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Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...

The illusion illustrated above in which the bounding rectangle and inner square both appear distorted.

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

The number of nondecreasing lists {a_1,a_2,...,a_n} consisting of n elements 1<=a_i<=k is given by the binomial coefficient N(n,k)=(n+k-1; n-1). For example, there are six ...

The four of Hilbert's axioms which concern the arrangement of points.

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...

A manifold is said to be orientable if it can be given an orientation. Note the distinction between an "orientable manifold" and an "oriented manifold," where the former ...

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.