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By 1910, inventor Mark Barr began using the Greek letter phi ( ) as a symbol for the golden ratio. [32] [e] It has also been represented by tau ( ), the first letter of the ancient Greek τομή ('cut' or 'section'). [35] Dan Shechtman demonstrates quasicrystals at the NIST in 1985 using a Zometoy model.
Archaic form of Phi. Phi (/ f aɪ /; [1] uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî; Modern Greek: φι fi) is the twenty-first letter of the Greek alphabet.. In Archaic and Classical Greek (c. 9th to 4th century BC), it represented an aspirated voiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as ph .
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 ratio of the hypotenuse to a leg is represented by c:b. Assume a , b , and c are in the smallest possible terms ( i.e. they have no common factors). By the Pythagorean theorem : c 2 = a 2 + b 2 = b 2 + b 2 = 2 b 2 .
Each intersection of edges sections the edges in the golden ratio: the ratio of the length of the edge to the longer segment is φ, as is the length of the longer segment to the shorter. Also, the ratio of the length of the shorter segment to the segment bounded by the two intersecting edges (a side of the pentagon in the pentagram's center) is ...
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The Greek letter phi, symbol for the golden ratio. Barr was a friend of William Schooling, and worked with him in exploiting the properties of the golden ratio to develop arithmetic algorithms suitable for mechanical calculators. [15] According to Theodore Andrea Cook, Barr gave the golden ratio the name of phi (ϕ).
Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number + ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ , golden mean base , phi-base , or, colloquially, phinary .