Melissa LowEDU 653CCSS.Math.Content.8.G.B.6 Explain a proof of thePythagorean Theorem and its converse.Pythagorean Theorem
A long long time ago...Pythagoras of Samos c.560–480 BC“was a Greek philosopher and religious leaderwho was responsible for importantdevelopments in the history of mathematics,astronomy, and the theory of music” (PBS)Around 532 BC he emigrated to Croton. It is said that this was due toescape Samos’ cruel rule. This may be part of the reason that none ofPythagoras work has survived (Encyclopedia Britannica).Pythagoras:demonstrating histheorem in the sand
Although, many still have creditedhim with his famous proof.In a right triangle, the square of longest side isequal to the sum of the square of the other two sides.Now known as the Pythagorean Theoremabc2 2 2a b c
Many have proven the PythagoreanTheorem since…Anthony Varela’s Proofhttp://www.sophia.org/pythagorean-theorem-proof/pythagorean-theorem-proof--5-tutorialAlan Kitchinghttp://youtu.be/pVo6szYE13YTyler Neylon’s Visual Animationhttp://www.youtube.com/watch?v=O0ehw3-FpGg
Emma’s Proof of the Pythagorean Theoremhttp://www.youtube.com/watch?v=uOTs2ck1_jUYou will need paper, pencil and a bag of Starburst!Try Emma’s Proof Yourself…
How can we use the Pythagorean Theorem?Finding the hypotenuse (longest side ofthe right triangle)It is important to know that “c” is alwaysacross from the right angle. It does notmatter which one we call a or b.68?2 2 22 2 22226 836 6410010010a b ccccccFinding a leg on the right triangle. (oneof the shorter sides of a triangle)This is still important! “c” is alwaysacross from the right angle. It does notmatter which one we call a or b.9?152 2 22 2 22229 1581 225-81 -8114414412a b cbbbbb
Now watch this Rap to Help you!JAKE SCOTT:The Best Pythagorean Theorem Rap Everhttp://youtu.be/nbopLhP4kpo
Sources"Proving the Pythagorean Theorem." PBS: Public Broadcasting Service. Web. 10May 2013.<http://www.pbs.org/teachers/mathline/concepts/historyandmathematics/act1wks.pdf>."Pythagoras: demonstrating his theorem in the sand". Photograph. EncyclopædiaBritannica Online. Web. 10 May. 2013.<http://www.britannica.com/EBchecked/media/123098/Pythagoras-demonstrating-his-Pythagorean-theorem-in-the-sand-using-a>."Pythagoras". Encyclopædia Britannica. Encyclopædia Britannica Online.Encyclopædia Britannica Inc., 2013. Web. 10 May. 2013<http://www.britannica.com/EBchecked/topic/485171/Pythagoras>.