Animated Proofs of the Pythagorean Theorem
In the Mathematics Department Seminar in Spring 2001, David
Dobbins presented several proofs of the Pythagorean Theorem.
Seeing what he had done, it occurred to me that many
geometry proofs lend themselves to presentation in the form
of "animated gifs". So I created such presentations for all
of the proofs he presented, except for one that used vector
algebra (in a somewhat fishy way, in my opinion). Here they
are:
- Euclid's proof is a challenge.
I think the animation helps a great deal, especially in sliding
a triangle into half a rectangle.
- Bhaskara's proof was accompanied
in his work by a second figure (which neither David nor I found
very helpful) and one word of commentary: "Behold!" I think the
gif is clearer.
- Eves' history of math text credits the following proof also
to Bhaskara, with a rediscovery by
Wallis. David describes this as
"the shortest proof possible", but I think the next one has a
claim to that title as well.
- Even U.S. President James A.
Garfield found a new (and very slick) proof of the theorem.