Pi Digits Generator

Yes. Pi comes from Gibbons's unbounded spigot algorithm running in BigInt integer arithmetic, and e and phi are computed with exact integer scaling (phi via an integer square root of 5 by Newton's method). No floating point is used, so there is no rounding error accumulating along the way. Cross-check the first few dozen digits against any published reference if you want to confirm.

Fifteen for interplanetary navigation, which is what NASA's JPL uses. Thirty-nine to compute the circumference of the observable universe to within an atom's width. Double-precision floating point carries about 15 to 17 significant decimal digits, so anything beyond that is unusable in ordinary code anyway.

Because arbitrary-precision arithmetic gets slower faster than linearly as digits grow, and this runs on your main thread. Beyond a few thousand digits the tab would visibly stall. Records in the millions or trillions of digits are set with specialised algorithms on dedicated hardware over days.

That is one of the better uses for it. Generate 100 or so digits, read them in groups of five, and rehearse in chunks. The digits of pi are believed to be normal, meaning every digit appears with equal frequency and there is no pattern to lean on, so chunking and repetition are the only techniques that work.

Phi is the golden ratio, (1 + sqrt(5)) / 2, approximately 1.6180339887. It is the number a rectangle's sides are in when removing a square from it leaves a rectangle of the same proportions. It is also the most irrational number, in the precise sense that it is hardest to approximate with fractions, which is why it turns up in phyllotaxis and in quasi-random sequences.

No. There is nothing to send: the whole computation happens in your browser with BigInt arithmetic. The page does not call out anywhere to produce them.