{"id":6872,"date":"2022-07-20T00:00:00","date_gmt":"2022-07-20T00:00:00","guid":{"rendered":"https:\/\/www.nextias.com\/current_affairs\/uncategorized\/20-07-2022\/pythagorean-geometry-in-vedic-era-texts\/"},"modified":"2022-07-20T00:00:00","modified_gmt":"2022-07-20T00:00:00","slug":"pythagorean-geometry-in-vedic-era-texts","status":"publish","type":"post","link":"https:\/\/www.nextias.com\/ca\/current-affairs\/20-07-2022\/pythagorean-geometry-in-vedic-era-texts","title":{"rendered":"Pythagorean Geometry in Vedic-era Texts"},"content":{"rendered":"<p><span style=\"font-size:13pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong><u>In Context<\/u><\/strong><\/span><\/span><\/span><\/p>\n<ul>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The position paper, part of Karnataka\u2019s submissions to the NCERT for a National Curriculum Framework, describes <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Pythagoras\u2019s theorem as \u201cfake news\u201d.<\/strong><\/span><\/span><\/span><\/li>\n<\/ul>\n<p><span style=\"font-size:13pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong><u>About<\/u><\/strong><\/span><\/span><\/span><\/p>\n<ul>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The Pythagoras theorem is <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>disputed in many international forums<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">. Not the content, but Pythagoras claiming it as his own.<\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">It has referred to a text called the <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Baudhayana Sulbasutra<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">, in which a specific shloka refers to the theorem.<\/span><\/span><\/span><\/li>\n<\/ul>\n<p><span style=\"font-size:13pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong><u>Pythagoras: Theorem named after him<\/u><\/strong><\/span><\/span><\/span><\/p>\n<ul>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">Evidence suggests that the <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Greek philosopher (around 570\u2013490 BC)<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> did exist. However, there is an element of mystery around him, largely because of the secretive nature of the school\/society he founded in Italy.\u00a0<\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Relatively little is known about his mathematical achievements<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">, because there is nothing today of his own writings.<\/span><\/span><\/span><\/li>\n<\/ul>\n<p><span style=\"font-size:13pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong><u>Pythagoras Theorem<\/u><\/strong><\/span><\/span><\/span><\/p>\n<ul>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The Pythagoras theorem describes the<\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong> relationship connecting the three sides of a right triangle<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> (one in which one of the angles is 90\u00b0):<\/span><\/span><\/span>\n<ul>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>a\u00b2 + b\u00b2 = c\u00b2<\/strong><\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">where<\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong> a and b are the two perpendicular sides,<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> and c is the length of the diagonal side.<\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">If any two sides of a right triangle are known, the theorem allows you to <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>calculate the third side.<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> Extended to the sides of squares and rectangles and their diagonals, the equation is of immense importance in construction, navigation and astronomy.<\/span><\/span><\/span><\/li>\n<\/ul>\n<p><span style=\"font-size:13pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong><u>How do we know that Indian mathematicians from the Vedic period knew this?<\/u><\/strong><\/span><\/span><\/span><\/p>\n<ul>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">There are references in the <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>sulbasutras<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">, which are texts pertaining to fire rituals <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>(yajanas) performed by Vedic Indians.<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> The oldest of these is the <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Baudhayana Sulbasutra.<\/strong><\/span><\/span><\/span>\n<ul>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The period of <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Baudhayana Sulbasutra <\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">is uncertain. It is estimated based on linguistic and other secondary historical considerations.<\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">In recent literature, <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Baudhayana Sulbasutra <\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">is taken to be from around<\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong> 800 BCE.<\/strong><\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">Baudhayana Sulbasutra contains a statement of what is called <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Pythagoras theorem <\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">(it was known rather as a geometric fact, and not as a \u2018theorem\u2019).<\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The yajna rituals involved construction of <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>altars (vedi) and fireplaces (agni) <\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">in a variety of shapes such as isosceles triangles, symmetric trapezia, and rectangles.<\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The sulbasutras describe steps towards construction of these figures with prescribed sizes.