MATHEMATICS MAGAZINE VOL. 73, NO. 1, FEBRUARY 2000 59

Proof Without Words: Pythagorean Runs

32 + 42 = 52

102 + 112 + 122 = 132 + 142

212 + 222 + 232 + 242 = 252 + 262 + 272

Tn I + 2 + -- +n * OT,-n)2 + + (4Tn )2 (4T l + 1)2 + . + (4T, + n2

For n = 3:

4- 24=4 (1+2+3) --Do 4.1 4.2 4*3

24 = + +

I + 5-

223 26

+ ~~~~~~~~~~~~~~~27

-MICHAELBOARDMAN

PACIFIC UNIVERSITY

FOREST GROVE, OR 97116

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