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Karl Friedrich Gauss: Facts & Overview

Instructor: Glenda Boozer
Karl Friedrich Gauss was a German mathematician, astronomer and physicist of the 18th and 19th centuries. He has sometimes been touted as the greatest mathematician since antiquity, and his name lives on in such things as the unit of magnetic field (the gauss) and the practice of clearing magnetic fields from equipment (degaussing).

Birth and Background

Johann Karl Friedrich Gauss (often referred to only as Karl Friedrich Gauss) was born on April 30, 1777, in Braunschweig, in what is now Germany but in those days was the Duchy of Braunschweig-Wolfenbuttel. His parents were poor, and his mother could not read and write, but she did remember that he was born on a Wednesday, eight days before the Feast of the Ascension, which is 40 days after Easter. Later, the young Gauss calculated his own date of birth based on that information, the clever little guy! He was always precocious and began making mathematical discoveries in his teens and early 20s.

Fortunately, the Duke took notice of this astonishingly brilliant young fellow and sent him to college. After that, he was even more productive and remained that way.

Discoveries

  • How to construct a 17-sided figure with only a compass and ruler. He was so proud of this that he wanted one on his tombstone. The stonecutter said it would be too difficult.

Heptadecagon construction

Seriously, this geometric construction, and the proof that it was correct, was important in lots of later mathematics.

  • Proof of the Fundamental Theorem of Algebra. This is the one that says every polynomial equation has the same number of roots as the highest degree of the variable. Linear equations have one solution, quadratic equations have two, and so on.
  • Finding the dwarf planet Ceres (formerly known as the asteroid Ceres - names keep changing!) after a short sighting. Giuseppi Piazzi had discovered it in 1800, but he didn't get to track it long enough to calculate its orbit by the usual methods before it went behind the Sun. Gauss came up with a new method, and voila! Ceres showed up almost exactly where he said it would be.

Ceres, from Hubble telescope

  • Advancements in surveying. Gauss took on the challenge of surveying the territory of Hanover and ended up inventing a device to measure more accurately, and making advances in geometry to account for curvature.
  • Studies of magnetism and gravitation. Gauss helped to measure the magnetic field of the earth, inventing the magnetometer in the process. This is why we measure magnetism in gausses.
  • Ideas in non-Euclidean geometry He didn't publish his notes on the subject of alternatives to Euclid's ideas of geometry, but those notes were influential in promoting acceptance of non-Euclidean geometry when, after his death, they came to light. He also spoke in defense of mathematicians who had published on the subject.
  • Modular arithmetic. This is like the arithmetic of a clock: 11:00 plus two hours is 1:00, at least on a 12-hour clock.
  • The Prime Number Theorem. This tells us about how prime numbers are distributed among the integers.
  • Gauss's Law. This is also known as the inverse-square law, and it describes the way that objects are affected less and less by gravity or magnetism as they get further from the source.
  • Gaussian distribution. This is the normal distribution, also known as the bell curve. Most of modern statistics makes use of this.

Gaussian distribution

Family Life

Gauss was married twice and had six children, three by each wife. His first wife, Johanna, died in 1809, and he married a friend of hers named Wilhelmina (Minna). When she died, his youngest daughter, Theresa, stayed and kept house for him until his death in 1855.

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