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Any two ranges {ABC...} and {A^'B^'C^'...} which are situated on the same or different lines are said to be homographic when the cross ratio of any four points on one range ...

An integer kappa equal to 0 or 1 which vanishes iff the product manifold M^4×R can be given a smooth structure. Here, M^n is a compact connected topological four-manifold.

A median triangle is a triangle whose sides are equal and parallel to the medians of a given triangle. The median triangle of the median triangle is similar to the given ...

A quantity which does not equal zero is said to be nonzero. A real nonzero number must be either positive or negative, and a complex nonzero number can have either real or ...

A straight angle is an angle equal to 180 degrees=pi radians. Two right angles make a straight angle, and two straight angles make a full angle.

Divide the sides of a quadrilateral into three equal parts. The figure formed by connecting and extending adjacent points on either side of a polygon vertex is a ...

If f is a function on an open set U, then the zero set of f is the set Z={z in U:f(z)=0}. A subset of a topological space X is called a zero set if it is equal to f^(-1)(0) ...

An n-dimensional vector, i.e., a vector (x_1, x_2, ..., x_n) with n components. In dimensions n greater than or equal to two, vectors are sometimes considered synonymous with ...

The Steiner triangle DeltaS_AS_BS_C (a term coined here for the first time), is the Cevian triangle of the Steiner point S. It is the polar triangle of the Kiepert parabola. ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...