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
Triangle (musical instrument) form of an equilateral triangle, early instruments were often formed as non-equilateral isosceles triangles. In the early days the triangles did not have an opening and had jingling rings along the lower side. Early examples of triangles include ornamental work at the open end, often in a scroll pattern. Historically, the triangle has been manufactured from a solid iron and later steel rod and bent into a triangular shape roughly equilateral. In modern times, the scroll pattern has been abandoned and triangles are made from either steel or brass. The triangle is often the subject of jokes and one liners