Why there is no mathematic law​ in pi representation?

[shahar]

Why there is no mathematic law​ in pi representation?

 

[mmm4444bot]

There are many different proofs of the existence of pi. (I'm not sure I understand what you're asking about.)

Is "phi" a typo?

There is a Law of Syllogisms, in geometry. :cool:

 

[HallsofIvy]

By "pi" you mean the ratio of the circumference of a circle to its diameter? But what do you mean by the "representation" of a number? "\(\displaystyle \pi\)" is a perfectly good "representation" of pi!

 

[shahar]

repsond

(1) phi is typo.

Pi is the number 3.14159... etc. etc.
(a) Why this number don't have a law that say what it the number that came after 9?
(b) The absurd is that is a can be calculate by an alogritm that say what next. Why the algorithm isn't a way to find the number pi easily?

 

[Dr.Peterson]

(1) phi is typo.

Pi is the number 3.14159... etc. etc.
(a) Why this number don't have a law that say what it the number that came after 9?
(b) The absurd is that is a can be calculate by an alogritm that say what next. Why the algorithm isn't a way to find the number pi easily?

I suppose you are referring primarily to the fact that the digits of the decimal expansion of pi don't repeat, and are said to follow no discernible pattern.

But the latter statement depends on what you mean by "pattern" (or, in your words, "law"). Clearly, as you point out, any given digit can be determined by any of the various algorithms by which it can be calculated; in fact, there is a known algorithm that can produce digits of pi in base 16 one at a time. Does that count as a "law" or "pattern"? But that is a very complicated "pattern", and is not what people mean when they say there is no pattern.

The claim that there is no such "law" at all requires defining exactly what that means, and I doubt it can be done. You are asking for a reason for a "fact" that has no real meaning.

 

[mmm4444bot]

… Why this number don't have a law that say what it the number that came after 9?

None of the Irrational numbers have formulas. We didn't need formulas; we discovered Irrational numbers (like Pi and the square root of two) using numerical methods, and it's a good thing we did. We need the Irrationals to fill the many holes on the Real number line between the nice Rational numbers. Now we have a smooth, continuous line, to model things (like time).

… Why the algorithm isn't a way to find the number pi easily?

How many digits of Pi do you need? The algorithms in math software can produce many digits of Pi quickly; humans can get them easily from the machines.

In applications, we don't need to write the exact value of Pi using numbers; we can get as many digits as we need. When mathematicians need to work with the exact value of Pi, they use a symbol or describe it in other ways (eg: area of unit circle, ratio of circumferece to diameter). :cool: