How do you get the number pi.

[Leifmk]

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

Although sometimes (shock, horror!) it yields results which can actually be very useful in other fields. And it's nigh-unto impossible to know ahead of time, so beware! See for example G. H. Hardy's A Mathematician's Apology, where he held forth relativity and number theory as examples of beautiful and utterly useless (and therefore harmless) mathematics. In 1940.

 

[Bartleby]

...you can't have been that busy that morning

I'd love to reply to this, but I'm far too busy.

 

[pboily]

Although sometimes (shock, horror!) it yields results which can actually be very useful in other fields. And it's nigh-unto impossible to know ahead of time, so beware! See for example G. H. Hardy's A Mathematician's Apology, where he held forth relativity and number theory as examples of beautiful and utterly useless (and therefore harmless) mathematics. In 1940.

For the most part, the practicionners of the art don't care for the applications.

To descend even further in the lack of class my analogy provided, the masturbatory seed can conceivably be preserved and used to get a female pregnant, but the two acts are not in the same league.

 

[Leifmk]

For the most part, the practicionners of the art don't care for the applications.

Oh, I spent enough time at my alma mater's "Institute for Applied Mathematics"; this is not news to me. (The "Applied" part of the name was considered a bit of a joke by everyone there. Well, except for those among the faculty who were too dry to have a sense of humour. Which was most but definitely not all of them.)

 

[pboily]

annoying, isn't it...

 

[Atticus]

To descend even further in the lack of class my analogy provided, the masturbatory seed can conceivably be preserved and used to get a female pregnant, but the two acts are not in the same league.

And you prefer pure mathematics?

 

[nihilistic]

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.
Turns out a Chinese astronomer, Tsu Chung Chi, beat me to it by ~1500 years.

You can do that much more efficiently by using continued fractions:

Try to compute pi as 3 + 1/(a + 1/(b + 1/(...))) for as many terms as possible, then reconstruct the fractions.

And you will have:

3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, 208341/66317, 312689/99532, 833719/265381, 1146408/36491, ...

 

[pboily]

And you prefer pure mathematics?

I "prefer" pure mathematics, but I'm just so damn good at "applications"...

 

[Cookie Crumbs]

I dozed off in a maths lesson once and came up with a way of calculating pi...which turned out to be the method Archimedes used. It simplifies to: (10n)sin(18/n), approaching pi as it n tends towards infinity.

 

[Truronian]

I dozed off in a maths lesson once and came up with a way of calculating pi...which turned out to be the method Archimedes used. It simplifies to: (10n)sin(18/n), approaching pi as it n tends towards infinity.

EDIT: Woops, misread that.

 

[Atticus]

I dozed off in a maths lesson once and came up with a way of calculating pi...which turned out to be the method Archimedes used. It simplifies to: (10n)sin(18/n), approaching pi as it n tends towards infinity.

Great! Next prove that the area of circle is pi times radius squared, where pi is defined to be the ratio of circumference and diameter.

 

[mdwh]

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.

We can state it - it's just that we can't make it equal to the ratio of two integers.

Same goes for the square root of 2. This is certainly a flaw of rational numbers, but then we fix that in the reals, so I don't see why this means the reals are flawed.

I mean, it's a bit like saying that integers are flawed because I can't do 1 divided by 2, but I don't see this means mathematics as a whole is flawed, it just means you have to pick a group which is closed under the operation you wish to perform.

 

[Perfection]

"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...."
— First Kings, chapter 7, verses 23 and 26

So Pi = 3

 

[Lotus49]

We can state it - it's just that we can't make it equal to the ratio of two integers.

Same goes for the square root of 2. This is certainly a flaw of rational numbers, but then we fix that in the reals, so I don't see why this means the reals are flawed.

I mean, it's a bit like saying that integers are flawed because I can't do 1 divided by 2, but I don't see this means mathematics as a whole is flawed, it just means you have to pick a group which is closed under the operation you wish to perform.

My point was simply that mathematics has a difficult time when dealing with the circle. I.e., it can never completely, accurately give the 100% correct answer... you have to round off the answers at some point. I have no problem with decimals, it's just that when you try to express Pi, or as you say the sqrt of 2, math undeniably seems... indecisive. Maybe even - confused. Thus my intent on pointing out that it is not necessarily perfect, as man has (indeed) 'created' it (not 'uncovered').

Take the Roman numerals for ex., what kind of inefficient, crappy system is that, compared to the Arabic numerals we now use. Well, maybe one day we'll say the same for what we now currently use. But anyway, this is all just a tool, measurement, invention etc. of man - and like others, it certainly has it's uses.

But, what if I was a mechanic (and you were, a spiritual man) - and I compared a multi-thousand horsepower diesel engine to... God Himself. Now, wouldn't you think that's a bit ridiculous? Pompous? Maybe a few other adjectives...?

In other words, let's not get too full of ourselves, in our persuits. It's fine to be a bit proud, and enthusiastic, but I caution that when you start comparing your creations/wisdom to God, you are inviting disaster (thus the Titanic reference in my original post).

