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An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

The constant ratio by which all distances are increased (or decreased) in a similarity. A similarity with ratio of magnification equal to 1 is called an isometry.

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

Radial line segments whose inward-pointing end produce the illusion of a circle or other figure. The apparent figure has the same color as the background, but appears ...

A two-dimensional map similar to the Hénon map but with the term -alphax_n^2 replaced by -alpha|x_n|. It is given by the equations x_(n+1) = 1-alpha|x_n|+y_n (1) y_(n+1) = ...

A curve similar to the sine function but possibly shifted in phase, period, amplitude, or any combination thereof. The general sinusoid of amplitude a, angular frequency ...

The line segment connecting opposite polyhedron vertices (i.e., two polyhedron vertices which do not share a common face) in a parallelepiped or other similar solid. Also ...

e^(i(ntheta))=(e^(itheta))^n. (1) From the Euler formula it follows that cos(ntheta)+isin(ntheta)=(costheta+isintheta)^n. (2) A similar identity holds for the hyperbolic ...