Five New Ways to Prove a Pythagorean Theorem ( Vol-4,Issue-7,July 2017 ) |
Author(s): |
Nurul Laily, Hobri, Dafik |
Keywords: |
Pythagoras theorem, right-angle riangle, Trapezoid, Square, Rectangle. |
Abstract: |
Pythagoras is one of the mathematicians who developed the basic theories of mathematics. One of his taunts that are well-known even by primary school students is a Pythagorean Theorem. This theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of each other sides square. There are many proofs which have been developed by a scientist, we have estimated up to 370 proofs of the Pythagorean Theorem. In this paper, we are trying to develop five new proofs of Pythagorean Theorem by using algebraic-geometric proof. The first proof is proven by the trapezoidal shape constructed by five right triangles. The second and third Proofs are proven by using the constructed parallelograms consisting four right triangles and two isosceles trapezoids. The fourth proof is proven by trapezoidal shape constructed of three pieces of a congruent trapezoid, and the fifth proof is proven by using a rectangle constructed by congruent square. Thus, we conclude that the proof of the Pythagorean Theorem can be proven by using the construction of flat trapezoid, parallelogram, square, and rectangular by means of a right-angle triangle. |
DOI: |
Paper Statistics: |
Cite this Article: |
Show All (MLA | APA | Chicago | Harvard | IEEE | Bibtex) |
Share: |
References: |
[1] G Leonardo da Vinci (April 15, 1452 - May 2, 1519)
[2] Loomis, E., S. The Pythagorean Proportion of1927. [3] Maor, E., The Pythagorean Theorem, A 4,000-Year History, Princeton University Press, Princeton, N.J., 2007, p. xii.. [4] Maor, E., The Pythagorean Theorem, A 4,000-Year History, Princeton University Press, Princeton, N.J., 2007, p. 5. [5] Maor, E., The Pythagorean Theorem, A 4,000-YearHistory,Princeton University Press, Princeton, NJ, 2007, p. 17. [6] Paulus Gerdes, Zum erwachenden geometrischen Denken, Dresden, Maputo,1985. [7] Wagner, Donald B, 2004.A proof of the Pythagorean Theorem by LiuHui. [Online].http://donwagner.dk/Pythagoras/Pythagoras.html |
Advanced Engineering Research and Science