Is Pi = 3.1415 or 3.33 ?

[erKa]

Pi is simply the ratio of the circumference to the diameter of a circle - there is nothing mystical or strange about it. It is irrational because this number cannot be expressed by "rations", or fractions, in our mathematical system. Rounding it to three is not an elegant solution - it would give you very wrong answers for a lot of things.

This concept must be restricted to our own "ape's mode" decimal notation. In esadecimal notation Pi is another strange number f.e. This is due to the fact that the man is an ape having 10 fingers on hands. But Mickey Mouse has only 8 fingers and Pi could be much different for him. The same rule for Napier's number (e = 2,78...)

[Tormod]

This concept must be restricted to our own "ape's mode" decimal notation. In esadecimal notation Pi is another strange number f.e. This is due to the fact that the man is an ape having 10 fingers on hands. But Mickey Mouse has only 8 fingers and Pi could be much different for him. The same rule for Napier's number (e = 2,78...)

 

No. You're confusing the actual value of Pi with our base 10 model for counting. Pi is simply the ratio of the area to the circumference of a circle - the number value would depend on which counting system you use.

[Southtown]

LOL — I average 3.14 posts per day. :)

 

http://hypography.com/forums/members/1876.html

 

(as of 12-11-05)

[wizzkid67]

Hi! Tormod ;)

 

My math is a little rusty but here goes nothing. I put this equation together, hoping, that it may help, in answering your question.

 

Example: The circumference of a circle is 10 centimeters. What is the radius?

 

Solution using Pi = 3.1415.

 

r = (C ÷ Pi) ÷ 2 r

C = 10 cm ÷ 3.1415

d = 3.18 cm ÷ 2 r

r = 1.59 cm

 

Checking my work.

 

(r x 2) Pi = C

3.18 x 3.1415 = C

9.9899 cm = C

9.98 cm = C

 

:cup: Close :cup:

 

 

Solution using Pi = 3.3333

 

r = (C ÷ Pi) ÷ 2 r

C = 10 cm ÷ 3.3333

d = 3.00 cm ÷ 2 r

r = 1.50 cm

 

Checking my work.

 

(r x 2) Pi = C

3 x 3.3333 = C

9.9999 cm = C

9.99 cm = C

 

;) Closer ;)

 

 

Is this right? Or does it really matter?

 

:cup:

 

i have to say if u use the same value for pi in the r=c/2pi

and the 2pi®=c your get an answer for the r that u are trying to get u could take pi to be 2.5

 

 

r=10/2.5*2 r=2

 

put that value back in to the other formula

 

2*2.5*2=10

 

its perfect yay

but 2.5 is not the value of pi 3.145......is

[Dinesh_college]

Who calculated(First) the value for Pi ?

[CraigD]

Who calculated(First) the value for Pi ?

Interesting question.

 

The first written description of Pi is widely believed to be from The Rhind Papayrus, from about 1650 BC. This text doesn’t actually name an actual symbol for Pi – math of that era doesn’t appear to have had a well-developed concept of “symbols” – but states that that a circle with diameter 9 has an area of 64, implying a value of Pi of 256/81, or about 3.16. The text doesn’t claim to have originated this value, implying that the calculation might be as old as around 3000 BC, but doesn’t give any clue who invented it.

 

I don’t believe that good approaches to estimating Pi really existed until about 300 BC. The Greeks around this time, and certainly Archimedes around 250 BC, appear to have understood that finding an exact value of Pi was likely to be impossible. Archimedes’s, (and apparently everybody’s for the next 2 thousand years) was geometric, approximating a circle with many isosceles triangles.

 

The first modern, non-geometric approaches (eg: Pi= 4 -4/3 +4/5 -4/7 +4/9 …), seem to have begun appearing around 1600, in Europe, though there’s some evidence that some may have appeared in India a century earlier. It was about this time that mathematicians began agreeing on a standard symbols for Pi, and by 1750, everybody has settled on using the Greek letter Pi, mostly, it seems, because Euler had.

