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In layman's terms, the genus is the number of "holes" an object has ("holes" interpreted in the sense of doughnut holes; a hollow sphere would be considered as having zero holes in this sense). [3] A torus has 1 such hole, while a sphere has 0. The green surface pictured above has 2 holes of the relevant sort. For instance:
Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing ...
In mathematics, the term homology, ... homology was the observation that certain low-dimensional shapes can be topologically distinguished by examining their "holes."
Hole types in engineering: blind (left), through (middle), interrupted (right). In engineering, machining, and tooling, a hole may be a blind hole or a through hole (also called a thru-hole or clearance hole). A blind hole is a hole that is reamed, drilled, or milled to a specified depth without breaking through to the other side of the ...
Down the Rabbit Hole: The Math That Helps the James Webb Space Telescope Sit Steady in Space. Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But he most ...
The definition rules out only handle-shaped holes. A sphere (or, equivalently, a rubber ball with a hollow center) is simply connected, because any loop on the surface of a sphere can contract to a point even though it has a "hole" in the hollow center. The stronger condition, that the object has no holes of any dimension, is called ...
Here there are n = 10 pigeons in m = 9 holes. Since 10 is greater than 9, the pigeonhole principle says that at least one hole has more than one pigeon. (The top left hole has 2 pigeons.) In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one ...
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.