All Items 2 Collection 1 The Octagon 2 Contributor 3 Basu, Soham (École polytechnique fédérale de Lausanne) 1 Velleman, Daniel J. (Department of Mathematics and Statistics, Amherst College) 1 Velleman, Daniel J. (Department of Mathematics and Statistics, Amherst College, Department of Mathematics and Statistics, University of Vermont) 1 Topic 5 Equations, Roots of 2 Fundamental theorem of algebra 2 Numbers, Complex 2 Polynomials 2 Algebra 1 Part Of 1 The Amherst College Octagon 2 Genre 1 Articles 2 Subject 5 Equations, Roots of 2 Fundamental theorem of algebra 2 Numbers, Complex 2 Polynomials 2 Algebra 1 On Gauss's First Proof of the Fundamental Theorem of Algebra Velleman, Daniel J. (Department of Mathematics and Statistics, Amherst College, Department of Mathematics and Statistics, University of Vermont) Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss’s proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss’s proof. On Gauss's First Proof of the Fundamental Theorem of Algebra The fundamental theorem of algebra: A visual approach Velleman, Daniel J. (Department of Mathematics and Statistics, Amherst College) The fundamental theorem of algebra says that for every nonconstant polynomial p with complex coefficients, there is a complex number z such that p(z) = 0. In this paper we present a method of visualizing functions on the complex plane, and use this method to illustrate why the fundamental theorem of algebra is true. We also discuss the history of the fundamental theorem of algebra and its proofs. The fundamental theorem of algebra: A visual approach