Right triangle and "G" and hypotenuse "A", then and where formula_40 is the golden ratio formula_41 Since the sides of this right triangle are in geometric progression, this is the Kepler triangle. Thales' theorem states that if "A" is any point of the circle with diameter "BC" (except "B" or "C" themselves) "ABC" is a right triangle where "A" is the right angle. The converse states that if a right triangle is inscribed in a circle then the hypotenuse will be a diameter of the circle. A corollary is that the length of the hypotenuse is twice the distance from the right
Floyd's triangle of an "n" × "n" magic square . Summing up the row sums in Floyd's triangle reveals the doubly triangular numbers (triangular numbers with an index that is triangular) 1 = 1 = T(T(1)) <br><br><br> 1 = 6 = T(T(2)) <br> 2 + 3 <br><br><br> 1 <br> 2 + 3 = 21 = T(T(3))<br> 4 + 5 + 6 <br> Floyd's triangle Floyd's triangle is a right-angled triangular array of natural numbers, used in computer science education. It is named after Robert Floyd. It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1