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If and only if (i.e., necessary and sufficient). The terms "just if" or "exactly when" are sometimes used instead. A iff B is written symbolically as A<->B, A<=>B, A<->B, or ...

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 ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

A system of coordinates obtained by inversion of the oblate spheroids and one-sheeted hyperboloids in oblate spheroidal coordinates. The inverse oblate spheroidal coordinates ...

The geometry resulting from the application of the inversion operation. It can be especially powerful for solving apparently difficult problems such as Steiner's porism and ...

An element admitting a multiplicative or additive inverse. In most cases, the choice between these two options is clear from the context, as, for example, in a monoid, where ...

The point S^' which makes the perimeters of the triangles DeltaBS^'C, DeltaCS^'A, and DeltaAS^'B equal. The isoperimetric point exists iff a+b+c>4R+r, (1) where a, b, and c ...

An isoscelizer of an (interior) angle A in a triangle DeltaABC is a line through points I_(AB)I_(AC) where I_(AB) lies on AB and I_(AC) on AC such that DeltaAI_(AB)I_(AC) is ...

Some elements of a group G acting on a space X may fix a point x. These group elements form a subgroup called the isotropy group, defined by G_x={g in G:gx=x}. For example, ...

Jacobi-Gauss quadrature, also called Jacobi quadrature or Mehler quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function ...