Genus (mathematics) and Torus

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Difference between Genus (mathematics) and Torus

Genus (mathematics) vs. Torus

In mathematics, genus (plural genera) has a few different, but closely related, meanings. In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Disk (mathematics)

In geometry, a disk (also spelled disc).

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Elliptic curve

In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.

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Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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Fundamental polygon

In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0.

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Klein bottle

In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Projective plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane.

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Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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