50 Constants Explained

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Pi represents the ratio of a circle’s circumference to its diameter. It is

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approximately equal to 3.14. Tau represents the ratio of a circle’s circumference to its radius,

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which is equal to 2π. Euler’s number is another important constant,

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appearing in many contexts. It is approximately equal to 2.718 and can be defined using this

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limit or this infinite sum. The imaginary unit, represented as i, has the property

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that its square is equal to –1. In other words, i is equal to the square root of –1.

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The Fibonacci sequence starts with 0 and 1, and each subsequent term is the sum

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of the two previous terms. If we take the reciprocal of all these terms and sum them,

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this series converges to a value called the Reciprocal Fibonacci constant,

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which is approximately 3.35. When we look at the ratios of consecutive Fibonacci numbers,

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this ratio converges to a value called the golden ratio, which is around 1.618. It is

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exactly equal to 1 plus the square root of 5 over 2. The reciprocal of the golden ratio plus 1 is

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equal to the golden ratio, which is also equal to the square of the golden ratio –1. Imagine a line

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segment of length a+b. The ratio of a to b is the same as the ratio of the whole segment to

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a. Squaring this part gives us the Supergolden ratio, approximately 1.46. On the other hand,

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if the ratio of a to b is equal to the ratio of 2a+b to a, we get the silver ratio, around 2.41,

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exactly equal to 1 plus the square root of 2. For three numbers connected by this ratio, we have the

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plastic ratio, approximately 1.32. We also have the golden angle, related to the golden ratio but

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for angles in a circle. It is approximately 137.5 degrees, or 2.4 radians. There is also the Magic

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Angle, the angle between the diagonal of a cube and any of its three connecting edges. This angle

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is around 54.7 degrees, its tangent is exactly equal