How do you get the number pi.

I actually have a whole book on how the exact number pi was discovered. :) It's called "The Story of Pi" (translation from Romanian by me).
 
You sure he wouldn't be a physicist?

God is by definition the perfect being, and if he/she/it would be a physicist, it would be concievable that there would be a more perfect being, namely a mathematician. Therefore God isn't a physicist.

To the original post: You can approximate the circumference of circle by drawing triangles inside it. I draw a little picture (with paint so it's a bit clumsy), which is attached. Now draw an altitude to each triangle like in the one on the left side. You'll get triangles with right angles. You know also the hypotenuse of these triangles (it's the radius of the circle) and one other angle (360/2n degrees, where n is the amount of original triangles, in this case n=8 so the angle is 22,5 degrees). Now you can use basic trigonometry to obtain the length of the side drawed little stronger, and if you sum the length of all these sides (that is multiply it with 2n) you'll get an approximation of the circumference. By increasing n you'll get better and better approximations.

It's also simple to approximate circumference from outside, details &c: exercice.

I believe at least Archimedes used the method above, he probably knew some triangles which would give rational values, and used them.
 

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Maybe I should have translated it a little different... :lol: Never realized how it sounds in English!

Edit: Crosspost crosspost crosspost crosspost.
 
I think the greeks had a pretty good approximation (22/7) of it in the BC times. It doesn't take to 'discover' pi either - simply draw a cirlce, cover it with a piece of string and divide the length of the string with the diameter of the circle.

In the modern sense, pi is defined I think as the smallest number for which

cos (x/2) = 0 holds.

Not sure here.. But isn't that recursive?
 
No, I meant, what does it mean to "solve for the simple shape of a circle"?

EDIT: Of course math is not ideal or most efficient answer to everything: it's mental masturbation!

I just meant that if I referred to mathematics for various dimensions/measurements for the shape of a mere circle, it can't give me a simple, concise answer. I.e., an answer that "never ends". To me, that doesn't sound logical, that sounds indecisive, and useless. Flawed. Not exactly what one would expect from 'the language of the Gods'.

Hence my fundamental belief that science (including math) is nothing more but man's best effort to understand and describe the created universe which he inhabits, and each of these studies being man's own invention, they are inexorably flawed, as he is.

Thus, when people compare God with mathematics (etc.), I can't help but see the foolishness. Laughter - only not humorous, but shameful & disgraceful. But, that's just me. You asked.
 
I just meant that if I referred to mathematics for various dimensions/measurements for the shape of a mere circle, it can't give me a simple, concise answer. I.e., an answer that "never ends".

If you are troubled by the fact that the decimal representation of pi never ends, you're wrong for two reasons. 1: Every question doesn't have simple answers. If you want to know anuthing, you must accept that the answers are sometimes complex. In this case no number with finite amount of digits can be the right answer. Simple answers are wrong, and that's why maths gives the best possible answer.

2: We can approximate pi with arbitrary precision, and that fact determines pi. We aren't actually saying that we have estimates for pi, but that pi is the limit of these estimates. Pi is the only number that is between every upper and lower estimate of circumference/diameter of a circle.

Thus, when people compare God with mathematics (etc.), I can't help but see the foolishness. Laughter - only not humorous, but shameful & disgraceful. But, that's just me. You asked.

Maybe that's because you don't know mathematics enough?
 
I just meant that if I referred to mathematics for various dimensions/measurements for the shape of a mere circle, it can't give me a simple, concise answer. I.e., an answer that "never ends". To me, that doesn't sound logical, that sounds indecisive, and useless. Flawed. Not exactly what one would expect from 'the language of the Gods'.

Hang on, hang on: you find me foolish/arrogant to think that if a God existed he would have to be a mathematician (so be good at solving problems) but you turn around and imply that God, the creator of all things for some, has the mental limitations of an undergraduate student?

In other words, I'm foolish because I think that if God exists, he will certainly understand what I can understand, and you are not foolish because you think that whatever you don't understand can be understood by neither God nor other mortals?

============================

If God can have existed (and can exist) for eternity (or a time period that never ends), and if he created the Universe, he will have absolutely no problem "creating" and "grasping" objects whose ratio perimeter/radius is an "unending decimal".

The fact that there is no "concise" or "simple" answer to a problem (although what could be simpler then a ration of real numbers?) YOU feel is pretty simple should tell you that this God fellow is pretty smart and can actually solve extremely difficult problems, independently of our intellectual limitations. (Well, what it should really tell you is that in this context, you don't understand when something is simple and when it is not.)

