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Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...

The epispiral is a plane curve with polar equation r=asec(ntheta). There are n sections if n is odd and 2n if n is even. A slightly more symmetric version considers instead ...

Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a ...

A fixed point for which the stability matrix has equal negative eigenvalues.

A fixed point for which the stability matrix has both eigenvalues negative, so lambda_1<lambda_2<0.

A fixed point for which the stability matrix has one zero eigenvector with negative eigenvalue lambda<0.

A fixed point for which the stability matrix has equal positive eigenvalues.

A fixed point for which the stability matrix has both eigenvalues positive, so lambda_1>lambda_2>0.

A fixed point for which the stability matrix has one zero eigenvector with positive eigenvalue lambda>0.

A fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new ...