Pascal's triangle Construct a "d"-dimensional triangle (a 3-dimensional triangle is a tetrahedron) by placing additional dots below an initial dot, corresponding to P(1) = 1. Place these dots in a manner analogous to the placement of numbers in Pascal's triangle. To find P("x"), have a total of "x" dots composing the target shape. P("x") then equals the total number of dots in the shape. A 0-dimensional triangle is a point and a 1-dimensional triangle is simply a line, and therefore P("x") = "1" and P("x") = "x", which is the sequence of natural numbers. The number of dots in each layer corresponds
Reuleaux triangle three-cornered shape of the Reuleaux triangle may be seen both as a symbol of the Trinity, and as "an act of opposition to the form of the circle". The Reuleaux triangle has also been used in other styles of architecture. For instance, Leonardo da Vinci sketched this shape as the plan for a fortification. A modern high-rise building, the Kölntriangle in Cologne, Germany, was built with a Reuleaux triangle cross-section. Together with the circular shape of its core, this gives varied depths to the rooms of the building. Another early application of the Reuleaux triangle, by Leonardo da Vinci circa