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
Equilateral triangle area of all those circumscribed around a given circle is equilateral. The ratio of the area of the incircle to the area of an equilateral triangle, formula_30, is larger than that of any non-equilateral triangle. The ratio of the area to the square of the perimeter of an equilateral triangle, formula_31 is larger than that for any other triangle. If a segment splits an equilateral triangle into two regions with equal perimeters and with areas "A" and "A", then If a triangle is placed in the complex plane with complex vertices "z", "z", and "z", then for either non-real cube