New Number System Allows Pi to be Exact

  • Thread starter Zuryn
  • Start date
  • Tags
    Pi
In summary, the conversation discusses the possibility of creating a new number system to make pi and e rational, but it is unlikely due to their algebraic independence. It is suggested that using pi itself as a base for numeration may be a solution, but it would result in all rational numbers being represented as irrational in the new system.
  • #1
Zuryn
9
0
Pi can be exact if we have a new number system. :mad:
 
Mathematics news on Phys.org
  • #2
Wanna expand on that?
 
  • #3
We already have an exact representation of pi: "pi".
 
  • #4
So what is your exact idea about this ?
What do you think if we do create a new number system to make Pi and e rational, but 1/2 is irrantional number?
....
 
  • #5
Obviously, we could choose pi itself as a base for our numeration system so that pi would be "1.0". Since pi and e are algebraically independent, I don't believe it is possible to choose a base so that pi and e are both represented by finite or repeating decimals. It is fairly easy to show that a number is "rational" in an INTEGER based numeration system if and only if it is "rational" in any INTEGER based numeration system but I'm pretty sure that all the rational numbers in an INTEGER based numeration system (e.g. base 10) would be "irrational" in a pi based numeration system.
 

Related to New Number System Allows Pi to be Exact

1. What is the new number system that allows Pi to be exact?

The new number system is called the transcendental number system, and it is based on the concept of transcendental numbers. These numbers, such as Pi, are infinite and non-repeating, making them difficult to represent accurately in traditional number systems.

2. How does the transcendental number system accurately represent Pi?

The transcendental number system uses a new symbol, called tau, to represent Pi. This symbol is defined as the ratio of a circle's circumference to its radius, rather than its diameter. This allows for an exact representation of Pi without any rounding or approximation.

3. What are the potential applications of this new number system?

This new number system has the potential to revolutionize fields such as mathematics, engineering, and physics. It could also have practical applications in industries that rely on precise measurements, such as construction and manufacturing.

4. How does the transcendental number system differ from other number systems?

Traditional number systems, such as decimal and binary, are based on the idea of finite numbers, meaning they have a set number of digits. The transcendental number system, on the other hand, is based on infinite numbers, allowing for an exact representation of numbers like Pi.

5. Are there any limitations to the transcendental number system?

While the transcendental number system allows for an exact representation of numbers like Pi, it may not be practical for everyday use. The use of tau as a new symbol may require significant changes in mathematical notation and could take time for people to adapt to. Additionally, it may not be compatible with certain computer systems or programming languages.

Similar threads

Replies
1
Views
1K
Replies
2
Views
354
Replies
7
Views
1K
Replies
56
Views
5K
  • General Math
2
Replies
40
Views
3K
Replies
4
Views
504
  • General Math
Replies
20
Views
2K
Replies
1
Views
824
Replies
13
Views
2K
Back
Top