 

So I’d say that between 3000 and 1650 BC, someone who’s name and history we’ll likely never know calculated the first values of Pi, but were wrong, while between 300 and 250 BC, Archimedes, or maybe someone not much earlier than him, came up with the first correct approximation.

[adam_rockstar]

Pi is simply the ratio of the circumference of a circle to its diameter

what can be so hard. how can Pi become 3.33.... anyway? isnt it good as it is.

[Guadalupe]

Hi! adam_rockstar :hyper:

 

 

Pi is simply the ratio of the circumference of a circle to its diameter

what can be so hard. how can Pi become 3.33.... anyway? isnt it good as it is.

 

 

Based on my research, Pi = 3.14159, is not constant and therefor not good enough.

 

MY quest is to find the number(s) that can give us the perfect circle.

 

 

:hyper:

[Guadalupe]

Hi! CraigD :hyper:

 

If, one were to find an equation that is constant, in finding the proof to a perfect circle, who would be interested and how would it affect math as we know it?

 

Would you know how one can go about protecting their equation (algorithm)? Would one have to create a software program? I am open to any suggestions you have to offer. Thank you.

 

 

:hyper:

[adam_rockstar]

fair enough guadalupe good luck .... keep me posted :hyper: :hyper:

[CraigD]

If, one were to find an equation that is constant, in finding the proof to a perfect circle, who would be interested and how would it affect math as we know it?

The mathematical community would be interested, and the whole of mathematics thrown into chaos by such a (successful) proof, as it would directly contradict sereal widely accepted proofs that Pi is transcendental – that is, cannot be written as an expression with a finite (polynomial) number of terms, beginning with von Lindemann’s 1882 transcendentality proofs.

 

I’d be surprised if such a proof is possible.

 

However, algorithm’s to approximate Pi with greater efficiency than before are invented fairly frequently, and are of intense interest to mathematicians. Finding a good Pi generating algorithm, even if not as efficient as the best known, can bring its author considerable fame and respect.

Would you know how one can go about protecting their equation (algorithm)?

Since there’s little practical demand for values of Pi more precise than the most accurate calculating software can use (around 10^12 digits), and algorithms able to generate values of Pi more accurate than this are already in the public domain, I don’t think there’s much commercial value for Pi algorithms. I don’t think one need worry about copyrighting or patenting such work.

 

There are areas of Math and number theory where one can create commercially valuable works – eg: cryptography. I just don’t think Pi algorithms are among them.

[Guadalupe]

The mathematical community would be interested, and the whole of mathematics thrown into chaos by such a (successful) proof, as it would directly contradict sereal widely accepted proofs that Pi is transcendental – that is, cannot be written as an expression with a finite (polynomial) number of terms, beginning with von Lindemann’s 1882 transcendentality proofs.

 

I’d be surprised if such a proof is possible.

 

However, algorithm’s to approximate Pi with greater efficiency than before are invented fairly frequently, and are of intense interest to mathematicians. Finding a good Pi generating algorithm, even if not as efficient as the best known, can bring its author considerable fame and respect.Since there’s little practical demand for values of Pi more precise than the most accurate calculating software can use (around 10^12 digits), and algorithms able to generate values of Pi more accurate than this are already in the public domain, I don’t think there’s much commercial value for Pi algorithms. I don’t think one need worry about copyrighting or patenting such work.

 

There are areas of Math and number theory where one can create commercially valuable works – eg: cryptography. I just don’t think Pi algorithms are among them.

 

 

Hypography Science Forums is very fortunate to have you as a member. :hyper:

 

 

 

:phones:

[Qfwfq]

There are areas of Math and number theory where one can create commercially valuable works – eg: cryptography. I just don’t think Pi algorithms are among them.

