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Let V=R^k be a k-dimensional vector space over R, let S subset V, and let W={w in V:w·n^^=0} be a subspace of V of dimension k-1, where n^^ is a unit normal vector of W. Then ...

The mittenpunkt (also called the middlespoint) of a triangle DeltaABC is the symmedian point of the excentral triangle, i.e., the point of concurrence M of the lines from the ...

Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle of the given three circles. If it lies outside the three circles, ...

A surface which a monkey can straddle with both legs and his tail. A simple Cartesian equation for such a surface is z=x(x^2-3y^2), (1) which can also be given by the ...

The geometric centroid of the first Morley triangle, which is also the center of Morley's circle, is called the first Morley center. It has triangle center function ...

The Moses circle is defined as the circle with center at the Brocard midpoint X_(39) that is tangent to the nine-point circle at the center of the Kiepert hyperbola X_(115). ...

What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center N as the pivot point. It therefore has trilinear equation ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

A vector field X on a compact foliated manifold (M,F) is nice if X is transverse to F and if X has a closed orbit C (called a nice orbit) such that the intersection C ...