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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 gnomon is itself isosceles if and only if the ratio of the sides to the base of the original isosceles triangle, and the ratio of the base to the sides of the gnomon, is the golden ratio, in which case the acute isosceles triangle is the golden triangle and its gnomon is the golden gnomon. [4]
Bisecting one of the base angles of the golden triangle subdivides it into a smaller golden triangle and a golden gnomon. Analogously, any acute isosceles triangle can be subdivided into a similar triangle and an obtuse isosceles triangle, but the golden triangle is the only one for which this subdivision is made by the angle bisector, because ...
These include the Calabi triangle (a triangle with three congruent inscribed squares), [10] the golden triangle and golden gnomon (two isosceles triangles whose sides and base are in the golden ratio), [11] the 80-80-20 triangle appearing in the Langley's Adventitious Angles puzzle, [12] and the 30-30-120 triangle of the triakis triangular tiling.
The theorem of the gnomon can be used to construct a new parallelogram or rectangle of equal area to a given parallelogram or rectangle by the means of straightedge and compass constructions. This also allows the representation of a division of two numbers in geometrical terms, an important feature to reformulate geometrical problems in ...
A gnomon (/ ˈ n oʊ ˌ m ɒ n,-m ə n /; from Ancient Greek γνώμων (gnṓmōn) ' one that knows or examines ') [1] [2] is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields, typically to measure directions, position, or time.
The obtuse isosceles triangle highlighted via the colored lines in the illustration is a golden gnomon.
The following 13 pages use this file: Gnomon (figure) Golden ratio; Golden triangle (mathematics) Isosceles triangle; Talk:Golden ratio/sandbox; Talk:Golden triangle (mathematics)