Carl Friedrich Gauss This Is Research Proposal

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He made three main contributions to the theory of numbers: congruence theory, studies on the separation of the circle into equal parts, and theory of quadratic forms.

Algebra and Analysis

Up to Gauss's time, no one had been able to prove that every algebraic equation has at least one root. Gauss offered three proofs. And he modified the definition of a prime number.

Astronomical Calculations

We discussed briefly his assistance to astronomers in relocating Ceres. His success in this effort spurred him to develop the mathematical methods he used further. In 1809 his Theoria motus corporum coelestium used the method of least squares to determine the orbits of celestial bodies from observational data. In arguing his method, Gauss invented the Gaussian law of error, or, as we know it today, the normal distribution.

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Non-Euclidean Geometry

Mathematicians, for centuries, had been attempting to prove Euclid's postulate concerning parallels (the sum of the angles of a triangle is two right angles). Gauss proved that a geometry could be developed without the parallel postulate, i.e. non-Euclidean geometry. And in his study of differential geometry developed the idea that the geometry of a curved surface could be considered as two-dimensional non-Euclidean geometry (Encyclopedia of World Biography, 2005, para. 13)

The pure greatness of Gauss is that his contributions are as influential today as they were in his time......

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