 

[nihilistic]

My point was simply that mathematics has a difficult time when dealing with the circle. I.e., it can never completely, accurately give the 100% correct answer... you have to round off the answers at some point. I have no problem with decimals, it's just that when you try to express Pi, or as you say the sqrt of 2, math undeniably seems... indecisive. Maybe even - confused. Thus my intent on pointing out that it is not necessarily perfect, as man has (indeed) 'created' it (not 'uncovered').

Take the Roman numerals for ex., what kind of inefficient, crappy system is that, compared to the Arabic numerals we now use. Well, maybe one day we'll say the same for what we now currently use. But anyway, this is all just a tool, measurement, invention etc. of man - and like others, it certainly has it's uses.

But, what if I was a mechanic (and you were, a spiritual man) - and I compared a multi-thousand horsepower diesel engine to... God Himself. Now, wouldn't you think that's a bit ridiculous? Pompous? Maybe a few other adjectives...?

In other words, let's not get too full of ourselves, in our persuits. It's fine to be a bit proud, and enthusiastic, but I caution that when you start comparing your creations/wisdom to God, you are inviting disaster (thus the Titanic reference in my original post).

And their point, and mine, is that you have no f*cking idea what you are talking about. What? You don't agree? LEt's take each of your points:

1. it can never completely, accurately give the 100% correct answer...

Wrong. Math can always give the exact value of Pi. The mathematical expression Pi denotes the exact value of Pi, as does Sum[((-1)^n)/(2n+1),{n,0,Inf}], as does 2ArcCos[0], etc.

2. I have no problem with decimals, it's just that when you try to express Pi, or as you say the sqrt of 2, math undeniably seems... indecisive.

Again, that only shows you have no idea what you are talking about. What after all is a transcendental number anyway?

3. Maybe even - confused. Thus my intent on pointing out that it is not necessarily perfect, as man has (indeed) 'created' it (not 'uncovered').

Non-sequitur? That's pretty much like saying, you breathe air, pigs breathe air, therefore you are a pig.

4. Take the Roman numerals for ex., what kind of inefficient, crappy system is that, compared to the Arabic numerals we now use. Well, maybe one day we'll say the same for what we now currently use. But anyway, this is all just a tool, measurement, invention etc. of man - and like others, it certainly has it's uses.

What? You are using "Roman Numerals" to demonstrate your knowledge of mathematics and to show that it is "confused"? No wonder you are confused. Please come back and debate again when you finish second grade math.

5. But, what if I was a mechanic (and you were, a spiritual man) - and I compared a multi-thousand horsepower diesel engine to... God Himself. Now, wouldn't you think that's a bit ridiculous? Pompous? Maybe a few other adjectives...?

In other words, let's not get too full of ourselves, in our persuits. It's fine to be a bit proud, and enthusiastic, but I caution that when you start comparing your creations/wisdom to God, you are inviting disaster (thus the Titanic reference in my original post).

You are the only person here bringing up theology again and again, so I'm puzzled as to who you might be accusing here as "ridiculous" for making those comparisons. Read the posts in the thread again, especially the one you replied to. The only "pompous ass" who kept bringing up that comparison is you. So you might as well keep whatever pointless warnings you have for yourself.

 

[mdwh]

My point was simply that mathematics has a difficult time when dealing with the circle. I.e., it can never completely, accurately give the 100% correct answer... you have to round off the answers at some point. I have no problem with decimals, it's just that when you try to express Pi, or as you say the sqrt of 2, math undeniably seems... indecisive. Maybe even - confused. Thus my intent on pointing out that it is not necessarily perfect, as man has (indeed) 'created' it (not 'uncovered').

Well, you have to round off if you want to express it as a ratio of two integers. We can represent it other ways. The "flaw" boils down to the fact that there exist numbers other than those which can be represented neatly by a ratio of two integers (or a finite decimal).

Indeed, there are uncountably infinitely number of irrationals, compared with a countably infinite number of rationals...

Take the Roman numerals for ex., what kind of inefficient, crappy system is that, compared to the Arabic numerals we now use. Well, maybe one day we'll say the same for what we now currently use.

I think that's a good example - isn't it a bit like a Roman saying that maths is flawed because they couldn't represent zero without using a new cute symbol? I would say that the flaw is in the decimal representation system (which is because a finite decimal can only represent a rational).

 

[Hygro]

...you can't have been that busy that morning

Hygro FTW

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.
Turns out a Chinese astronomer, Tsu Chung Chi, beat me to it by ~1500 years.

That was a busy morning?

The joys of academic research.

 

[pboily]

Mechanic: I understand how the diesel engine works. If God doesn't know how one works and how to build one of those, he cannot be an all powerful God. In general, an all-powerful God can certainly do anything I can. So an all-powerful God is at least as good as a mechanic.

"Spiritual" Man: Pompous ass! I don't fully understand how diesel engines work, but they are certainly flawed because they cannot run forever. How can you claim that God is a diesel engine?

 

[Truronian]

If God's a diesel engine, does that make Jesus a cylinder?

 

[Catharsis]

If God's a diesel engine, does that make Jesus a cylinder?

V_Jesus=πr²l