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Explaination of the given proof
Many different proofs of the Pythagorean theorem have been devised. Euclid's proof is one of the most complicated and least intuitive.
Many different proofs of the Pythagorean theorem have been devised. Euclid's proof is one of the most complicated and least intuitive.
One "proof," below, appeared in an ancient manuscript with no explanation other than the word "look!" Can you see just by looking that the square on the hypotenuse and the two squares on the other sides must take up equal amounts of area?
One proof, below, appeared in an ancient manuscript with no explanation other than the word "look!" Essentially, the triangles in the large square, the hypotenuses of which form the border of the small square, form the two congruent rectangles in the upper right hand and lower left hand corners of the diagram. Therefore, the other two sections of the large square in this portion of the diagram possess the same area as the smaller square in the first diagram. The area of one the two small squares in the second portion of the diagram is given by ''a<sup>2</sup>'', and the other by ''b<sup>2</sup>'', therefore, the area of the small square in the first portion of the diagram is given by ''a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup>'', the Pythagorean theorem.
[[image:Pythagoras.gif]]
[[image:Pythagoras.gif]]
[[Category:Geometry]]
[[Category:Geometry]]
[[Category:Mathematics]]
[[Category:Mathematics]]