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
Pythagoras Peak theorem concerning a right-angled triangle is well known. Pythagoras Peak Pythagoras Peak is the highest peak, 1,275 m, in the central Tula Mountains, standing along the north side of Beaver Glacier, 8 nautical miles (15 km) southeast of Mount Storer. The peak has a prominent notch, the eastern aspect being a right-angled triangle with a perpendicular northern face. It was photographed from Mount Riiser-Larsen in February 1958 by ANARE (Australian National Antarctic Research Expeditions) led by Phillip Law, but was first visited and surveyed in December 1958 by G.A. Knuckey, ANARE surveyor. It was named by the Antarctic Names Committee