## Johann Carl Friedrich Gauss, 1777 - 1850, Germany

## Mathematician, Physicist.

Johann was a child prodigy.

At the age of 3 years, he was able to correct a mistake his father made while doing his accounts.

And then there is the story of a teacher in an elementary mathematics class setting them the task of finding the sum of all the numbers 1 to 100. Gauss had the correct answer in seconds, while the rest of the class was unsuccessful after half an hour.

While still a teenager he was able to publish an account of the significant discoveries he made in number theory.

*Johann Carl Gauss*

Johann was born into a poor family, but his abilities were noticed by the local Duke, who subsequently paid his tuition fees to the University of Technology from 1792 - 1795 and then to the University of Gottingen, from 1795 - 1798.

###

*University of Gottingen*

While still a student in 1796 he gave proof that every polynomial equation of degree n, has n roots, real or complex.

In 1801 he published his major work on algebraic number theory, which was the basis for the development of modular arithmetic, prime number theorems, triangular numbers, and their connection with Pascal's triangle and the binomial theorem.

*Triangular numbers. In general, Tn = n(n+1)/2*

In 1840 Gauss published his book on optics, and how an image is formed by a lens.

### Construction, using only paraxial rays

He used only the light rays close to the axis of the system, the so-called paraxial approximation, which allows the construction of the image formed. Rays too far from the axis would give rise to distortion,

In 1800, the Italian astronomer Giuseppe Piazzi discovered, very briefly, the asteroid Ceres. Before he could get sufficient data points to enable him to local it again later, it disappeared behind the sun.

Many astronomers tried to find it again, unsuccessfully, but Gauss could not resist the lure of a problem to be solved and was completely successful

*Ceres. Astronomically very small, <500km*

Another area of interest was the earth's magnetic field. At the time, there was no way of knowing the field's strength or direction. Gaus set to and made a magnetometer, to measure both those quantities.

In recognition of the original work done by Gauss, the magnetic field is currently measured in units of Gauss.

Later, he decided to make a geographic survey of his local area around Hanover, but to do that he needed to be able to measure angles accurately. He designed and made a Heliotrope, something like a modern theodolite.

*Heliotrope, for a survey of Hanover.*

Gauss made many major contributions to mathematics and science, for which he was rightfully honored, but he strongly discouraged his sons from following in his footsteps, because he was sure they would not be able to maintain his standard, and it would "lower the family name". I'm not surprised they emigrated.

Gauss is recognized as one of the greatest mathematicians ever.

He worked hard, was a perfectionist, and would not publish his results until he was sure there was nothing more he could do to improve it. After he had died, while his papers were being sorted, they found an extraordinary number of important results that should have been published.

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