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Problems with Pi

08/25/2009 7:31 PM

If the area of a circle is represented by the formula Pi(r2) and pi is an infinite quantity (by definition immeasureable ) therefore the area of a circle can not be ascertained!

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#121
In reply to #120
Find in discussion

Re: Problems with Pi

09/01/2009 12:39 AM

Well logically as Socrates was mostly starving, it was probably just before Plato's breakfast, lunch or dinner time.

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#93

Re: Problems with Pi

08/29/2009 9:23 PM

I found this in Wiki whilst wondering if "exact" and "adequate precision" are indeed the same thing. http://en.wikipedia.org/wiki/Pi

"While the value of π has been computed to more than a trillion (1012) digits,[15] elementary applications, such as calculating the circumference of a circle, will rarely require more than a dozen decimal places. For example, a value truncated to 11 decimal places is accurate enough to calculate the circumference of a circle the size of the earth with a precision of a millimeter, and one truncated to 39 decimal places is sufficient to compute the circumference of any circle that fits in the observable universe to a precision comparable to the size of a hydrogen atom."

But, and this may be "off topic", "any circle that fits in the observable universe"? Would the locus around a point actually be a circle, or indeed 'join up', if that point was not "exactly" at the centre of the universe?

I am of course thinking in terms of modeling the circumference in the actual universe, not of just drawing a circle on a graphical representation of the universe

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#95
In reply to #93

Re: Problems with Pi

08/29/2009 9:53 PM

There's no such thing as a circle in reality. A circle is an idealized shape. I reality, all circles are polygons.

See, I can be pedantic too guys.

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#96
In reply to #95

Re: Problems with Pi

08/29/2009 11:21 PM

Roger 'pedantic' would be nearer; 'all circles are polygons when digitally defined'.

"There's no such thing as a circle in reality" - Computer graphics and CNC mill agree, Compass, Lathe, Rotary table and Cylindrical grinder are somewhat perplexed as to how to make the facets.

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#97
In reply to #95

Re: Problems with Pi

08/29/2009 11:27 PM

Roger,

In general I dislike metaphysical arguments but you are wrong to say that because nobody can construct the two dimensional object of a circle in a three dimensional world that circles do not exist. The circle is a pivotal concept of geometry. Are you also claiming that concepts don't exist? That's stupid. Oh wait a minute, that's also a concept, so stupidity doesn't exist. We are all brilliant and above average. Wait a minute...

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#113
In reply to #95

Re: Problems with Pi

08/31/2009 9:49 AM

"See, I can be pedantic too guys."

Oh, I wouldn't take it that far. You're just a linear thinker, that's all. The rest of prefer circular reasoning.

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#98

Re: Problems with Pi

08/30/2009 1:26 AM

Dear friends. I must applaud you all on your well thought out arguments. I am new to this site and I am quite impressed by the intelligent intellects that compose it. My understanding of mathematical principles is limited by my lack of education in this discipline. I made the statement merely to get feedback from those with greater understanding regarding a topic that I was unable to get my 'arms around' But I have come to the conclusion that CR4 exists as an engineering forum,not a High School math club debating exercise. My only hope is that the participants in this discussion had some fun (some of the arguments seem to suggest so) After all, everyone knows you cant divide by zero! But you guys know why!!! Thank You All!! Cogito Ergo Sum, K

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#103

Re: Problems with Pi

08/30/2009 10:57 AM

The Dao of Meow!

How many time do you get a situation where the 'maths' gives a result and then the practical approach shows there was a mistake in the maths ?

Or as has been pointed out before, how many times have we seen someone lost in the maths never reach a reasonable solution?

How long has Excel been around?

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#115
In reply to #103

Re: Problems with Pi

08/31/2009 10:00 AM

"... how many times have we seen someone lost in the maths never reach a reasonable solution?"

You mean someone like those investigators who couldn't figure out how that statistician drowned in a lake having an average depth of one centimeter?

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#104

Re: Problems with Pi

08/30/2009 1:24 PM

It can be obtained, it will simply have it's own, infinitely long string of decimal places.

