Pythagora's Theorem

Pythagora's Theorem (GIF Anim.)

GIF Animation made with GIF Construction Set by Alchemy Mindworks

The previous proof is Bhaskara's (An ancient hindu mathematician). The following is from James Abram Garfield (1831-1881), 20th. president of the U.S. (assasinated)

Garfield's proof The triangle ABC is rectangle (right angle at A).

  • Draw CD perpendicular to BC in C, such that CD = BC.

  • Draw a line parallel to AB, containig D. This line shall meet the line containing A and C in (say) Z.

  • Now, you can easily see that ABC and CDZ are equal (congruent) triangles, with AB = CZ, and AC = DZ.

  • Call a = BC = CD, b = AC = DZ, and c = AB = CZ.

  • Note that ABDZ is a trapecium with area
    A = (AC+CZ)(AB+ZD)/2 = (b+c)(c+b)/2 ......(1)

  • Also, A is the sum of the areas of ABC, CDZ and BCD. That is A = bc/2 + bc/2 + a.a/2 .......................(2)

  • Equating (1) and (2) -and simplifying-, we are done.