The Golden Number

The Golden Number

Author: Stephen Caesar
Subject: Mathematics
Date: 9/2/2003

A major proof that the Universe is a huge computer program created by an intelligent agent is the so-called “golden number.” Known as phi, it was first calculated by Euclid, the father of geometry, around 300 BC. It is found by dividing a line segment into two unequal parts so that the longer part is in the same proportion to the shorter part as the entire line segment is to the longer part. Euclid calculated the ratio of the lengths of the 2 parts as 1.6180339887…. This ratio appears all over the natural world (Livio 2003: 65). Astrophysicist Dr. Mario Livio, head of the science division at the Space Telescope Science Institute in Baltimore and a leading expert on the “golden number,” writes: “The number phi would have remained in the relative obscurity of pure mathematics were it not for its propensity to pop up where least expected” (Ibid. 66).

One example is the head of a sunflower, the florets of which form clockwise and counterclockwise spiral patterns, intertwined with and criss crossing each other. As the florets twist in upon each other, heading toward the center of the flower, there is a specific ratio of the number of florets twisting one way to the number of florets twisting the other. “Amazingly,” Livio remarks, “if you calculate these as ratios (55/34, 89/55, 144/89, 233/144), you find that they get closer and closer to the value of the golden ratio phi!” (Ibid. 66).

In 1837, Auguste Bravais, a crystallographer, and his brother Louis, a botanist, discovered that as new leaves sprout forth from the stalk of a growing plant, they advance at a certain angle determined by phi. “By arranging themselves according to an angle determined by phi,” notes Livio, “the leaves can fill the spaces in the most efficient way possible, with the least amount of overlap” (Ibid. 66).

Directly related to the golden number is the golden rectangle, in which the ratio of the rectangle’s length to its width is equal to phi. This was first formulated by the 17th-century mathematician Jacob Bernoulli, who noticed that if you keep making smaller and smaller golden rectangles, each one inside the last one, and then connect certain points as you go inward, you get an inward curving line called a logarithmic spiral. If you then draw a straight line from the point around which the logarithmic spiral forms to any point on the curve itself, that line will always cross the curve at exactly the same angle (Ibid. 66-7). Again, this appears in nature. Duke University biologist Vance Tucker studied falcons for several years and found that when they bank they follow a slightly curved trajectory toward their prey, rather than diving straight down. This curved dive matches Bernoulli’s logarithmic spiral (Ibid. 67). Livio notes:

Nature just loves logarithmic spirals. You can find them in phenomena ranging from the shell of the chambered nautilus to hurricanes and spiral galaxies. Sometimes, as in the case of the nautilus, they are a natural outcome of a pattern of additive growth. And it is through that pattern that the golden ratio is intimately related to the Fibonacci sequence, a celebrated series of numbers discovered by the early thirteenth-century Italian mathematician Leonardo of Pisa, known as Fibonacci (Ibid. 67).

The Fibonacci sequence goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc., in which each number is equal to the sum of the two preceding numbers: 1+1=2; 1+2=3; 2+3=5; 3+5=8; 5+8=13; 8+13=21; 13+21=34; 21+34=55; 34+55=89; 55+89=144; 89+144=233. This exactly matches the ratio of the sunflower florets. The higher you go with Fibonacci numbers, the closer you approach the exact value of phi (Ibid. 67-8). Livio remarks:

Thus Fibonacci numbers are a kind of golden ratio in disguise, and they, too, pop up in the most unexpected places. One is in the microtubules of an animal cell, which are hollow cylindrical tubes of a protein polymer. Together they make up the cytoskeleton, a structure that gives shape to the cell and also appears to act as a kind of cell ‘nervous system.’ Each mammalian microtubule is typically made up of thirteen columns, arranged in five right-handed and eight left-handed structures (5, 8, and 13 are all Fibonacci numbers). Furthermore, occasionally one finds double microtubules with an outer envelope made up—you guessed it—of 21 columns, the next Fibonacci number (Ibid. 68).

The spiral arms of many galaxies are close to logarithmic spirals. Also, a spinning black hole can change from heat-up to cool-down phase only when the square of its mass is exactly equal to phi times the square of its angular momentum (Ibid. 68). Livio comments on this:

This seemingly magical appearance of phi stems from another unique mathematical property of the golden ratio: its square can be obtained simply by adding 1 to phi (you can check that statement with a pocket calculator) (Ibid. 68 [emphasis added]).

The occurrence of the golden ratio throughout Nature is powerful evidence for an intelligent designer who created this huge computer program known as the Cosmos.


Livio, M. 2003. The Golden Number. Natural History 112, no. 2.

Stephen Caesar holds his master’s degree in anthropology/archaeology from Harvard. He is a staff member at Associates for Biblical Research and the author of the e-book The Bible Encounters Modern Science, available at

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