Notated by the Greek letter “**pi(?)**”, represents the **ratio between a circle’s circumference (perimeter) to its diameter (distance from side to side passing through the center), and is a fundamental element of many mathematical fields, most significantly Geometry.** Though modern mathematicians have calculated more than one TRILLION decimal places beyond the standard “3.14,” pi(?) is an irrational number that continues on to infinity! It’s an important ingredient in the formula for the **area of a circle, A=?r².**

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The number π (/paɪ/) is a mathematical constant. Originally defined as the ratio of a circle’s circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter “π” since the mid-18th century, though it is also sometimes spelled out as “pi(?)”.

By the above definitions, pi(?) should be equally significant to

** 1. √2, the ratio of Diagonal to Side of a Square,
2. √3/2, the ratio of Height to Base of an Equilateral Triangle,
3. (e/2), the ratio of Continuous Compounding to Simple Interest,
4. or a host of other ratios.**

pi(π) the ratio of the circumference of a circle to its diameter, or in symbol form, π, looks to be simple. But, in fact, it is an “irrational number,” implying that its exact value is inherently unknowable. Computer scientists have calculated billions of digits of pi(π), starting with 3.14159265358979323…, but because no recognizable pattern emerges in the succession of its digits, we could continue calculating the next digit, and the next, and the next, for millennia, and we’d still have no idea which digit might emerge next. The digits of pi(π) continue their senseless procession all the way to infinity.

pi(π) is ubiquitous, i.e. it crops up even in places which have no connection to circles. For example, among a collection of random whole numbers, the probability that any two numbers have no common factor — that they are “relatively prime” — is equal to **6/\(π^2\)**.

pi(π)’s ubiquity goes beyond math. The number crops up in the **natural world**, too. It appears everywhere there’s a circle, of course, such as the **disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds**. pi(π) also appears in the physics that describes **waves, such as ripples of light and sound**. It even enters into the equation that defines how precisely we can know the state of the universe, known as Heisenberg’s uncertainty principle.

pi(π) can also be found in the shapes of rivers. “**Meandering ratio**,” or the ratio of the river’s actual length to the distance from its source to its mouth as the crow flies, determines, a river’s windiness. Rivers that flow straight from source to mouth have small meandering ratios, while ones that lurk along the way have high ones. **Strangely, the average meandering ratio of rivers approaches is — pi(π).**

**Albert Einstein**, used **fluid dynamics and chaos theory** to prove the above-mentioned fact. Einstein showed that rivers tend to bend into loops. Accordingly, the slightest curve in a river will generate faster currents on the outer side of the curve, causing erosion and a sharper bend. This process will gradually tighten the loop, until chaos causes the river to suddenly double back on itself, at which point it will begin forming a loop in the other direction.

**The logic:** The length of a near-circular loop is like the circumference of a circle, and the straight-line distance from one bend to the next is diameter-like, thus making the ratio of the lengths would be pi(π)-like.