Calabi triangle triangle or the Calabi triangle. Thus, the Calabi triangle may be defined as a triangle that is not equilateral and has three placements for its largest square. The Calabi triangle is isosceles. The ratio of the base to either leg is which approximates to 1.55138752454. In terms of trigonometric functions, it is It is the largest positive root of and has continued fraction representation [1, 1, 1, 4, 2, 1, 2, 1, 5, 2, 1, 3, 1, 1, 390, ...]. The Calabi triangle is obtuse with base angles 39.1320261...° and third angle 101.7359477...°. Calabi triangle The Calabi triangle is a
Integer triangle inequality. An important characteristic of the automedian triangle is that the squares of its sides form an arithmetic progression. Specifically, formula_91 so formula_92. A triangle family with integer sides formula_93 and with rational bisector formula_94 of angle A is given by with integers formula_99. There exist infinitely many non-similar triangles in which the three sides and the bisectors of each of the three angles are integers. There exist infinitely many non-similar triangles in which the three sides and the two trisectors of each of the three angles are integers. However, for "n" > 3 there exist no triangles in which