{"id":4339,"date":"2022-09-12T14:33:45","date_gmt":"2022-09-12T12:33:45","guid":{"rendered":"https:\/\/erlebnisland-mathematik.de\/?page_id=4339"},"modified":"2023-01-26T11:32:15","modified_gmt":"2023-01-26T10:32:15","slug":"advanced-text-pythagoras-to-lay","status":"publish","type":"page","link":"https:\/\/erlebnisland-mathematik.de\/en\/advanced-text-pythagoras-to-lay\/","title":{"rendered":"Advanced text Pythagoras to lay"},"content":{"rendered":"

[vc_row drowwidth=”sidebar-biest-default sidebar-biest”][vc_column][vc_column_text]<\/p>\n

Pythagoras to lay<\/h1>\n

This exhibit is about another illustrative proof of the Pythagorean theorem<\/em>. The well-known theorem states that the side lengths \"a\", \"b\" and \"c\" of a right triangle satisfy the equation \"a^2+b^2=c^2\" (where \"a\" and \"b\" are the two sides enclosing the right angle, — called the cathetes<\/em> — and \"c\" is the opposite side — the hypotenuse<\/i>).<\/p>\n

This time the proof is given in the form of a puzzle that the visitor must solve himself in order to comprehend it: Above the catheti are two squares, each divided into four triangles. Each of these triangles is coloured and the two opposite triangles in the square are each congruent<\/em> (“<\/em>congruent”<\/em>) and coloured the same.<\/p>\n

If you now cleverly lay the total of eight triangles around, they fill exactly the square above the hypotenuse (see figure 1). This proves the Pythagorean theorem, because equality of content<\/em> follows from equality of decomposition<\/em>.[\/vc_column_text][vc_single_image image=”1307″ img_size=”large” alignment=”center”]Figure 1: Arrangement of the exhibit[\/vc_single_image][vc_column_text]You can find more interesting facts about the Pythagorean theorem and another proof here<\/a>.[\/vc_column_text][vc_column_text]<\/p>\n

Literature<\/h3>\n

[\/vc_column_text][vc_column_text][1] Dewdney, A.K.: Reise in das Innere der Mathematik<\/em>, Berlin, 2000.<\/p>\n

[2] Fraedrich, A.M.: Die Satzgruppen des Pythagoras<\/em>, Mannheim, 1995.<\/p>\n

[3] Maor, E.: The Pythagorean Theorem: A 4,000-year History<\/em>, Princeton, 2007.<\/p>\n

[4] Schupp, H.: Elementargeometrie<\/em>, Stuttgart, 1977.<\/p>\n

[5] Singh, S.: Fermats letzter Satz<\/em>, M\u00fcnchen, 2000.<\/p>\n

[6] v. Wedemeyer, I.: Pythagoras, Weisheitslehrer des Abendlandes<\/em>, Ahlerstedt, 1988.[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

[vc_row drowwidth=”sidebar-biest-default sidebar-biest”][vc_column][vc_column_text] Pythagoras to lay This exhibit is about another illustrative proof of the Pythagorean theorem. The well-known theorem states that the side lengths , and of a right triangle satisfy the equation (where and are the two sides enclosing the right angle, — called the cathetes — and is the opposite side — … Advanced text Pythagoras to lay<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"folder":[],"class_list":["post-4339","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/pages\/4339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/comments?post=4339"}],"version-history":[{"count":4,"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/pages\/4339\/revisions"}],"predecessor-version":[{"id":4343,"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/pages\/4339\/revisions\/4343"}],"wp:attachment":[{"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/media?parent=4339"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/erlebnisland-mathematik.de\/en\/wp-json\/wp\/v2\/folder?post=4339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}