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A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral ...

Given a circular table of diameter 9 feet, which is the minimal number of planks (each 1 foot wide and length greater than 9 feet) needed in order to completely cover the ...

The third Morley triangle is made by rotating line BC toward vertex A about vertex B by angle (B+4pi)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 ...

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

A hexagon (not necessarily regular) on whose polygon vertices a circle may be circumscribed. Let sigma_i=Pi_i(a_1^2,a_2^2,a_3^2,a_4^2,a_5^2,a_6^2) (1) denote the ith-order ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

Archimedes' axiom, also known as the continuity axiom or Archimedes' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

There are two curves known as the butterfly curve. The first is the sextic plane curve given by the implicit equation y^6=x^2-x^6 (1) (Cundy and Rollett 1989, p. 72; left ...

Find the figure bounded by a line which has the maximum area for a given perimeter. The solution is a semicircle. The problem is based on a passage from Virgil's Aeneid: "The ...