Why is the diagram on the left required to prove the Pythagorean Theorem, when the diagram on the right seems sufficient to do so?
http://jwilson.coe.uga.edu/EMT668/emt668.student.folders/HeadAngela/essay1/image1.gif
2007-12-19 23:40:22 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The Greeks of Pythagoras' day -- let alone the Egyptians who seem to have originally figured it out -- didn't have algebra, or some of the other formalism we have.
For us it's easy to say (a+b)^2 - 4*(1/2)*ab = a^2 + b^2.
But for them it was easier to instead draw the picture on the left.
2007-12-20 07:05:56 · answer #1 · answered by Curt Monash 7 · 0⤊ 0⤋
You are proving that the green plus yellow squares on the left equal the blue square on the right.
green has an area of a²
yellow has an area of b²
blue has an area of c²
the triangles each have areas of ab/2... because there are 4 of them, that's a total of 4(ab/2) or just 2ab.
Basically the two diagrams equal this equation.
a² + 2ab + b² = 2ab + c²
Cancel the 2ab (the red and purple triangles) and you have the Pythagorean Theorem
a² + b² = c²
The first diagram is only showing geometrically what we know to be (a + b)² = a² + 2ab + b². So you technically don't need to "see" the green and yellow squares to prove the theorem. It would be sufficient to use the second diagram and the algebraic manipulation above to prove the theorem.
2007-12-19 23:52:03 · answer #2 · answered by Puzzling 7 · 2⤊ 0⤋
The assertion of the thought became into got here across on a Babylonian pill circa 1900-1600 B.C. no count number if Pythagoras (c.560-c.480 B.C.) or somebody else from his college became into the 1st to discover its information can not be claimed with any diploma of credibility. Euclid's (c 3 hundred B.C.) components furnish the 1st and, later, the nicely-known reference in Geometry.
2016-10-08 23:38:53 · answer #3 · answered by ? 4 · 0⤊ 0⤋
Because its not
The diagram on the left shows four of the triangles, plus a squared and b squared
The diagram on the right shows four of the triangles, plus c squared.
Removing 4 triangles, and you find that a squared + b squared = c squared
2007-12-19 23:51:40 · answer #4 · answered by H T 3 · 2⤊ 0⤋
thats a right triangle wid squares drawn on respective sides and the squares of the base and perpendicular(on suitable arrngement )will coincide the square of the hypotenuse...
2007-12-20 01:17:16 · answer #5 · answered by PRIYADARSHINII 2 · 0⤊ 0⤋
These 2 are two independant proofs
2007-12-19 23:51:47 · answer #6 · answered by Mein Hoon Na 7 · 0⤊ 1⤋
no need to proove..self explanatory
2007-12-19 23:50:29 · answer #7 · answered by prasunkuls 2 · 0⤊ 3⤋