# PHI - the golden ratio

Phi, the Fibonacci sequence, the golden ratio, the golden section, the golden mean, the divine proportion. It’s known as many things, but the ratio they all refer to is the same, 1 : 1.61803399...

Found in art, architecture, design, and most intriguingly, in nature, this ratio has been used throughout history and today for its aesthetic beauty.

"The golden ratio was first studied by ancient mathematicians because of its frequent appearance in geometry. There is evidence that it was understood and used as far back in history as ancient Egypt. In the Great Pyramid of Giza built around 2600 BC, the golden ratio is represented by the ratio of the length of the face (the slope height), inclined at an angle θ to the ground, to half the length of the side of the square base, equivalent to the secant of the angle θ. The above two lengths were about 186.4 and 115.2 metres respectively. The ratio of these lengths is the golden ratio 1.618. The largest isosceles triangle of the sriyantra design used in ancient India, described in the Atharva-Veda (circa 1200-900 BC) is one of the face triangles of the Great Pyramid in miniature, showing almost exactly the same relationship between π and the golden ratio as in its larger counterpart. It is believed that after tracing the path of Venus in the sky, the ancients found that the ratio of the length of the long arm of the pentagon shape to the length of the shorter arm was 1.618. The ancient Greeks usually attributed its discovery to Pythagoras (or to the Pythagoreans, notably Theodorus) or to Hippasus of Metapontum. Hellenistic mathematician Euclid spoke of the "golden mean" this way, "a straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser". The golden ratio is represented by the Greek letter \varphi (phi, after Phidias, a sculptor who commonly employed it) or less commonly by τ (tau, the first letter of the ancient Greek root τ(ε/ο)μ- meaning cut)."