Proof of the pythagorean theorem president garfield found a proof of the pythagorean theorem. Lets build up squares on the sides of a right triangle. Pdf a new long proof of the pythagorean theorem researchgate. Pythagoras theorem then claims that the sum of the areas of two small squares equals the area of the large one. This forms a square in the center with side length c c c and thus an area of c2. This book has been collected as many as 370 different proofs of. There are many different proofs, but we chose one that gives a delightful visual. Bhaskaras first proof bhaskaras proof is also a dissection proof.
In a little different form, this proof appeared in the mathematics magazine. Pdf the pythagorean theorem is the most famous theorem in the world. Garfield later became the 20th president of the united states. The proof depends on calculating the area of a right trapezoid two different ways. In this proof, triangle abc is right angle and its right side is angle c. There are well over 371 pythagorean theorem proofs, originally collected and put into a book in 1927, which includes those by a 12yearold einstein who uses the theorem two decades later for.
He was one of the most important hindu mathematicians of the second century ad. James garfields proof of the pythagorean theorem faculty web. Pythagorean theorem and its many proofs cut the knot. We can write the area of the outside square two different ways which are equal. The pythagorean theorem wpafb educational outreach. Proving the pythagorean theorem proposition 47 of book i of. Proof 1 of pythagoras theorem for ease of presentation let 1 2 ab be the area of the right.
The two key facts that are needed for garfields proof are. There are many different proofs of the pythagorean theorem. In mathematics, the pythagoreantheorem or pythagoras theorem is a relationin euclidean geometry among the. Pythagoras theorem statement, formula, proof and examples. The pythagorean theorem says that for right triangles, the sum of the squares of the leg measurements is equal to the hypotenuse measurement squared. Pythagoras lived in the 500s bc, and was one of the. There seems to be about 500 different proofs of this theorem. In a rightangled triangle, we can calculate the length of any side if the other two sides are given.
Create your own real world problem and challenge the class. He used the following diagrams in proving the pythagorean theorem. The pythagorean theorem is the most famous theorem in the world. We shall give two proofs of the converse rather different in nature. Proof of the pythagorean theorem basic mathematics. Here in this article, i will show a new long proof of the theorem. Five new ways to prove a pythagorean theorem international.
1288 725 1220 469 1019 1404 908 258 1638 1549 349 1187 1310 226 478 1487 808 744 1391 167 1352 391 794 64 1014 1005 1357 564 730 321 1338 1424 1016 953 132 700 1200