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单词 GarfieldsProofOfPythagoreanTheorem
释义

Garfield’s proof of Pythagorean theorem


James Garfield, the 20th president of the United States, gave the following proof of the Pythagorean TheoremMathworldPlanetmathPlanetmath in 1876. Consider the following trapezoidMathworldPlanetmath (note that this picture is half of the diagram used in Bhaskara’s proof of the Pythagorean theorem (http://planetmath.org/ProofOfPythagoreasTheorem)).

Recall that the area of a trapezoid with two parallelMathworldPlanetmathPlanetmath sides (in this case, the left and right sides) s1 and s2 and height h is

hs1+s22

So the area of the trapezoid above is

(a+b)a+b2=(a+b)22

The area of the yellow triangle (and that of the blue triangle) is

ab2

while the area of the red triangle (also a right triangle) is

c22

The two areas must be equal, so

(a+b)22=2ab2+c22
a2+2ab+b22=ab+c22
a2+2ab+b2=2ab+c2
a2+b2=c2

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更新时间:2025/5/5 5:39:25