How Many Decimals of Pi Do We Really Need?

Post by pedrosorio » Sat, Mar 19, 2016, 3:25 AM UTC

xiaq wrote: post #37

julie1 wrote: post #22

Earlier quoted context omitted.

A branch of physics used to be taught a long time ago called "numerical analysis" to deal with this issue. We even used to be careful about the difference between 'precise and exact'. Pi = acos(0) is absolutely exact. But computer don't know about symbolic calculus. So to put the value in a register we used tricks. Pi as a the converging value at the infinite of the Taylor development is awesome. But computer don't k…

I can't speak for other nations, but they still teach numeric analysis in Chinese universities as an undergraduate course. In my university it is a required subject. Many of us have countless dreadful memories of Runge-Kutta method, Euler's method, Newton's method, rate of convergence, numerical stability and error margins, just to name a few of the dreads...

Post by mchahn » Sat, Mar 19, 2016, 3:29 AM UTC

skykooler wrote: post #40

todd8 wrote: post #27

Earlier quoted context omitted.

Hand-held calculators might have been carried on many NASA missions, but not the early ones. The first missions started in 1961 and hand-held HP calculators weren't invented until more than ten years later. By that time we had already been to the moon 6 or 7 times. The first actual hand-held calculator I every saw was a Bowman Brain (simple 4 function calculator) it was for sale in 1971 at the MIT COOP (the bookstore…

Did the astronauts use slide rules? I know the E6B is pretty common for pilots still.

Post by hanniabu » Sat, Mar 19, 2016, 3:33 AM UTC

diskcat wrote: post #42

drewolbrich wrote: post #26

If you know the diameter of the observable Universe and you want to calculate its circumference with the accuracy of the diameter of a proton, the number of digits of pi that you need is 43.

I think this assumes the order of magnitude of the size of the observable universe. Clearly if the diameter of the universe is smaller than a proton then you don't need 43 digits of pi to calculate its circumference to smaller than the diameter of a proton. So if the diameter of the universe is 10^1000000^100000000 proton wide the precision you need for pi would be way higher than 43?

Post by julie1 » Sat, Mar 19, 2016, 3:37 AM UTC

xiaq wrote: post #37

julie1 wrote: post #22

Earlier quoted context omitted.

A branch of physics used to be taught a long time ago called "numerical analysis" to deal with this issue. We even used to be careful about the difference between 'precise and exact'. Pi = acos(0) is absolutely exact. But computer don't know about symbolic calculus. So to put the value in a register we used tricks. Pi as a the converging value at the infinite of the Taylor development is awesome. But computer don't k…

I can't speak for other nations, but they still teach numeric analysis in Chinese universities as an undergraduate course. In my university it is a required subject. Many of us have countless dreadful memories of Runge-Kutta method, Euler's method, Newton's method, rate of convergence, numerical stability and error margins, just to name a few of the dreads...

Post by gmuslera » Sat, Mar 19, 2016, 3:39 AM UTC