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An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

The natural parametric equations of a curve are parametric equations that represent the curve in terms of a coordinate-independent parameter, generally arc length s, instead ...

Let (xi_1,xi_2) be a locally Euclidean coordinate system. Then ds^2=dxi_1^2+dxi_2^2. (1) Now plug in dxi_1=(partialxi_1)/(partialx_1)dx_1+(partialxi_1)/(partialx_2)dx_2 (2) ...

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called ...

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

To inscribe an equilateral triangle in an ellipse, place the top polygon vertex at (0,b), then solve to find the (x,y) coordinate of the other two vertices. ...

Differential Geometry