φ Chart of Terms ★ Fibonacci

This is an excerpt from Master Fibonacci: The Man Who Changed Math. All citations are catalogued on the Citations page.

Term	Defined or Named By	Symbol/Value	Definition
Golden Mean	Euclid		Point C is between points A and B so that the ratio of the short part of the segment (BC) to the long part (AC) equals the ratio of the long part (AC) to the entire segment (AB)
Golden Ratio Phi Golden Proportion Divine Proportion Golden Section	Euclid Barr (re Phidias) Pacioli Da Vinci	Phi (Φ) 1.618. . . phi (φ) 0.618. . . Greek letter Tt	A straight line is in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. 1. Ratio of smaller part of a line (CB) to larger part (AC): CB/AC = ratio of larger part (AC) to the whole line (AB). Therefore, CB/AC = AC/AB. 2. Ratio between two successive Fibonacci numbers (after F8)
Golden Angle		137.5°	1. Angle subtended by smaller arc when two arcs of a circle are in Golden Ratio 2. Angle that divides a full angle in a Golden Ratio (but measured in opposite direction so that it measures less than 180 degrees)
Golden Rectangle			1. Ratio of length to width is the Golden Ratio, 1:phi 2. Sides the lengths of Fibonacci numbers
Golden Triangle Sublime Triangle			1. Ratio of a side to base of an isosceles triangle is phi 2. Base angle 72° bisected creating two self-similar internal triangles 36°
Golden Spiral			Logarithmic spiral whose growth factor is φ (about 6.9) for every quarter turn it makes