July 10, 1796 — Carl Friedrich Gauss discovered today that every positive integer is representable as a sum of at most three triangular numbers.

According to Gauss: The triangular number T_n solves the “handshake problem” of counting the number of handshakes if each person in a room with n + 1 people shakes hands once with each person. In other words, the solution to the handshake problem of n people is T_n−1. The function T is the additive analog of the factorial function, which is the products of integers from 1 to n.

As one of the world’s most famous mathematicians, Gauss’s achievements include his contributions to number theory, proving the fundamental theorem of algebra, independently arriving at the least squares method (line of best fit), and introducing the bell curve (Gaussian distribution) in statistics.

Sources

• historyorb
• wichita.edu
• wikipedia/Triangularnumber