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
Automedian triangle satisfying the formula "a" = "b" + "c". That is, in order for the three numbers "a", "b", and "c" to be the sides of an automedian triangle, the sequence of three squared side lengths "b", "a", and "c" should form an arithmetic progression. If "x", "y", and "z" are the three sides of a right triangle, sorted in increasing order by size, and if 2"x" < "z", then "z", "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