<\/span><\/span><\/span><\/li>\n<\/ul>\n<p style=\"text-align:center\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Xdb0KjesD37IT6n2o90RROIuS-QSKCsRdhx6j1HuZkzBUaTVrG96HlweDjRFRVi9dbknftc-qxXOGSoM7qXxcxNw0qgX7sOKAFVZL3AM674hDtt_Nkgugm_uF7OdPmbdzgSQ-Z8ImI-ixsj9U9a7XcE\" style=\"height:169px; width:587px\" \/><\/span><\/span><\/span><\/p>\n<p style=\"text-align:center\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Image Courtesy: <\/strong><\/span><\/span><\/span><a href=\"https:\/\/indianexpress.com\/article\/explained\/pythagorean-geometry-in-vedic-era-texts-centuries-before-pythagoras-8039772\/\" style=\"text-decoration:none\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#1155cc\"><strong><u>IE<\/u><\/strong><\/span><\/span><\/span><\/a><\/p>\n<p><span style=\"font-size:13pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong><u>How did the Knowledge of Equation Evolve?<\/u><\/strong><\/span><\/span><\/span><\/p>\n<ul>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The earliest evidence is from the <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Old Babylonian civilisation (1900-1600 BCE)<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">.<\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">They referred to it as the <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Diagonal Rule.<\/strong><\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The earliest evidence of a proof comes from a period after the<\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong> sulbasutras.<\/strong><\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The oldest surviving axiomatic proof of the theorem is in the Elements of Euclid from around 300 BCE.<\/span><\/span><\/span><\/li>\n<\/ul>\n<div>\n<table cellspacing=\"0\" style=\"border-collapse:collapse; border:none; table-layout:fixed; width:624px\">\n<tbody>\n<tr>\n<td style=\"background-color:#d9ead3; border-bottom:1px solid #000000; border-left:1px solid #000000; border-right:1px solid #000000; border-top:1px solid #000000; vertical-align:top\">\n<p><span style=\"font-size:13pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong><u>Veda<\/u><\/strong><\/span><\/span><\/span><\/p>\n<ul>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>About:<\/strong><\/span><\/span><\/span>\n<ul>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">A Veda is a <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>collection of poems or hymns composed <\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">in archaic Sanskrit by<\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong> Indo-European-speaking peoples<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> who lived in northwest India during the 2nd millennium BCE.\u00a0<\/span><\/span><\/span><\/li>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">There are four Vedas, the <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Rig Veda, Sama Veda, Yajur Veda and Atharva Veda.\u00a0<\/strong><\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Rig Veda:<\/strong><\/span><\/span><\/span>\n<ul>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Rigveda, or \u201cVeda of Verses<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">,\u201d the earliest of those, is composed of about 1,000 hymns addressed to various deities and mostly arranged to serve the needs of the priestly families who were the custodians of that sacred literature.<\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Sama Veda:<\/strong><\/span><\/span><\/span>\n<ul>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Samaveda, or \u201cVeda of Chants,\u201d<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> is made up of a selection of verses\u2014drawn almost wholly from the Rigveda\u2014that are provided with musical notation and are intended as an aid to the performance of sacred songs.<\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Yajur Veda:<\/strong><\/span><\/span><\/span>\n<ul>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">The <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Yajurveda, or \u201cVeda of Sacrificial Formulas,\u201d<\/strong><\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"> contains prose formulas applicable to various rites, along with verses intended for a similar purpose.<\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"list-style-type:disc\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Atharva Veda:<\/strong><\/span><\/span><\/span>\n<ul>\n<li style=\"list-style-type:circle\"><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\">It is a later compilation that includes <\/span><\/span><\/span><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>incantations and magic spells.<\/strong><\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><span style=\"font-size:12pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#000000\"><strong>Source: <\/strong><\/span><\/span><\/span><a href=\"https:\/\/indianexpress.com\/login\/\" style=\"text-decoration:none\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size:11pt\"><span style=\"font-family:'Book Antiqua',serif\"><span style=\"color:#1155cc\"><strong><u>IE<\/u><\/strong><\/span><\/span><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In Context The position paper, part of Karnataka\u2019s submissions to the NCERT for a National Curriculum Framework, describes Pythagoras\u2019s theorem as \u201cfake news\u201d. About The Pythagoras theorem is disputed in many international forums. Not the content, but Pythagoras claiming it as his own. It has referred to a text called the Baudhayana Sulbasutra, in which [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":6873,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[21],"tags":[25],"class_list":["post-6872","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-current-affairs","tag-gs1"],"acf":[],"jetpack_featured_media_url":"https:\/\/wp-images.nextias.com\/cdn-cgi\/image\/format=auto\/ca\/uploads\/2023\/07\/2727162Screenshot_6.png","_links":{"self":[{"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/posts\/6872","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/comments?post=6872"}],"version-history":[{"count":0,"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/posts\/6872\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/media\/6873"}],"wp:attachment":[{"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/media?parent=6872"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/categories?post=6872"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.nextias.com\/ca\/wp-json\/wp\/v2\/tags?post=6872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}