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When all the points P on one line are related by an isometry to all points P^' on another, the midpoints of the segments PP^' are either distinct and collinear or coincident.

A homogeneous polynomial in two or more variables.

In the American system, 10^(42).

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

Expanding the Riemann zeta function about z=1 gives zeta(z)=1/(z-1)+sum_(n=0)^infty((-1)^n)/(n!)gamma_n(z-1)^n (1) (Havil 2003, p. 118), where the constants ...

A transformation in which the coordinate system is changed, leaving vectors in the original coordinate system "fixed" while changing their representation in the new ...

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation a^2x^2(x^2+y^2)-b(ay-x^2-y^2)^2=0, where a>0, b>a^2. The curve ...

A subset of a topological space is called clopen if it is both closed and open.

A complex rotation is a map of the form z|->ze^(itheta), where theta is a real number, which corresponds to counterclockwise rotation by theta radians about the origin of ...