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Number Theory

Making any integer with four 2s

A mathematical puzzle challenges people to create target numbers using exactly four instances of the digit 2 and various mathematical operations. The complexity ranges from elementary calculations to advanced mathematical concepts, until Paul Dirac discovered a general solution using nested square roots. The puzzle serves as an engaging educational tool across different mathematical skill levels.

calculator-app

Google hired Hans-J. Boehm to develop a calculator app that would provide mathematically correct answers, leading to an innovative solution combining rational arithmetic with recursive real arithmetic (RRA). The journey involved exploring various number representation methods, from bignums to constructive real numbers, ultimately resulting in a hybrid approach using rational numbers multiplied by RRA numbers with symbolic representations.