DevTools

Math Curiosities

Choose one of five mathematical curiosities, enter any positive integer, and watch the complex trajectory that emerges from an absurdly simple rule. All computation runs locally.

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Features

FAQ

Has the Collatz conjecture been proven?

No. Every positive integer tested up to approximately 3×10²⁰ eventually enters the 4→2→1 loop, but no rigorous mathematical proof exists. It remains one of the most famous unsolved problems in mathematics.

What is a happy number?

Repeatedly sum the squares of each digit. Numbers that eventually reach 1 are "happy"; others fall into a fixed 8-number cycle. About 14% of positive integers are happy.

Does Kaprekar's constant work for all four-digit numbers?

Almost. Any four-digit number whose digits are not all the same will reach 6174 within 7 iterations of "descending sort minus ascending sort." Identical digits (e.g. 1111) yield 0 immediately.

What is the digital root used for?

It provides a quick sanity check for arithmetic (casting out nines), and is used in checksum calculations and digital signatures. Any number's digital root equals its remainder modulo 9, except multiples of 9 yield 9.

Is any data uploaded?

No. All sequence computation and chart rendering happen entirely in your browser and are never sent to any server.

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