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65537 is the largest known Fermat prime, and the 65537-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. The 65537-gon has so many ...

A paradox mentioned in the Greek work Mechanica, dubiously attributed to Aristotle. Consider the above diagram depicting a wheel consisting of two concentric circles of ...

A polygon which has both a circumcircle (which touches each vertex) and an incircle (which is tangent to each side). All triangles are bicentric with R^2-x^2=2Rr, (1) where R ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2pi. Picking random points on a circle is ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

The circumcenter of mass is a concept that can be defined by analogy with one of the the constructions for the geometric centroid for the case of polygons. The geometric ...

The metric properties discovered for a primitive figure remain applicable, without modifications other than changes of signs, to all correlative figures which can be ...