Try putting the radius equal to one over the square root of pi:

r=1/√pi

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#105

Re: Problems with Pi

08/30/2009 2:00 PM

It's that time of year again...

Blackberry & Apple...
Del

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#107
In reply to #105

Re: Problems with Pi

08/31/2009 3:00 AM

Korean PI is also very tasty

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#117
In reply to #105

Re: Problems with Pi

08/31/2009 1:31 PM

Del:

A paradigm, proving Pi are NOT square!

My gramma says 'Thank you'.

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#106

Re: Problems with Pi

08/30/2009 7:33 PM

Hi Kay,

Roger and a few others have covered your query very well, however I thought this might also help cement the concept.

You are no doubt used to seeing Cartesian graphs (x,y graphs) with numbers along the horizontal and vertical axes. If you plot a trigonometric function, eg y=sin(x), on such an axis system you get the familiar sinusoidal curve like this:

The curve reaches a maximum at exactly 1 on the y axis, but it cuts the x axis somewhere near 3, then near 6, then near 9 etc. Obviously the cutting points can be quite accurately defined as 3.141592654, 6.283185, etc. However as you point out in your post, they cannot be exactly defined on this axis using decimal numbers.

But they do cut the axis at exact points - there is no mysterious gap in the curve or the axis - there is a definite crossing point.

In mathematics it would be unusual to plot the sine curve like this (more likely in engineering). But for maths it is usually plotted with the vertical axis in decimal and the horizontal axis in units of pi, like this:

Now we do have exactly defined crossing points - the points are pi, 2pi, 3pi etc etc. And if your question was "at what exact values does the curve cross the x axis" your answer would be plus or minus n*pi (where n is any integer). That is the exact answer.

If you wanted an answer that would help you then measure out something for a building or whatever, you would probably switch to a decimal approximation to whatever accuracy was required. Why? Because your ruler would be laid out in integer units not pi units. If your ruler was laid out in pi units, then you would just measure off pi metres exactly as you would measure off 3.14159 metres.

Interestingly, although you can't represent pi exactly on the decimal number line, you can represent one on the pi number line. It's pi/pi and 2 is 2pi/pi etc.

But the pi number line is no good for giving you an exact answer for the square root of two, for that you would make a new number line, with √2, 2√2, 3√2 etc as your tick marks along the axis.

These symbols represent exact numbers as surely as 1, 2, 3, 4 etc do, it's just that once you choose your tick marks, you have favoured exact values for a certain type of number.

The decimal system is very convenient but only because we're all so used to it and it has a certain naturalness to it (it represents the number of fingers we have very well for instance). Just remember it only defines exact values for a particular type of number, but it does not have any claim to universal exact numerical representation.

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#108

Re: Problems with Pi

08/31/2009 8:53 AM

"If the area of a circle is represented by the formula Pi(r2) and pi is an infinite quantity (by definition immeasureable ) therefore the area of a circle can not be ascertained!"

And to think I've been wasting all this time trying to find the first real number greater than Pi.

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#109
In reply to #108

Re: Problems with Pi

08/31/2009 9:23 AM

"the first real number greater than Pi" No mere number can ever be "greater" than Pi

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#110
In reply to #109

Re: Problems with Pi

08/31/2009 9:33 AM

How about 4?

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#116
In reply to #110

Re: Problems with Pi

08/31/2009 12:41 PM

Four what? Candles?

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#118
In reply to #116

Re: Problems with Pi

08/31/2009 1:49 PM

Sure. Why not?

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#123
In reply to #116

Re: Problems with Pi

09/01/2009 1:24 AM

In my mother tongue, PI (pronunciation of PI) means legs.

So 4 can be 4 legs. Sometimes, we prove that basically we are 4 legged animal.

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#125
In reply to #123

Re: Problems with Pi

09/01/2009 3:01 AM

"In my mother tongue, PI (pronunciation of PI) means legs."

As in, "Dude! Dig that bird's Π! Have you ever seen such a perfect ratio of circumference to diameter?! Oh baaaaaby! I'd sure like to find all her decimal places!"

Something like that?

