Triangle their internal angles, measured here in degrees. A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral. Triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise (see Non-planar triangles, below). In rigorous treatments, a triangle is therefore called a "2-simplex" (see also Polytope). Elementary facts about triangles were presented by Euclid in books 1–4
Golden triangle (mathematics) spiral is also known as an equiangular spiral, a term coined by René Descartes. "If a straight line is drawn from the pole to any point on the curve, it cuts the curve at precisely the same angle," hence "equiangular". Closely related to the golden triangle is the golden gnomon, which is the obtuse isosceles triangle in which the ratio of the length of the equal (shorter) sides to the length of the third side is the reciprocal of the golden ratio. The golden gnomon is also uniquely identified as a triangle having its three angles in 1:1:3 proportion. The