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“A calculator app? Anyone could make that.”

Not true.

A calculator should show you the result of the mathematical expression you entered. That’s much, much harder than it sounds.

What I’m about to tell you is the greatest calculator app development story ever told.

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So Boehm had no choice but to go even deeper. It was time to get serious.

We started off with integers (bignum), went to rational numbers, then algebraic numbers. What’s next?

Constructive real numbers.

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Multiplying a number by 2 doubles the error. I asked for 2π to within 0.01 decimals, so you need an approximation of π that’s within 0.005 decimals.

Let’s say you come up with 3.141, which is indeed less than 0.005 away from π. Multiply that by 2 and you’re done!