Pascal’s Triangle was originally developed by the ancient Chinese, but Blaise Pascal was the first person to discover special patterns contained inside the triangle. They teach his ideas in various schools online in math courses. You probably also heard of this guy from your high school math teacher.

Triangular numbers appear in Pascal’s Triangle. In fact, the 3rd diagonal of Pascal’s Triangle gives all triangular numbers as shown below:

1. Fill in these three forms with one of the the primary colors: red, yellow, or blue. The coloring is to fill the form entirely in each case. One color per shape.

2. If possible, provide an explanation for your choice of color.

In 1923 Wassily Kandinsky circulated a questionnaire at the Bauhaus, asking respondents to fill in a triangle, square, and circle witht he primary colors of red, yellow, and blue. He hoped to discover a universal correspondence between form and color, embodied in the equation red=square, yellow=triangle, blue=circle.

The name given to the act of a political candidate presenting his or her ideology as being “above” and “between” the “left” and “right” sides (or “wings”) of a traditional (e.g. UK or US) democratic “political spectrum”. It involves adopting for oneself some of the ideas of one’s political opponent (or apparent opponent). The logic behind it is that it both takes credit for the opponent’s ideas, and insulates the triangulator from attacks on that particular issue. Opponents of triangulation, who believe in a fundamental “left” and “right”, consider the dynamic a deviation from its “reality” and dismiss those that strive for it as whimsical. Source: Wikipedia

Obama: Triangulation 2.0? Published on Monday, January 24, 2011 by The Nation by Ari Berman

Immediately following the Democrats’ 2010 electoral shellacking, a broad spectrum of pundits urged President Obama to “pull a Clinton,” in the words of Politico: move to the center (as if he wasn’t already there), find common ground with the GOP and adopt the “triangulation” strategy employed by Bill Clinton after the Democratic setback in the 1994 midterms. “Is ‘triangulation’ just another word for the politics of the possible?” asked the New York Times. “Can Obama do a Clinton?” seconded The Economist. And so on. The Obama administration, emphatic in charting its own course, quickly took issue with the comparison. According to the Times, Obama went so far as to ban the word “triangulation” inside the White House. Politico called the phrase “the dirtiest word in politics.”

These pointers discuss triangles and their higher-dimensional generalizations (simplices). I am particularly interested in triangulation by which I mean partitioning regions into triangles, tetrahedra, or higher dimensional simplices, for various applications including finite element mesh generation and surface interpolation. (The other meaning of triangulation involves determining locations and distances from certain measurements.) For more material on the first type of triangulation, see the mesh generation section of Geometry in Action or the list of my own triangulation papers. For other kinds of partitions, see the page on dissection.