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#126
In reply to #125

Re: Problems with Pi

09/01/2009 4:40 AM

Dude - have another OT point

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#127
In reply to #126

Re: Problems with Pi

09/01/2009 5:05 AM

Well?

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#128
In reply to #127

Re: Problems with Pi

09/01/2009 5:24 AM

Well?

Well - An engineer dies and reports to the pearly gates.


Saint Peter checks his dossier and, not seeing his name there,
accidentally sends him to Hell.

It doesn't take long before the engineer becomes rather dissatisfied
with the level of comfort in Hell, and soon begins to design and build
improvements.

Shortly thereafter, Hell has air conditioning, flush toilets and
escalators. Needless to say, the engineer is a pretty popular guy.

One day, God calls Satan and says with a sneer, 'So, how are things
in Hell?'

Satan replies: 'Hey, things are going great. We've got air conditioning,
flush toilets and escalators – and there's no telling what this engineer
will come up with next.'

'What!' God exclaims. 'You've got an engineer? That's a mistake – he
should never have been sent to Hell. Send him to me.'

'Not a chance!' Satan replies. 'I like having an engineer on the staff,
and I'm keeping him!'

God insists: 'Send him back or I'll sue.'

Satan laughs uproariously and answers: 'Yeah, right. And where are you
going to get a lawyer?'

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#129
In reply to #128

Re: Problems with Pi

09/01/2009 5:44 AM

Good one. Transcendian posted that one on 08/26 in another thread. Different wording, tho.

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#130
In reply to #129

Re: Problems with Pi

09/01/2009 6:56 AM

Yep they seem to e-evolve, but it turned up in my mail loop just as you asked 'well?', which is still a mystery (about what?), so I figured the Lord our Pi moves in mysterious ways.

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#137
In reply to #130

Re: Problems with Pi

09/01/2009 3:44 PM

Well?

As in "Well? When are you gonna give me my bloody OT? It's still at 5!"

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#139
In reply to #137

Re: Problems with Pi

09/01/2009 6:23 PM

That's more like it!

Do we have an 8?

8 going once.....

Going twice.....

Going.....Pi (an irrational choice, to be sure, but I'm trying my darndest to stay on-topic.)

.

(Hmm...my spider-sense tells me there's a squirrel nearby...)

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#142
In reply to #139

Re: Problems with Pi

09/01/2009 11:10 PM

Never seen such an earnest OT plea before. Congratulations is eight enough?

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#147
In reply to #139

Re: Problems with Pi

09/02/2009 2:06 AM

scurrilous suggestion.....completely scurrilous.....

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#140
In reply to #137

Re: Problems with Pi

09/01/2009 8:34 PM

Well, hopefully you didn't sit staring up to now, but if you are as desperate as you sound, which I doubt, try hitting refresh (shortly after someone mentions those yummy points).

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#136
In reply to #128

Re: Problems with Pi

09/01/2009 10:19 AM

Great.

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#135
In reply to #110

Re: Problems with Pi

09/01/2009 9:02 AM

Europium

I'm finding it hard to believe we have "engineers" (?) who don't know the difference between an infinite number and a number with infinite digits! Glad to see you having fun with it - you made my day.

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#112
In reply to #109

Re: Problems with Pi

08/31/2009 9:45 AM

Hey Kyzine - how about e. Though it's smaller than Pi, it is at least equal to Pi, (although I agree, perhaps not greater than Pi).

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#114
In reply to #112

Re: Problems with Pi

08/31/2009 9:54 AM

You got something against the number 4? Is that it? Well, here's one that'll really bake your noodle: 3.2.

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#122
In reply to #114

Re: Problems with Pi

09/01/2009 1:12 AM

Not at all. 4 is just bigger. 3.2 is closer and also handy in converting 1/8" to mm, but it's not particularly mystical or omnipresent as god-like Pi. Is it?

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#124
In reply to #122

Re: Problems with Pi

09/01/2009 2:45 AM

"No mere number can ever be "greater" than Pi"

4 > Pi

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#131
In reply to #112

Re: Problems with Pi

09/01/2009 8:00 AM

Hi RobertOz - You have had me pondering for a quite while - is that e as in Young's Modulus, if so it's indeed a ratio, and quite sexy, but limited to 'materials'.

