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Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

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 circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

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 geometry in which Archimedes' axiom does not hold.

An Archimedean circle is a circle defined in the arbelos in a natural way and congruent to Archimedes' circles, i.e., having radius rho=1/2r(1-r) for an arbelos with outer ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

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.