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 sharing no common factor) as with formula_4 and formula_5 coprime, formula_6 odd, and to satisfy the triangle inequality formula_7 (if the quantity inside the absolute value signs is negative) or formula_8 (if that quantity is positive). Then this triangle’s medians formula_9 are found by using the above expressions for its sides in the general formula for medians: where the second equation in each case reflects the automedian feature formula_11 From this can be seen the similarity relationships There is a primitive integer-sided automedian triangle that is not generated from a right triangle: namely, the equilateral triangle with sides of unit