Abstract: A solution of the ancient Greek problem of trisection of an arbitrary angle employing only compass and straightedge and its algebraic proof are presented. It is shown that while Wantzel’s theory of 1837 concerning irreducibility of the cubic x³-3x-1=0 is correct it does not imply impossibility of trisection of arbitrary angle since rather than a cubic equation the trisection problem is shown to depend on the quadratic equation y²-3+c=0 where c is a constant. The earlier formulation of the problem by Descartes the father of algebraic geometry is also discussed. If one assumes that the ruler and the compass employed in the geometric constructions are in fact Platonic ideal instruments then the trisection solution proposed herein should be exact.

Brief Biography of the Speaker:
Siavash H. Sohrab received his PhD in Engineering Physics in 1981 from University of California, San Diego, his MS degree in Mechanical Engineering from San Jose State University in 1975, and his BS degree in Mechanical Engineering from the University of California, Davis in 1973. He then joined Northwestern University in 1982 as postdoctoral research assistant and became Visiting Assistant Professor in 1983, Assistant Professor of Mechanical Engineering in 1984, and since 1990 he is Associate Professor of Mechanical Engineering at the Northwestern University. From 1975-1978 he worked as a scientist doing research on fire protection and turbulent combustion at NASA Ames research center in California. His research interests have been on combustion, fluid dynamics, thermodynamics, and statistical and quantum mechanics.