🥧 PiForge
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What is π?
π (pi) is the ratio of a circle's circumference to its diameter. No matter the size of the circle — a coin, a bicycle wheel, or the Earth — divide the distance around it by the distance across it and you always get the same number: 3.14159 26535 89793… The digits go on forever with no repeating pattern. No fraction equals π exactly; it's called an irrational number. Mathematicians have computed over 105 trillion decimal digits and still haven't found the end — because there isn't one.
The circumference wraps around the diameter exactly π times — 3 full lengths plus a 0.14159… leftover:
Circle Explorer
Drag the slider to change the circle's diameter — the graphic and all values update live.
Estimate π with Random Darts
This experiment estimates π using only randomness — no equations required. Here's how:
Shape Calculators
π appears in every formula involving a circular cross-section — spheres, cylinders, and arcs all depend on it.
Digit Frequency
How evenly does each digit 0–9 appear? A truly random-looking sequence would be perfectly flat.
Digit Color Map
Each digit 0–9 gets a color. If π is truly random-looking, the grid should look like static.
Find a Number in π
Search the first 1,500 decimal digits of π for any string you enter. Short sequences (3–5 digits) are almost always found. Longer strings like a full birthday may not appear — that's expected, not a bug. Try your zip code, a short number, or just 314.
π in the Real World
π shows up anywhere there's a curve, a cycle, or a repeating pattern.
π Never Ends, Never Repeats
22/7 ≈ 3.1428 is a handy estimate, but it's not π. No fraction equals π exactly — numbers like this are called irrational. π goes even further: it's also transcendental, meaning it can't be the answer to any polynomial equation with whole-number coefficients. Most famous irrationals (like √2 or the golden ratio) are at least algebraic. π is in a stranger category.
This proves it's impossible to square a circle using only a compass and straightedge — ruled out by mathematics, not just difficulty.
eiπ + 1 = 0
Connects five fundamental numbers: e (≈ 2.718, natural growth), i (√−1), π, 1, and 0. Raising e to an imaginary power traces a circle. At angle π radians (180°), you land exactly at −1.