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A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.

The partial differential equation u_(xx)+(y^2)/(1-(y^2)/(c^2))u_(yy)+yu_y=0.

Let f*g denote the cross-correlation of functions f(t) and g(t). Then f*g = int_(-infty)^inftyf^_(tau)g(t+tau)dtau (1) = ...

The involute of the deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid involute for n=3 x_i = 1/9[2cost-cos(2t)] (3) y_i = 1/9[2sint+sin(2t)], (4) ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

Also known as the difference of squares method. It was first used by Fermat and improved by Gauss. Gauss looked for integers x and y satisfying y^2=x^2-N (mod E) for various ...

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

The illusion shown above which was discovered by Helmholtz in the 19th century. Despite the fact that the two above figures are identical in size, the white hole looks bigger ...

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

A three-dimensional coordinate system in which the axes do not satisfy the right-hand rule.