Root system inner product is the Killing form. The cosine of the angle between two roots is constrained to be a half-integral multiple of a square root of an integer. This is because formula_32 and formula_33 are both integers, by assumption, and formula_34 Since formula_35, the only possible values for formula_36 are formula_37 and formula_38, corresponding to angles of 90°, 60° or 120°, 45° or 135°, 30° or 150°, and 0° or 180°. Condition 2 says that no scalar multiples of "α" other than 1 and -1 can be roots, so 0 or 180°, which would correspond to 2"α" or −2"α", are
Isosceles triangle appear frequently in architecture and design, for instance in the pediments and gables of buildings. The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends