- #1
shrumeo
- 250
- 0
Hello,
I doubt it, but is there any number system (base) where π or e run out of digits?
I doubt it, but is there any number system (base) where π or e run out of digits?
Can we really?daster said:We can create a number system where [itex]\pi=1[/itex], but that's not really worth it.
matt grime said:in base pi he means, then pi has the representation 1 in this radix.
Janitor said:By the way, last week I ran into the name 'Doran Shadmi' at another website.
matt grime said:... He posts now under lama at scienceforums.net, doron being now banned, and has reached the stage of having his threads instantly locked...
Hurkyl said:All right, break it up.
A non-whole-number base wouldn't make much sense...what would the digits be? If you just use the digits 0,1,2,3 then there can be totally different representations of the same number--pi^2 (about 9.869604401) could be represented as 100, but it could also be represented as 30.1102... Only whole number bases have the nice property that the largest possible number of N digits before the decimal is equal to the smallest possible number of N+1 digits before the decimal, like how 99.9999... (largest number in base 10 with two digits before the decimal) is equal to 100.000... (smallest number in base 10 with three digits before the decimal).matt grime said:in base pi he means, then pi has the representation 1 in this radix.
It's not that difficult to think of really. I mean choosing Natural Numbers to navigate the real number line although makes sense to us doesn't have any significance on the real number line.JesseM said:A non-whole-number base wouldn't make much sense...what would the digits be? If you just use the digits 0,1,2,3 then there can be totally different representations of the same number--pi^2 (about 9.869604401) could be represented as 100, but it could also be represented as 30.1102... Only whole number bases have the nice property that the largest possible number of N digits before the decimal is equal to the smallest possible number of N+1 digits before the decimal, like how 99.9999... (largest number in base 10 with two digits before the decimal) is equal to 100.000... (smallest number in base 10 with three digits before the decimal).
It usually helps if you post your problem, I think you may have posted on the wrong thread.babygrl said:would you all mind helping me out?
I think that pretty much says it all right there. Any attempt to treat the ratio of a geometric circle as though its just some kind of arbitrary abstract number that we can call whatever we please is going to be pretty futile.krab said:pi cannot be 1 as long as 1 represents the multiplicative identity element, and pi the ratio of circumference to diameter. Base cannot change that.
No, pi and e are both irrational numbers which means they cannot be expressed as a fraction in the form of a/b where a and b are integers. They have a never-ending and non-repeating decimal representation.
Pi and e are considered irrational because they cannot be expressed as a fraction and have an infinite number of non-repeating decimal digits. This means that they cannot be represented as a precise value, unlike rational numbers which have a finite decimal representation.
Yes, there are mathematical proofs that show the irrationality of pi and e. The most famous proof for the irrationality of pi was discovered by the ancient Greek mathematician, Euclid. For e, the proof was given by Swiss mathematician Johann Heinrich Lambert in the 18th century.
Yes, irrational numbers like pi and e are used in various mathematical calculations and formulas. They have important applications in fields such as geometry, physics, and engineering. In fact, pi and e are considered two of the most important and useful mathematical constants.
Yes, there are infinitely many irrational numbers besides pi and e. Some well-known examples include the square root of 2, the golden ratio, and the Euler-Mascheroni constant. It is believed that the majority of real numbers are irrational, meaning there are countless other irrational numbers that have yet to be discovered or calculated.