,"date":"2013-12-22T04:00:37","date_gmt":"2013-12-21T22:30:37","guid":{"rendered":"http:\/\/jollymaths.com\/blog\/?p=96"},"modified":"2019-12-31T18:17:46","modified_gmt":"2019-12-31T12:47:46","slug":"100x100-srinivasa-ramanujan-biography-magic-square","status":"publish","type":"post","link":"https:\/\/jollymaths.com\/blog\/100x100-srinivasa-ramanujan-biography-magic-square\/","title":{"rendered":"Srinivasa Ramanujan – 100-by-100 Biography Magic Square"},"content":{"rendered":"

Ramanujan and Magic Squares<\/span><\/h2>\n

Srinivasa Ramanujan<\/a> had a special affinity toward numbers. His taxi-cab number (1729)<\/a> incident is popular. A Mathematician without parallel, he made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions.\u00a0His works have been collected and analyzed throughout the world<\/a><\/p>\n

Incidentally, in the opening page<\/a> of the first Ramanujan\u2019s notebook<\/a>, there begins by working out a 3 x 3 Magic Square!<\/a><\/p>\n

Having worked on a variety of special Magic squares<\/a> ourselves, we could not think of a greater tribute to Srinivasa Ramanujan than this!<\/p>\n

Summary<\/h3>\n

This is one of the biggest number puzzles we have done so far<\/a>! This Biography Magic Square<\/a> summarizes the important events that happened in the life of Sri Srinivasa Ramanujan.<\/span><\/p>\n

The important dates in the life of Srinivasa Ramanujan were compiled from various sources. These dates were taken two digits at a time, representing either the date of the month or the month or the first\/second half of the four-digit year. \u00a0 \u00a0 \u00a0As an example, Ramanujan\u2019s date-of-birth 22-12-1887, is taken as four separate entries as \u00a0 \u00a022 \u00a0 \u00a012 \u00a0 \u00a018 and 87. In short, Ramanujan\u2019s entire life history is reproduced here, from his birth to till date in\u00a0 Ramanujan-style<\/strong>.<\/em><\/span><\/p>\n

\"Srinivasa<\/a>
Srinivasa Ramanujan 100 x 100 biography MagicSquare<\/figcaption><\/figure>\n

Construction<\/h3>\n

Important dates<\/strong> from Ramanujan\u2019s life were collected and these were then arranged horizontally in a row, from left to right. This row would form the top row<\/strong> of this biography magic square. The rest of the magic square is constructed after assembling this row.<\/p>\n

This magic square has the properties of a conventional magic square<\/strong>, namely the sum of the entries along each row\/column\/diagonal sum up to the same magic-sum 2183.<\/p>\n

It has these additional properties<\/strong>:
\n– starting from left to right, or, from top to bottom, we have embedded magic squares<\/strong> of orders 4 x 4 , 8 x 8, 12 x 12, 16 x 16, 20 x 20, and then in increased orders of 25 x25, 30 x 30, 36 x 36, 42 x 42, 49 x 49, 56 x 56, 64 x 64, 72 x 72, 81 x 81, 90 x 90, and finally 100 x 100. This is thus a cascade of magic-squares-inside-a-magic-sqaure<\/a>!<\/p>\n

Thus the total 100 x 100 Ramanujan Biography Magic square will contain the following 184 smaller magic squares of sizes as listed below:<\/p>\n

\n

Size of Magic Square\u00a0 \u00a0 \u00a0 Number of such Magic Squares\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Total Entries<\/p>\n

\n

4 x 4\u00a0 Magic squares\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 25\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 25\u00a0\u00a0 ( 4 x 4 )\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 400\u00a0\u00a0 squares<\/p>\n

5 x 5\u00a0 Magic squares\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 20\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 20\u00a0\u00a0 ( 5 x 5 )\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 500\u00a0\u00a0 squares<\/p>\n

6 x 6\u00a0 Magic squares\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 24\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 24\u00a0\u00a0 ( 6 x 6 )\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 864\u00a0\u00a0 squares<\/p>\n

7 x 7\u00a0 Magic squares\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 28\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 28\u00a0\u00a0 ( 7 x 7 )\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0 1372\u00a0\u00a0 squares<\/p>\n

8 x 8\u00a0 Magic squares\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 32\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 32\u00a0\u00a0 ( 8 x 8 )\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0 2048\u00a0\u00a0 squares<\/p>\n

9 x 9\u00a0 Magic squares\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 36\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 36\u00a0\u00a0 ( 9 x 9 )\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0 2916\u00a0\u00a0 squares<\/p>\n

10 x 10\u00a0 Magic squares \u00a0 \u00a0 19\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a019 (10 x 10 )\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0 1900\u00a0\u00a0 squares<\/p>\n

\n

Total \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 184\u00a0 (Different sized squares)\u00a0\u00a0 10,000\u00a0\u00a0 Squares<\/p>\n

\n

Sidenote<\/h3>\n

We have constructed a smaller 16 x 16 version of this Biography Magic Square<\/a> with fewer details, which you can find here<\/a>.<\/p>\n

This was earlier published in an article\u00a0“A Unique Novel Homage to the\u00a0Great Indian Mathematician<\/em>”\u00a0in the March 2013<\/a> (Volume 23, Pg 146-147)\u00a0Mathematics Newsletter<\/a> published by the Ramanujan Mathematics Society<\/a>. (download free<\/a>).<\/p>\n","protected":false},"excerpt":{"rendered":"

Ramanujan and Magic Squares Srinivasa Ramanujan had a special affinity toward numbers. His taxi-cab number (1729) incident is popular. A Mathematician without parallel, he made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions.\u00a0His works have been collected and analyzed throughout the world Incidentally, in the opening page of the first Ramanujan\u2019s … Continue reading Srinivasa Ramanujan – 100-by-100 Biography Magic Square<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10,2,12,8,3,11],"tags":[21],"class_list":["post-96","post","type-post","status-publish","format-standard","hentry","category-biography-magic-sqaure","category-magic-square","category-magic-square-inside-a-magic-square","category-recreational-math","category-special-magic-square","category-srinivasa-ramanujan","tag-srinivasa-ramanujan"],"_links":{"self":[{"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/posts\/96","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/comments?post=96"}],"version-history":[{"count":12,"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/posts\/96\/revisions"}],"predecessor-version":[{"id":589,"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/posts\/96\/revisions\/589"}],"wp:attachment":[{"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/media?parent=96"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/categories?post=96"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jollymaths.com\/blog\/wp-json\/wp\/v2\/tags?post=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}