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The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
For example, claims have been made about golden ratio proportions in Egyptian, Sumerian and Greek vases, Chinese pottery, Olmec sculptures, and Cretan and Mycenaean products from the late Bronze Age. These predate by some 1,000 years the Greek mathematicians first known to have studied the golden ratio.
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 golden ratio (phi) represented as a line divided into two segments a and b, such that the entire line is to the longer a segment as the a segment is to the shorter b segment. Date: 23 March 2007: Source: Image:Golden ratio line.png: Author: Traced by Stannered: Other versions: Derivative works of this file: Golden ratio line percentages.svg
Example of Golden Triangle method on a painting. Compositional elements fall within the triangles. The golden triangle rule is a rule of thumb in visual composition for photographs or paintings, especially those which have elements that follow diagonal lines. The frame is divided into four triangles of two different sizes, done by drawing one ...
The golden ratio budget echoes the more widely known 50-30-20 budget that recommends spending 50% of your income on needs, 30% on wants and 20% on savings and debt. The “needs” category covers ...
The angle of B is exactly 222.49°, so the ratio of the areas B/A is about the same as the golden ratio.}} |Source=Own work by uploader to same specifications as bitmap version |Author File usage No pages on the English Wikipedia use this file (pages on other projects are not listed).
Pages in category "Golden ratio" The following 26 pages are in this category, out of 26 total. This list may not reflect recent changes. ...