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Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
As a result, the sum of these spaces is also dense in the space L 2 (S n−1) of square-integrable functions on the sphere. Thus every square-integrable function on the sphere decomposes uniquely into a series of spherical harmonics, where the series converges in the L 2 sense.
Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point.
Schematic of a BARS system. Pressure chamber. Two BARS devices, one open for loading or unloading and the other closed. BARS (or "split sphere", transliteration from Russian: БАРС abbreviation of Russian: Беспрессовая Аппаратура Высокого Давления «РАЗРЕЗНАЯ СФЕРА», (bespressovaya apparatura vysokogo davleniya «razreznaya sfera ...
Dyson Sphere Program takes place in a futuristic science fiction world, where a society exists primarily in a virtual computer space, which demands a great deal of power and computational ability. To expand that, they have sent one of their members, the player, into the real universe to construct a Dyson sphere from resources in a nearby star ...
Simplified schematics of YIG-resonator coupling to microstrip network YIG filter partially disassembled. The electromagnet is on the left. The module with YIG sphere and input and output coils is on the right. Yttrium iron garnet spheres (YIG spheres) serve as magnetically tunable filters and resonators for microwave frequencies.
English: Sphere wireframe - orthogonal projection of a sphere. The image shows lines, which are drawn as they were painted onto the surface of a sphere. The angular distance between two lines is 10°. The SVG file is created by the below C++-program, which calculates each edge of a line as an ellipse-bow.
The Riemann sphere is only a conformal manifold, not a Riemannian manifold. However, if one needs to do Riemannian geometry on the Riemann sphere, the round metric is a natural choice (with any fixed radius, though radius is the simplest and most common choice). That is because only a round metric on the Riemann sphere has its isometry group be ...
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