The Golden Ratio Mathematics

The short answer is 1 61803398875 and many people call it the divine proportion. Expressed algebraically for quantities a and b with a b 0. The figure on the right illustrates the geometric relationship.

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It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.

The golden ratio mathematics. φ 1 2 5 2. Golden ratio also known as the golden section golden mean or divine proportion in mathematics the irrational number 1 square root of 5 2 often denoted by the greek letter ϕ or τ which is approximately equal to 1 618. To warm up we will try to construct an equiangular spiral. The long answer will require some figures and some math.

The square root of 5 is approximately 2 236068 so the golden ratio is approximately 0 5 2 236068 2 1 618034. That rectangle above shows us a simple formula for the golden ratio. In mathematics two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. This is an easy way to calculate it when you need it.

When the short side is 1 the long side is 1 2 5 2 so. The golden ratio is an irrational number represented by the greek letter phi φ that s used to create geometries with what many people consider the most eye pleasing proportions. The golden ratio was discovered by the pythagoreans around 500 b c.