Thales's theorem theorem is named after Thales because he was said by ancient sources to have been the first to prove the theorem, using his own results that the base angles of an isosceles triangle are equal, and that the sum of angles in a triangle is equal to 180°. Dante's "Paradiso" (canto 13, lines 101–102) refers to Thales's theorem in the course of a speech. The following facts are used: the sum of the angles in a triangle is equal to 180° and the base angles of an isosceles triangle are equal. Since = = , ∆OBA and ∆OBC are isosceles
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