{"id":57,"date":"2020-05-27T12:02:47","date_gmt":"2020-05-27T12:02:47","guid":{"rendered":"http:\/\/themindpalace.in\/?p=57"},"modified":"2021-08-26T05:17:25","modified_gmt":"2021-08-26T05:17:25","slug":"pythagoras-theorem","status":"publish","type":"post","link":"https:\/\/themindpalace.in\/index.php\/2020\/05\/27\/pythagoras-theorem\/","title":{"rendered":"Pythagoras&#8217;  and his theorem"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><a href=\"#summary\">Summary of phthagoras<\/a><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>There is geometry in the humming of the strings, there is music in the spacing of the spheres<span style=\"font-size: inherit;\"><\/span><\/p><cite><strong>Pythagoras<\/strong><\/cite><\/blockquote>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_884d7f-9e\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<h1 class=\"wp-block-heading\" id=\"summary\">Summary<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Around 2000 years ago there was an amazing discovery in the world of Mathematics &#8211; The Pythagoras Theorem, which became a fundamental theorem in the area of geometrical uses.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Who is Pythagoras<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Pythagoras was born in the mid-sixth century in Samos(Greece). He lived a wealthy and stress-free childhood. So he had the opportunity to learn more than the average kids at his time he was inspired by his teachers namely Thales and Anaximander. He learned about maths, philosophy, geometry, astronomy, and cosmology. After he left Greece he arrived in Egypt, the geometry of pyramids fascinated him. Through his education and studies he is known as the first pure mathematician.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"488\" height=\"571\" src=\"http:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/Pythagoras_with_tablet_of_ratios.jpg\" alt=\"Pythagoras with tablet of ratios\" class=\"wp-image-137\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/Pythagoras_with_tablet_of_ratios.jpg 488w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/Pythagoras_with_tablet_of_ratios-256x300.jpg 256w\" sizes=\"auto, (max-width: 488px) 100vw, 488px\" \/><figcaption><strong>Pythagoras<br><\/strong><em>Image credit <a title=\"via Wikimedia Commons\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Pythagoras_with_tablet_of_ratios.jpg\">Raphael<\/a> \/ Public domain<\/em><\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp; He did not like how the sages in Egypt got respect just because they have the answers to the universe and understanding life therefore he studied more about philosophy, maths and nature. He wanted to educate people on his beliefs and religion and wanted to create a community of equality and belief.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp; His discoveries were not only discovered by him, Most if not all were discovered together with his followers the Pythagoreans&#8217; life since borders were changing rapidly and new rulers were coming into power, the pressure for discoveries heightened.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">A brief history of Pythagoras\u2019 theorem<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; The statement of this theorem was discovered on a Babylonian tablet around 1900-1600 B.C. This theorem is a fundamental building block of maths.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp; Heath, a mathematician wrote &#8220;A history of Greek Mathematics&#8221; and he lists Pythagoras theorem. This theorem was used,  way before Pythagoras was even born. Since the days of ancient Babylonians and Egyptians, although it may not have been stated as explicitly as Pythagoras. Pythagoras and his followers actually wrote it down and proved it.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp; The Egyptians used a knotted rope as an aid to constructing right angles in their buildings. The rope had 12 evenly spaced knots, which could be formed into a right angle thus giving an angle of exactly 90 degrees.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">The Pythagoras Theorem<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Pythagoras Theorem states that &#8220;In a right triangle the area of the square on the hypotenuse is equal to the sum of the areas of the squares of its remaining two sides.&#8221;  The side opposite to the right angle is called the hypotenuse, it&#8217;s also the longest side of the triangle.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"569\" src=\"http:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/Pythagorean_theorem.jpg\" alt=\"\" class=\"wp-image-62\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/Pythagorean_theorem.jpg 626w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/Pythagorean_theorem-300x273.jpg 300w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><figcaption>Pythagoras\u2019 theorem<br><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Pythagorean_theorem.jpg\">Ntozis<\/a> \/ Public domain<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">This theorem can be written as an equation&nbsp;relating the lengths of the sides&nbsp;<em>a<\/em>,&nbsp;<em>b<\/em>&nbsp;and&nbsp;<em>c<\/em>, often called the &#8220;Pythagorean equation&#8221; :<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"729\" src=\"http:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/pythogoras-1024x729.png\" alt=\"\" class=\"wp-image-60\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/pythogoras-1024x729.png 1024w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/pythogoras-300x214.png 300w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/pythogoras-768x547.png 768w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/pythogoras.png 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Pythagorean equation<br>Image by <a href=\"https:\/\/pixabay.com\/users\/Tumisu-148124\/?utm_source=link-attribution&amp;utm_medium=referral&amp;utm_campaign=image&amp;utm_content=4710334\">Tumisu<\/a> from <a href=\"https:\/\/pixabay.com\/?utm_source=link-attribution&amp;utm_medium=referral&amp;utm_campaign=image&amp;utm_content=4710334\">Pixabay<\/a><\/figcaption><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Uses of Pythagoras theorem <\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>The Pythagorean Theorem is used to calculate the steepness of hills or mountains.&nbsp;<\/li><li>In building constructions to make sure they are keeping the walls exactly in square form, that is in 90 degrees.