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From the Fun Fact files, here is a Fun Fact at the Easy level:

Proofs without Words

Figure 1
Figure 1

There are many facts which can be proved just by looking at a picture! For instance:


x2 - y2 = (x+y) (x-y)

can be illustrated by drawing a large square, cutting a small square out of the corner, and cutting off the rectangular portion at the top and placing on the side to illustrate the right hand side of this identity.

Presentation Suggestions:
Write down the identity and then draw the picture, asking students to see if they can figure out how the picture explains the identity. Or, draw the picture and ask if they can figure out what it should prove!

The Math Behind the Fact:
Almost any "Proof without Words" from Mathematics Magazine or Nelsen's recent book (see reference) will serve as a short, snappy Fun Fact!

How to Cite this Page:
Su, Francis E., et al. "Proofs without Words." Mudd Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

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References:
Subjects:    algebra, combinatorics, other
Level:    Easy
Fun Fact suggested by:   Lesley Ward
Suggestions? Use this form.
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