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The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 points known as Kirkman points. Each ...

The term two-sided ideal is used in noncommutative rings to denote a subset that is both a right ideal and a left ideal. In commutative rings, where right and left are ...

Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").

The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The two-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the line ...

A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles. The numbers a_n of two-regular ...

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 ...

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...