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A golden triangle. The ratio a/b is the golden ratio φ. The vertex angle is =.Base angles are 72° each. Golden gnomon, having side lengths 1, 1, and .. A golden triangle, also called a sublime triangle, [1] is an isosceles triangle in which the duplicated side is in the golden ratio to the base side:
The triangle formed by two diagonals and a side of a regular pentagon is called a golden triangle or sublime triangle. It is an acute isosceles triangle with apex angle and base angles . [46] Its two equal sides are in the golden ratio to its base. [47] The triangle formed by two sides and a diagonal of a regular pentagon is ...
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
The golden angle is the angle subtended by the smaller (red) arc when two arcs that make up a circle are in the golden ratio. In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as ...
In mathematics, the supergolden ratio is a geometrical proportion close to 85/58. Its true value is the real solution of the equation x 3 = x 2 + 1. The name supergolden ratio results from analogy with the golden ratio, the positive solution of the equation x 2 = x + 1. A triangle with side lengths ψ, 1, and 1 ∕ ψ has an angle of exactly ...
Triangle – 3 sides Acute triangle; Equilateral triangle; Heptagonal triangle; Isosceles triangle. Golden Triangle; Obtuse triangle; Rational triangle; Heronian triangle. Pythagorean triangle; Isosceles heronian triangle; Primitive Heronian triangle; Right triangle. 30-60-90 triangle; Isosceles right triangle; Kepler triangle; Scalene triangle ...
In mathematics, the silver ratio is a geometrical proportion close to 70/29.Its exact value is 1 + √2, the positive solution of the equation x 2 = 2x + 1.. The name silver ratio results from analogy with the golden ratio, the positive solution of the equation x 2 = x + 1.
where α is the smaller acute angle of the Pythagorean triangle and the metallic mean index is = = = +. For example, the primitive Pythagorean triple 20-21-29 incorporates the 5th metallic mean. Cotangent of the quarter of smaller acute angle of the 20-21-29 Pythagorean triangle yields the precise value of the 5th metallic mean.