Actually, I think an algorithm that could efficiently reel off endless pi digits could be used as the basis for a pseudo-random generator, especially if it could be run for an arbitrary base. Suitably parametrizing the mapping between pi digits and output would constitute a secret key and I doubt the adversary's task would be tractable.

 

What do you think Craig?

[CraigD]

Actually, I think an algorithm that could efficiently reel off endless pi digits could be used as the basis for a pseudo-random generator, especially if it could be run for an arbitrary base. Suitably parametrizing the mapping between pi digits and output would constitute a secret key and I doubt the adversary's task would be tractable.

 

What do you think Craig?

Let me make sure I know what you're suggesting by describing what I think it is.

 

Alice wants to send a message to Bob that can't be read by anyone else. Let's assume the message is an ordinary 8-bit character stream.

 

Alice and Bob are allowed to exchange a secret key. The key must be much smaller than the message they intend to send (otherwise, they could just exchange a one-time pad, and be confident that their message couldn't be read by anyone else)

 

They exchange a large random number K representing a position in the continuing decimal (the base isn't important, unless they're concerned with minimizing the length of their exchanged cyphertext) representation of Pi. (artificially small example: K=147139495)

 

Alice takes her plaintext (eg: HELLO) expands it into 3 digit decimal numbers (eg: 072069076076079) and adds it modulo 10 to the digits of Pi from decimal positions 147139495 to 147139509 (822902317666316), to generate the cyphertext (eg: 894961383632385). Bob reverse this procedure to get the original message.

 

This scheme can also be used if Alice and Bob exchange a secret key of a seed value (A) for a simple pseudo-random number generator (eg: A=(A*B + C) mod D, repeat) – call this SPRNG.

 

:hihi: I’m fairly sure using a decimal position in Pi is weaker than using an number generator like the preceeding. Because there are efficient Pi digit-generators, if you have some knowledge of the plaintext (eg: it’s a natural language), you can narrow the keyspace for K fairly quickly and efficiently. To use this attack on SPRNG, but I think the keyspace narrows much less quickly.

 

Pi-spelunking may be good for other things, though. Some people have experimented with the notion that some special kinds of texts can be compressed by finding where they occur within Pi (the position in Pi can be represented by a number with fewer bits than the message). :hihi: And who can forget the closing chapters of Carl Sagan’s ”Contact”, where various secret information is found when the digits of Pi in base 11 are arranged to correctly?

[InfiniteNow]

:hihi: And who can forget the closing chapters of Carl Sagan’s ”Contact”, where various secret information is found when the digits of Pi in base 11 are arranged to correctly?

Sagan always was one clever dude...

[InfiniteNow]

Tuesday, 7 March

- THEORY GROUP SEMINAR: Dr. Jason Kumar, Texas A&M University, "The Phenomenology of Pi-Stability and an Infinite Number of Vacua," 2:00pm, RLM 7.104.

 

Just received my weekly physics email regarding events at the University... I may just need to attend this one. Sweet!

[Qfwfq]

Pity that the Sagan example is only one example, and obviously not one of a good algorithm.

 

Because there are efficient Pi digit-generators, if you have some knowledge of the plaintext (eg: it’s a natural language), you can narrow the keyspace for K fairly quickly and efficiently.

Since you posted "to see if you had understood me", the answer is "not quite". :steering:

 

a) You can also vary the initial digit as part of the key, that's why I said efficiently and endlessly, in order to amplify keyspace.

 

:hyper: I talked about a mapping from digit sequence to output sequence, not meaning message space but the output of just the PSRNG itself. Mapping wasn't perhaps the best term, I would want it to vary from one digit to the next, at least over a period not to short a fraction of the needed sequence length. Best of course would be a non-periodic sequence generator, if you have an efficient one that doesn't quite meet the requirements of being PSR, the use of it to vary the mapping of single digits would make a better one. The combination of its key (or the period used) with any further key of the single digit map, the base and initial pi digit, would be the overall key. Ample enough keyspace?