Foundations of geometry and therefore are valid theorems in absolute geometry. Proposition I.31 proves the existence of parallel lines (by construction). Also, the Saccheri–Legendre theorem, which states that the sum of the angles in a triangle is at most 180°, can be proved. The theorems of absolute geometry hold in hyperbolic geometry as well as in Euclidean geometry. Absolute geometry is inconsistent with elliptic geometry: in elliptic geometry there are no parallel lines at all, but in absolute geometry parallel lines do exist. Also, in elliptic geometry, the sum of the angles in any triangle is greater than 180°. Logically, the axioms do
Golden triangle (mathematics) adjacent vertices to the center. This will form a golden triangle. This is because: 180(10-2)/10=144 degrees is the interior angle and bisecting it through the vertex to the center, 144/2=72. The golden triangle is also uniquely identified as the only triangle to have its three angles in 2:2:1 proportions. The golden triangle is used to form a logarithmic spiral. By bisecting the base angles, a new point is created that in turn, makes another golden triangle. The bisection process can be continued infinitely, creating an infinite number of golden triangles. A logarithmic spiral can be drawn through the vertices. This