Geometric topology | Surfaces

Boy's surface

In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space. Boy's surface was first parametrized explicitly by Bernard Morin in 1978. Another parametrization was discovered by Rob Kusner and Robert Bryant. Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point. Unlike the Roman surface and the cross-cap, it has no other singularities than self-intersections (that is, it has no pinch-points). (Wikipedia).

Boy's surface
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Related pages

Congruence (geometry) | Perimeter | Rational function | Symmetry | End (topology) | Singular point of an algebraic variety | Möbius strip | Algebraic surface | Three-dimensional space | David Hilbert | Rational surface | Roman surface | Willmore energy | Immersion (mathematics) | Minimal surface | Morin surface | Rotational symmetry | Sphere eversion | Polar coordinate system | Real projective plane | Euclidean space | Magnitude (mathematics) | Complex conjugate | Projective plane | Geometry | Pinch point (mathematics)