Geometry

By David A. Smith

Geometry is useful not only in algebra, analysis, chemistry, physics, and engineering, but is indeed useful everywhere possible. Standard topics for an undergraduate studying geometry (usually spread out through several courses) surely include triangles, regular polygons, isometry and similarity, circles and spheres in Euclidean space (perhaps in other spaces as well). Students studying geometry eventually become aware of coordinates, complex numbers, and solids, but a science or engineering student should also study at least one of the following: ordered geometry, affine geometry, projective geometry, absolute geometry, or hyperbolic geometry. Mostly importantly is the study of the foundations of geometry, because proof-writing and logical deduction is definitely a necessity of any geometry practitioner.