In particular, we can actually understand these "unending decimals", so God should have no problem with them.

=====================================

Unless you belong to a specific Christian sect I do not know about, a sect that is in the habit of thinking their God is no more intelligent or powerful then they themselves are ...

=====================================

It sounds an awful lot more like you plain don't like the fact that some of us don't believe in God, and think us asses for this. Why not just say so directly, rather than hide it in an "Intelligent Design"-like argument?
 
If you are troubled by the fact that the decimal representation of pi never ends, you're wrong for two reasons. 1: Every question doesn't have simple answers. If you want to know anuthing, you must accept that the answers are sometimes complex. In this case no number with finite amount of digits can be the right answer. Simple answers are wrong, and that's why maths gives the best possible answer.

2: We can approximate pi with arbitrary precision, and that fact determines pi. We aren't actually saying that we have estimates for pi, but that pi is the limit of these estimates. Pi is the only number that is between every upper and lower estimate of circumference/diameter of a circle.



Maybe that's because you don't know mathematics enough?


Of course it's the ratio of diameter : circumference of a circle, and the numeric value basically cannot be completely stated in it's entirety. Thus, you need a cute symbol to 'represent' a number, that you can't actually ever state. It's not that it isn't 'simple', it's that it's impossible. Thus, it's flawed. Imperfect. Not 'Godly'. Assuming "God is a mathematician" along the exact same lines as 'pboily', something seems a bit funny here.

Hang on, hang on: you find me foolish/arrogant to think that if a God existed he would have to be a mathematician (so be good at solving problems) but you turn around and imply that God, the creator of all things for some, has the mental limitations of an undergraduate student?

In other words, I'm foolish because I think that if God exists, he will certainly understand what I can understand, and you are not foolish because you think that whatever you don't understand can be understood by neither God nor other mortals?

============================

If God can have existed (and can exist) for eternity (or a time period that never ends), and if he created the Universe, he will have absolutely no problem "creating" and "grasping" objects whose ratio perimeter/radius is an "unending decimal".

The fact that there is no "concise" or "simple" answer to a problem (although what could be simpler then a ration of real numbers?) YOU feel is pretty simple should tell you that this God fellow is pretty smart and can actually solve extremely difficult problems, independently of our intellectual limitations. (Well, what it should really tell you is that in this context, you don't understand when something is simple and when it is not.)

In particular, we can actually understand these "unending decimals", so God should have no problem with them.

=====================================

Unless you belong to a specific Christian sect I do not know about, a sect that is in the habit of thinking their God is no more intelligent or powerful then they themselves are ...

=====================================

It sounds an awful lot more like you plain don't like the fact that some of us don't believe in God, and think us asses for this. Why not just say so directly, rather than hide it in an "Intelligent Design"-like argument?

Earlier:

to me, that is a proof that there is no God, as a God would necessarily have to be a mathematician. it's my chosen profession, after all, so if it's good enough for me, it would be good enough for old God.

...followed by pondering what type of scientific field of study God would specialize in, I simply find this one of the silliest things I've ever read. No doubt there was some light-heartedness to it, thus my reply was as well (relative to an otherwise serious subject).

"Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." -A. Einstein

Regardless of how advanced you may be in your field, there should never come a time when an ego gets that far out of check, as to say the things that you were (and co.) were tending towards. At least, that's my humble opinion, and now I've expressed it. That's all I intended. There will be no deep, theological debate. And no need for insults. We're all free to make expressions. You're free to insult God, if you choose, and I'm free to disapprove. But, at the end of the day we're all just seeking wisdom (via different routes perhaps), and none of us is perfect. This also includes our inventions, such as mathematics. Refined, yes. Perfect, by no means. And to presume so, is just as foolish as saying the Earth is at the center of the Universe, as they did once upon a time. That's how it stikes me, and that's all I intended to express. Now that I've done that, and hopefully have made it all clear (thought it was obvious, from the beginning), I see no need for quarrel. But naturally, "the Truth" is something that some people react to with anger. Because they know they are wrong. Otherwise, they would simply disregard.

Persuing a technical field, that eventually enables you to talk circles around any member of the general populace, is not wisdom.
 
Persuing a technical field, that eventually enables you to talk circles around any member of the general populace, is not wisdom.
Of course it's not wisdom. Wisdom is overrated. Intelligence is far more superior.

