The Golden Number

by Stephen Caesar

A major proof that the universe is a huge computer program created by an intelligent agent is the “golden number,” or phi. It was first calculated by Euclid, the father of geometry, around 300 BC, 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 segment is to the longer part. The ratio of the lengths of the 2 parts is 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 and a leading expert on the “golden number,” writes that “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).

For example, the florets of a sunflower form clockwise and counterclockwise spiral patterns, intertwining and crisscrossing each other. As the florets twist in upon each other, heading toward the center of the flower, there is a ratio of the number of florets twisting one way to the number 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.).

As new leaves sprout forth from the stalks of some growing plants, they advance at an angle determined by phi. By doing this, notes Livio, “the leaves can fill the spaces in the most efficient way possible, with the least amount of overlap” (ibid.).

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 17th-century mathematician Jakob 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 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. 66-67). Duke University biologist Vance Tucker found that when falcons bank, they follow a slightly curved trajectory toward their prey. This curve 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.

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, etc. 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. 67-68).

Fibonacci numbers appear in the microtubules of mammal cells (hollow tubes that give cells their shape). Each microtubule has 13 columns, arranged in 5 right-handed and 8 left-handed structures. Sometimes, double microtubules have outer envelopes with 21 columns [5, 8, 13, and 21 are Fibonacci numbers] (ibid.).

The arms of spiral galaxies are close to logarithmic spirals. 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.).

Livio comments: “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…” (ibid.).

The existence of the golden ratio 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.

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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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