This term refers to a knot which is defined in cylindrical polar coordinates by the equations "r equals 2 plus cosine of p theta over q", and "z equals sin of p theta over q", where p and q are relatively prime integers.
This term refers to a knot which is defined in cylindrical polar coordinates by the equations "r equals 2 plus cosine of p theta over q", and "z equals sin of p theta over q", where p and q are relatively prime integers. The fundamental group of one of these objects is equal to the cartesian product of the integers with themselves. The Kolmogorov-Arnold-Moser theorem concerns quasiperiodic orbits described by trajectories moving on the surface of one of these objects, which can be viewed as the cartesian product of two circles. By the Heawood conjecture, 7 colors are needed to color this genus one surface, which can be obtained by gluing opposite edges of a rectangle together with no twists. For 10 points, identify this kind of three-dimensional surface with a single hole, whose name describes the shape of a donut.
This term refers to a knot which is defined in cylindrical polar coordinates by the equations "r equals 2 plus cosine of p theta over q", and "z equals sin of p theta over q", where p and q are relatively prime integers.
torus [accept word forms like toroidal before "objects"]