Airy diskIn optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, optics, and astronomy. The diffraction pattern resulting from a uniformly illuminated, circular aperture has a bright central region, known as the Airy disk, which together with the series of concentric rings around is called the Airy pattern. Both are named after George Biddell Airy.
Riemann sphereIn mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane: the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value for infinity. With the Riemann model, the point is near to very large numbers, just as the point is near to very small numbers. The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as well-behaved.
Modulation (music)In music, modulation is the change from one tonality (tonic, or tonal center) to another. This may or may not be accompanied by a change in key signature (a key change). Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization. Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.
Cross-ratioIn geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points A, B, C, D on a line, their cross ratio is defined as where an orientation of the line determines the sign of each distance and the distance is measured as projected into Euclidean space. (If one of the four points is the line's point at infinity, then the two distances involving that point are dropped from the formula.
