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
Integer triangle "x" + "y", and "y" − "x" are the three sides of an automedian triangle. For instance, the right triangle with side lengths 5, 12, and 13 can be used in this way to form the smallest non-trivial (i.e., non-equilateral) integer automedian triangle, with side lengths 13, 17, and 7. Consequently, using Euclid's formula, which generates primitive Pythagorean triangles, it is possible to generate primitive integer automedian triangles as with formula_28 and formula_27 coprime and formula_88 odd, and formula_89 (if the quantity inside the absolute value signs is negative) or formula_90 (if that quantity is positive) to satisfy the triangle