lpetrich
Contributor
Carl Friedrich Gauss (or Gauß) was born 241 years ago, as I write this.He was one of the world's greatest mathematicians, and his greatness even extended into his childhood, if one is to believe some anecdotes about him. The best-known of them is where a teacher once asked his students to add up all the integers from 1 to 100. He may have thought that that would keep the class very busy, but young Carl got the answer very quickly: 5050.
When 19 years old, he discovered that every regular polygon that can be constructed with ruler and compass has (power of 2) * (product of distinct Fermat primes) number of sides. He also found how to construct a regular heptadecagon (17-sided polygon) with ruler and compass, something that he was proud of enough to want that polygon on his tombstone. But the stonemason who was to carve it begged off, because it would look too much like a circle.
At 21 he wrote a textbook on number theory, Disquisitiones Arithmeticae ("Arithmetical Investigations" in Latin) -- he was one of the last of notable scientists to write in Latin. However, it was only published 3 years later. It contains some of his number-theory results.
When dwarf planet Ceres was discovered, he calculated its orbit from observations of it. He also went on to discover a rather general method of curve fitting: the method of least squares. This method assumes a curve that is a linear combination of some curves, and one tries to find the linear-combination coefficients. Using squares makes the math easier -- the coefficients satisfy a system of linear equations.
He also worked on non-Euclidean geometry, though he never published anything on the subject. He did not publish much, preferring to publish only very high-quality results. He also discovered his Theorema Egregium (Remarkable Theorem). It states that one can determine curvatures on a 2-surface by measuring only distances and angles on it, without needing how that surface is embedded in some higher-dimensional space like a 3-space. His student Bernhard Riemann extended Gauss's work to arbitrary numbers of dimensions, and that work is a cornerstone of Albert Einstein's theory of gravity, general relativity.