An academic of any type is far more noble in the knowledge of their respective subjects than any layman who claims to have wisdom about the subject - this includes philosophy and theology.
 
Of course it's not wisdom. Wisdom is overrated. Intelligence is far more superior.

An academic of any type is far more noble in the knowledge of their respective subjects than any layman who claims to have wisdom about the subject - this includes philosophy and theology.

Well, if you're open to new theories, I have one that explores the possiblity that certain, select personality types which continually aim for higher and higher levels of academic attainment, do so in order to justify their pompous-assed superiority complex in relation to the 'common folk'. Indeed, cementing their perception - giving them the only peace of mind that is actually within their reach.

Basically, a compensation. As most things are, I may come to find. Another example is how those that crave power and influencial positions in life, do so to compensate for the fact that deep within themselves, they feel inadequate - and thus need the constant reassurance and ego stroking, to put this feeling to rest.

But in the end, we're all flawed, all weak, and imperfect. Logically, the intelligent, rational mind could at least accept this (as it is obvious), and remain open to possibilities. I find your attitude, as manifested in the post above, purely a defense mechanism. Surely you can realize, that even if you study & learn every single thing man has collectively ever discovered, or speculated upon - you can still be a fool. A well-educated one, but still miss the mark when it comes to enlightenment. Because what are you doing, anyway? Learning from the brainstorming and discoveries of others that came before you? That's fine... but a mind that can think for itself, and make wise judgements, and have a sensible outlook - no amount of tuition can buy you that.

But, who cares about that... when you can go learn a few complicated equations, and be the master of your own little universe, eh? Put on the blinders, and play defense... within your own mind. But you can never really have knowledge, or wisdom... until you know where it comes from.
 
Well, if you're open to new theories, I have one that explores the possiblity that certain, select personality types which continually aim for higher and higher levels of academic attainment, do so in order to justify their pompous-assed superiority complex in relation to the 'common folk'.

There certainly are some that kind of people, but it doesn't mean that all educated people would be. And while education isn't proof of "superiority", it certainly isn't proof of inferiority either.

But, who cares about that... when you can go learn a few complicated equations, and be the master of your own little universe, eh? Put on the blinders, and play defense... within your own mind. But you can never really have knowledge, or wisdom... until you know where it comes from.

I'm not going to start a quarrel here either, but merely as a fact I must say that if you think maths is about learning equations, you don't know much about maths. See these equations don't come from nowhere, somebody must state and prove them, and that's what the real maths is about. As much it is hybris to say God is mathematician, it is form you to teach maths to people who have devoted many years on the subject. They don't just learn by heart equations to excell, they really think about these things. You're arguments does not show that you would have thought so much about these things.

and the numeric value basically cannot be completely stated in it's entirety. Thus, you need a cute symbol to 'represent' a number, that you can't actually ever state.

1. As I said before, it isn't any deficiency that decimals of pi can't be completely stated, but the other way round, but the other way round: no number with finitely may decimals can be the real ratio.

2. Why is the symbol pi any worse than symbols 1,2,3,4 &c? There is a symbol to squareroot 2 also, is it just as flawed? The number pi can be very well stated, and it has been a few times in this thread already. This isn't about the failure to state pi, but you're failure to accept that answers aren't always that simple.
 
I just meant that if I referred to mathematics for various dimensions/measurements for the shape of a mere circle, it can't give me a simple, concise answer. I.e., an answer that "never ends". To me, that doesn't sound logical, that sounds indecisive, and useless. Flawed. Not exactly what one would expect from 'the language of the Gods'.

You just take the limit as the number of triangles approaches infinity.

There's your perfect answer :)
 
I know that 355/113 is a good approximation for pi.
I discovered this one busy morning, by using my calculator to multiply pi by whole numbers until the answer was nearly a whole number.
...you can't have been that busy that morning :rolleyes:
 
And no need for insults.
:confused: The best I can come up with is that I said that in the context (of mathematics), you are not able to say what is an easy or a difficult problem. That cannot be what you mean.

Maybe when I made the ref. to ID?

And to presume so, is just as foolish as saying the Earth is at the center of the Universe, as they did once upon a time.

<snip>

Persuing a technical field, that eventually enables you to talk circles around any member of the general populace, is not wisdom.

I definitely agree: as I mentioned earlier, mathematics is mental masturbation, no matter how one twists it.

EDIT: as an aside, you made a mention about mathematics as a human invention... I would say that at least half of those I know think of us an uncovering stuff instead of discovering stuff.
 
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