But in 1947, a mathematician named Claude Ambrose Rogers offered a different perspective. Start with any lattice, he said — even a suboptimal one. Rather than draw a sphere around each point, draw an ...

In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible. Contact structures assign ...

A great circle is an equivalent of a straight line in planar geometry - it is the shortest path between two points on a sphere. Doing geometry on a sphere requires using spherical trigonometry and ...

1. Generate some sphere-meshes. Run the sphere-generation script - python make-sphere-mesh.py - to generate some sphere meshes. The denser, the better. By default, the script will try to generate ...

Books Received Published: 10 December 1938 Analytic Geometry and Calculus Nature 142, 1018 (1938) Cite this article ...

Elon Rimon, Daniel E. Koditschek, The Construction of Analytic Diffeomorphisms for Exact Robot Navigation on Star Worlds, Transactions of the American Mathematical Society, Vol. 327, No. 1 (Sep., 1991 ...

2.2. Analytical Solution of the Four-Sphere Head Model The solution of Equation (1) takes different forms for tangential and radial dipoles, and any dipole can be decomposed into a linear combination ...