But maybe, that e is for echidna, which equals speed of Cetacea squared.

Feel free to unconfuse me.

However the bit in brackets would be GA - except perhaps for 'perhaps'

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#132
In reply to #131

Re: Problems with Pi

09/01/2009 8:24 AM

sorry to confuse... I mean e as in Euler's number (e = 2.7182818284590.... and on and on like pi) which apart from other things has the magical property of creating the only function that is its own derivative...

i.e. if y=ex then dy/dx = ex

It rivals Pi for its habit of popping up everywhere, and it's the basis of natural logs (i.e. ln or log to base e).

read it all here: http://en.wikipedia.org/wiki/E_(mathematical_constant)

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#133
In reply to #132

Re: Problems with Pi

09/01/2009 8:38 AM

Ah - 'base' the illusive not made thought on my part. Yes very salubrious chap that Euler. I agree - numerically less but nearly as universally intrusive. Would you settle for "On the Right Hand of Pi"?

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#134
In reply to #133

Re: Problems with Pi

09/01/2009 8:49 AM

Done!

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#138
In reply to #132

Re: Problems with Pi

09/01/2009 4:35 PM

"I mean e as in Euler's number"

Good thing you clarified that before my attorney got hold of you.

e®

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#141
In reply to #138

Re: Problems with Pi

09/01/2009 10:09 PM

You can tell your attorney I hold the rights to all derivatives of e®

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#143
In reply to #141

Re: Problems with Pi

09/01/2009 11:42 PM

Good lord, I've been writing zeros as though they were free all this time. I must owe you a fortune!

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#144
In reply to #143

Re: Problems with Pi

09/02/2009 12:25 AM

nah - it works like music royalties... google simply counts up all the zeroes on the web and in print and then I get a cut of your ISP bill. It's not much per zero, but you can imagine it adds up. Whoa - got to go, one of my white rhinos is digging up the truffle beds again and the chief gamekeeper is off today (one just can't get good help)!

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#145
In reply to #144

Re: Problems with Pi

09/02/2009 12:43 AM

White Rhinos.....I appreciate your refined sense of style. May I suggest an orangutan to help you punctuate your statements with expressions of emotion? Think of the Orangutan as a real life emoticon. Really will drive you're points home.

For instance, after you told me about your White Rhino problem your orangutan could have done this:

And I would have immediately understood your distress.

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#146
In reply to #145

Re: Problems with Pi

09/02/2009 1:43 AM

Love it! A million times better than

Reminds me of http://www.bushorchimp.com/ (reading between the lines I don't think you're a rabid Bush fan so I'll post the link).

Unfortunately we don't have a lot of orangutans to photograph (the snow leopards got into their enclosure - very messy but a real hit on youtube). However I do have a whole lot of oyster photos for reasons I won't go into in this forum, which I reckon could make terrific emoticons... eg:

angry

bemused

bewildered (yet oddly jocund)

It's a surefire hit - I'll cut you in on the royalties.

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#148
In reply to #146

Re: Problems with Pi

09/02/2009 9:00 AM

Great idea. Here's some more oyster emoticons:

Happy

Introspective

World-Weary

Hungry

For some reason I'm suddenly craving oysters.

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#149
In reply to #141

Re: Problems with Pi

09/02/2009 9:10 AM

Dude, your attorney's just playin' you fo' da money. And all those plane fares to DC where his mistress (and mine) works at the USPTO. What your attorney isn't telling you is that I hold the rights to eigenfunctions (which also begins with an e®). All of them, to perpetuity.

You owe me a lot of back royalties, pal. Shall I put them on your tab?

e®

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#150
In reply to #149

Re: Problems with Pi

09/02/2009 6:18 PM

eigenfunctions schmeigenfunctions... I'll see you in court!

(by the way - I'm tryin to get hold of a guy called Bernie Madoff - doesn't seem to be answering his phone. Seeing as you're in the US could you ask him to gimme a call if you see him. Tell him it's rather urgent.)

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