Lévy C curve with a straight line. An isosceles triangle with angles of 45°, 90° and 45° is built using this line as its hypotenuse. The original line is then replaced by the other two sides of this triangle. At the second stage, the two new lines each form the base for another right-angled isosceles triangle, and are replaced by the other two sides of their respective triangle. So, after two stages, the curve takes the appearance of three sides of a rectangle with the same length as the original line, but only half as wide. At each subsequent stage, each straight line
Special right triangle than 256: Isosceles right-angled triangles cannot have sides with integer values, because the ratio of the hypotenuse to either other side is , but cannot be expressed as a ratio of two integers. However, infinitely many "almost-isosceles" right triangles do exist. These are right-angled triangles with integral sides for which the lengths of the non-hypotenuse edges differ by one. Such almost-isosceles right-angled triangles can be obtained recursively, "a" is length of hypotenuse, "n" = 1, 2, 3, ... Equivalently, where {"x", "y"} are the solutions to the Pell equation , with the hypotenuse "y" being the odd terms of the