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In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere.
It consists of a pot with a small hole at the bottom through which the water can escape. The amount of escaping water gives the measure of time. As given by the Torricelli's law, the rate of efflux through the hole depends on the height of the water; and as the water level diminishes, the discharge is not uniform.
In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. [8] In September 2023, Desmos released a beta for a 3D calculator, which added features on top of the 2D calculator, including cross products, partial derivatives and double-variable parametric equations. [9]
In algebraic topology and graph theory, graph homology describes the homology groups of a graph, where the graph is considered as a topological space. It formalizes the idea of the number of "holes" in the graph. It is a special case of a simplicial homology, as a graph is a special case of a simplicial complex. Since a finite graph is a 1 ...
Find the two points with the lowest and highest x-coordinates, and the two points with the lowest and highest y-coordinates. (Each of these operations takes O ( n ).) These four points form a convex quadrilateral , and all points that lie in this quadrilateral (except for the four initially chosen vertices) are not part of the convex hull.
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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:
The even-hole-free graphs are the graphs containing no induced cycles with an even number of vertices. The trivially perfect graphs are the graphs that have neither an induced path of length three nor an induced cycle of length four. By the strong perfect graph theorem, the perfect graphs are the graphs with no odd hole and no odd antihole.