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An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d. Therefore, for ...

The bracket polynomial is one-variable knot polynomial related to the Jones polynomial. The bracket polynomial, however, is not a topological invariant, since it is changed ...

Consider n strings, each oriented vertically from a lower to an upper "bar." If this is the least number of strings needed to make a closed braid representation of a link, n ...

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

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 ...

The Cantor diagonal method, also called the Cantor diagonal argument or Cantor's diagonal slash, is a clever technique used by Georg Cantor to show that the integers and ...

"Casting out nines" is an elementary check of a multiplication which makes use of the congruence 10^n=1 (mod 9). Let decimal numbers be written a=a_n...a_2a_1a_0, ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...