<\/li><li>Navigation, to calculate the shortest distance to reach a destination point<\/li><li>and many more<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"558\" src=\"http:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/forester-triangle-1024x558.png\" alt=\"Measuring the height of the tree using a part of Pythagoras\u2019 theorem\" class=\"wp-image-61\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/forester-triangle-1024x558.png 1024w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/forester-triangle-300x164.png 300w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/forester-triangle-768x419.png 768w, https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/05\/forester-triangle.png 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Measuring the height of the tree using a part of Pythagoras\u2019 theorem<br>Image by <a href=\"https:\/\/pixabay.com\/users\/Conmongt-1226108\/?utm_source=link-attribution&amp;utm_medium=referral&amp;utm_campaign=image&amp;utm_content=2921203\">Christian Dorn<\/a> from <a href=\"https:\/\/pixabay.com\/?utm_source=link-attribution&amp;utm_medium=referral&amp;utm_campaign=image&amp;utm_content=2921203\">Pixabay<\/a><\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Summary of phthagoras There is geometry in the humming of the strings, there is music in the spacing of the spheres Pythagoras Summary Around 2000 years ago there was an amazing discovery in the&#46;&#46;&#46;<\/p>\n","protected":false},"author":2,"featured_media":61,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[475,14],"tags":[16,15,17],"class_list":["post-57","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-posts-in-english","category-mathematics","tag-pythagoras","tag-pythagoras-theorem","tag-uses-of-pythagoras-theorem"],"cp_meta_data":{"_edit_lock":["1629955045:2"],"_edit_last":["2"],"_layout":["inherit"],"_thumbnail_id":["61"],"_oembed_95287caaddeb112cd4edfcbd8e525566":["<iframe title=\"Introduction of Computers  Part1\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SzIGR3gp_F4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; 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The fixed point is called the center of the circle. The fixed distance is called the radius of the circle.\u2026","rel":"","context":"In &quot;10th Class&quot;","block_context":{"text":"10th Class","link":"https:\/\/themindpalace.in\/index.php\/category\/ncert-school-syllabus\/10th-class-ncert-syllabus\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/Slide1.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/Slide1.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/Slide1.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/Slide1.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":1303,"url":"https:\/\/themindpalace.in\/index.php\/2020\/10\/20\/quadrilaterals\/","url_meta":{"origin":57,"position":2},"title":"QUADRILATERALS","author":"Nancy Diana","date":"October 20, 2020","format":false,"excerpt":"Summary of quadrilaterals Solved exercise of quadrilaterals Summary As the word \u2018Quad\u2019 means four, and lateral means sides.A quadrilateral is a plane figure that has four sides or edges, and also have four corners or vertices.AC and BD are the diagonals of the quadrilateral ABCD. Properties of quadrilaterals Angle sum\u2026","rel":"","context":"In &quot;English Medium&quot;","block_context":{"text":"English Medium","link":"https:\/\/themindpalace.in\/index.php\/category\/posts-in-english\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/introduction-1.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/introduction-1.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/introduction-1.jpg?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":1931,"url":"https:\/\/themindpalace.in\/index.php\/2020\/11\/19\/triangles-and-its-types\/","url_meta":{"origin":57,"position":3},"title":"Triangles and their Types","author":"Nancy Diana","date":"November 19, 2020","format":false,"excerpt":"Summary of Triangles and its TypesSolved exercises of Triangles and its Types9th class mathematics Triangle Triangle is a closed curve made up of three line segments. It has three vertices, sides and angles. Here, in\u00a0\u2206ABC, \u2022AB, BC and CA are the three sides. \u2022A, B and C are three vertices.\u2026","rel":"","context":"In &quot;English Medium&quot;","block_context":{"text":"English Medium","link":"https:\/\/themindpalace.in\/index.php\/category\/posts-in-english\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/types-of-triangel.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/types-of-triangel.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/types-of-triangel.jpg?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":680,"url":"https:\/\/themindpalace.in\/index.php\/2020\/08\/28\/rational-numbers\/","url_meta":{"origin":57,"position":4},"title":"Rational Numbers","author":"Nancy Diana","date":"August 28, 2020","format":false,"excerpt":"Summary of rational numbers An Introduction to Number system Summary A set of values used to represent different quantities is known as \u201cNumber System\u201d. \u00a0\u00a0\u00a0 For example, a number system can be used to represent the number of students or the number of viewers watching a certain TV program, the\u2026","rel":"","context":"In &quot;8th Class&quot;","block_context":{"text":"8th Class","link":"https:\/\/themindpalace.in\/index.php\/category\/ncert-school-syllabus\/8th-class-ncert-syllabus\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/Slide16.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/Slide16.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/Slide16.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/Slide16.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/10\/Slide16.jpg?resize=1050%2C600&ssl=1 3x"},"classes":[]},{"id":2020,"url":"https:\/\/themindpalace.in\/index.php\/2020\/11\/30\/the-triangle-and-its-properties\/","url_meta":{"origin":57,"position":5},"title":"The Triangle and its Properties","author":"Nancy Diana","date":"November 30, 2020","format":false,"excerpt":"Solved exercise on triangle and its properties Exercise 1. In \u2206PQR, D is the mid-pointof\u00a0QRPM\u00a0isPD\u00a0is \u00a0If QM = MR? Solution:PM is altitude.PD is median.No, QM \u2260 MR. 2. Draw rough sketches for the following (a) In \u2206ABC, BE is a median.(b) In \u2206PQR, PQ and PR are altitudes of the\u2026","rel":"","context":"In &quot;7th Class&quot;","block_context":{"text":"7th Class","link":"https:\/\/themindpalace.in\/index.php\/category\/ncert-school-syllabus\/7th-class-ncert-syllabus\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/properties-of-triangel.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/properties-of-triangel.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/properties-of-triangel.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/properties-of-triangel.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/themindpalace.in\/wp-content\/uploads\/2020\/11\/properties-of-triangel.jpg?resize=1050%2C600&ssl=1 3x"},"classes":[]}],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/57","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/comments?post=57"}],"version-history":[{"count":15,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/57\/revisions"}],"predecessor-version":[{"id":2603,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/57\/revisions\/2603"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/media\/61"}],"wp:attachment":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/media?parent=57"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/categories?post=57"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/tags?post=57"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}