3 ms·
Sorry to nag but the 'goodness' of 22/7 is due to the size of the denominator, not to the number of digits you have to memorize (actually 2, not 3, but anyway).
by pfortuny 14y ago
Sorry to nag but the 'goodness' of 22/7 is due to the size of the denominator, not to the number of digits you have to memorize (actually 2, not 3, but anyway). You get less than a .001 relative error with a denominator less than 10, that is why it is a good approximation: nothing to do with memory.
The thing is: as pi is transcendental, there are very very good rational approximations in that sense (this is an old theorem due to Liouville): http://mathworld.wolfram.com/LiouvillesApproximationTheorem.html http://mathworld.wolfram.com/LiouvillesApproximationTheorem...., there is no 'memorizing' going on there.
- lutusp 14y ago> The thing is: as pi is transcendental, there are very very good rational approximations in that sense (this is an old theorem due to Liouville) ... Expressed another way, for every estimate of Pi's value, however large, there are two integers that, expressed as a ratio, will produce the same result.