Ordinary calculators round. Constructive Calculator doesn’t.
It computes with constructive real numbers, an arbitrary-precision engine that keeps every result exact and gives you as many correct digits as you ask for. The rounding errors that quietly accumulate in ordinary calculators simply never happen.
Left: exp(π√163) looks like a whole number, but scroll past the
decimal point and twelve 9s appear before it diverges. Right: 1/243,
whose digits weave two simple sequences together before the block repeats.
The number a wartime censor mistook for a code.
In Surely You’re Joking, Mr. Feynman!, Feynman recalls
spotting this on an adding machine at Los Alamos: 1/243 = 0.00
4 11 5 22 6 33
7 44 8 55 9… Two sequences
interleave: 4, 5, 6, 7, 8, 9… woven through 11, 22, 33, 44, 55… In his words
it “goes a little cockeyed after 559 when you’re carrying, but it soon
straightens itself out and repeats itself nicely” (the block is 27 digits long).
He slipped it into a letter; the censors flagged the digits as a suspected code, and he
wrote back that it couldn’t be one, because “there’s no more information
in the number .004115226337… than there is in the number 243.” An exact
calculator shows you that number in full; a rounding one collapses it to 0.00412 and the
pattern disappears.
What it does
- Exact, not approximate. cos(π/3) is exactly 0.5, √2 × √2 is exactly 2, ln(e) is exactly 1.
- Scroll for more digits. Every result is computed on demand; swipe √2 or π for tens, hundreds, or thousands of correct digits.
- A scientific keypad. Trigonometry in degrees or radians and their inverses, exponentials and logarithms, powers and roots, factorials, percentages, π and e.
- Exact big integers. 52! (the number of ways to shuffle a deck) prints in full, all 68 digits.
- Built for clarity. A running tape of recent calculations, locale-aware digit grouping, and copy at any precision.
Constructive Calculator is an independent port of Hans Boehm’s constructive-reals calculator, the arbitrary-precision engine behind Android’s Calculator, rebuilt natively for iPhone.