Friday, September 26, 2008

19600

19600 = 1402, a perfect square.

19600 = 24 x 52 x 72.

19600
is one of only three numbers that are simultaneously square and tetrahedral. Tetrahedral numbers correspond to the number of balls in a triangular pyramid in which each side contains n + 1 balls. They are the sum of consecutive triangular numbers. 19600 is the 48th tetrahedral number.

19600 =
1402
= 1 + 3 + 6 + 10 + 15 + . . . + 1176.

The others are 1 = 1
2 = 1 and 4 = 22 = 1 + 3.

A triangular pyramid with side length 5 contains 35 spheres. Each layer represents one of the first five triangular numbers.

19600 has a representation as a sum of two squares: 19600 = 842 + 1122.


A contestant in Nathan’s Famous Hot Dog Eating Contest in New York who consumes 66 hot dogs (the world record) would ingest a total of 19,600 calories.

Sources:
Wolfram MathWorld; Wikipedia; CalorieLab

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