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1

1987

Bronze Baronet of the Realm
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I had a question pop up in my head just now, and can remember asking a teacher the same thing when I was younger.

How is Pi derived?

I'm well aware that it's circumference/diameter etc...

My question is, if pi is irrational, doesn't either the circumference or diameter have to be irrational. Otherwise pi could be expressed as a ratio, and irrational numbers can't be.

And if so, how do we have computers looking for the billionth(?) digit in Pi? What is the program that lets a calculator look at something irrational?

I'm not a pi skeptic either. I've just always been good at math and this is one of those questions that I didn't have the ability to make sense
 
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Edaw

Edaw

Parody
<Gold Donor>
13,283
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1987 said:
I had a question pop up in my head just now, and can remember asking a teacher the same thing when I was younger.

How is Pi derived?

I'm well aware that it's circumference/diameter etc...

My question is, if pi is irrational, doesn't either the circumference or diameter have to be irrational. Otherwise pi could be expressed as a ratio, and irrational numbers can't be.

And if so, how do we have computers looking for the billionth(?) digit in Pi? What is the program that lets a calculator look at something irrational?

I'm not a pi skeptic either. I've just always been good at math and this is one of those questions that I didn't have the ability to make sense
Click to expand...
Adow GIF by A Discovery of Witches


 
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Ukerric

Ukerric

Bearded Ape
<Silver Donator>
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1987 said:
I had a question pop up in my head just now, and can remember asking a teacher the same thing when I was younger.

How is Pi derived?

I'm well aware that it's circumference/diameter etc...

My question is, if pi is irrational, doesn't either the circumference or diameter have to be irrational. Otherwise pi could be expressed as a ratio, and irrational numbers can't be.

And if so, how do we have computers looking for the billionth(?) digit in Pi? What is the program that lets a calculator look at something irrational?

I'm not a pi skeptic either. I've just always been good at math and this is one of those questions that I didn't have the ability to make sense
Click to expand...
Pi is irrational.

There are multiple formulas that have Pi in them and are used to derive the approximate value of Pi. The "classical" is Pi/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... but it is very inefficient to calculate Pi. Most of the formulae are based on (surprise!) geometry calculations, but they all involve an infinite series (sum from 0 to infinity of some stuff) that slowly converge toward the "real" value of Pi.
 
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Tuco

Tuco

I got Tuco'd!
<Gold Donor>
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1987 said:
My question is, if pi is irrational, doesn't either the circumference or diameter have to be irrational.
Click to expand...
I'm not a mathematician, but yes.

If you've got a circle with a diameter of 10 inches, the circumference is 10 * π, which is an irrational number. If you've got a circle with a circumference of 42 inches, the diameter is 42 / π.

You can either "maintain" its irrationality by keeping the pi around (ex, 10π), or you can approximate by accepting some significant digits. My favorite is M_PI in C++ Mathematical Constants (The GNU C Library) which is usually 3.14159265358979323846

types_of_approximation.png


1481553833-20161212.png
 
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1

1987

Bronze Baronet of the Realm
3,575
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I actually just found an explanation for this that makes sense.

It's not much different than doing instantaneous rate of change in calc 1. Tangent slope as limit of h approaches zero or whatever (been a while since we did this).

A circle is essentially an imaginary shape since it has infinite sides. So pi is essentially that ratio calculated as the limit of the number of sides approaches infinity.
 
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Kharzette

Kharzette

Watcher of Overs
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Like an integral or whatever. That tall skinny f thing? I never made it through calc.
 
1

1987

Bronze Baronet of the Realm
3,575
8,160
Kharzette said:
Like an integral or whatever. That tall skinny f thing? I never made it through calc.
Click to expand...
Its typically well before integral calc. More like the very beginning of differential calc, which is typically covered first.
 
Edaw

Edaw

Parody
<Gold Donor>
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ToeMissile said:
Only if it’s a quadrilateral.
Click to expand...

Determine what type of quadrilateral CAKE is, given C(1,-4), A(3,0), K(-1,2) and E(-3,-2).
Show all work clearly.
Support your conclusion with a brief reasoning. (10 pts.)

Here is some graph paper.

standard-graphing-paper.png




Screenshot 2024-02-20 at 12-18-26 Help people good at math!.png


Excuse Me What GIF by Robert E Blackmon
 
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Ukerric

Ukerric

Bearded Ape
<Silver Donator>
8,311
10,289
1987 said:
I actually just found an explanation for this that makes sense.

...

A circle is essentially an imaginary shape since it has infinite sides. So pi is essentially that ratio calculated as the limit of the number of sides approaches infinity.
Click to expand...
That's the original method by Archimedes.
 
Chris

Chris

Potato del Grande
19,436
-10,732
1987 said:
I actually just found an explanation for this that makes sense.

It's not much different than doing instantaneous rate of change in calc 1. Tangent slope as limit of h approaches zero or whatever (been a while since we did this).

A circle is essentially an imaginary shape since it has infinite sides. So pi is essentially that ratio calculated as the limit of the number of sides approaches infinity.
Click to expand...
That makes a lot more sense than Circumference/Diameter
 
Hateyou

Hateyou

Not Great, Not Terrible
<Bronze Donator>
16,648
43,315
1987 said:
I had a question pop up in my head just now, and can remember asking a teacher the same thing when I was younger.

How is Pi derived?

I'm well aware that it's circumference/diameter etc...

My question is, if pi is irrational, doesn't either the circumference or diameter have to be irrational. Otherwise pi could be expressed as a ratio, and irrational numbers can't be.

And if so, how do we have computers looking for the billionth(?) digit in Pi? What is the program that lets a calculator look at something irrational?

I'm not a pi skeptic either. I've just always been good at math and this is one of those questions that I didn't have the ability to make sense
Click to expand...
IMG_2939.jpeg
 
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Tuco

Tuco

I got Tuco'd!
<Gold Donor>
47,390
80,857
Chris said:
That makes a lot more sense than Circumference/Diameter
Click to expand...
That's one of the fun things about math. More so than a lot of fields, people understand mathematic ideas with wildly different approaches. And in some cases a preferred approach for someone is much more complex. And some people understand concepts at a deeper, more connected level where inferences and relationships are obvious. In this case, circumference/diameter as a ratio relating to pi just makes sense to me, and I wonder if I would be naturally a better mathematician if a deeper concept like integrals wasn't my preferred method of groking it.

For example, related to circles and pi, Euler's Identity ( Euler's identity - Wikipedia ) is e^(i * pi) + 1 = 0. For a modest programmer who does a bit of math like me it takes a few minutes reviewing the material to understand why that ostensibly goofy equation works. Conversely Gauss allegedly said something like "If his formula was not immediately apparent to a student upon being told it, that student would never become a first-class mathematician.".
 
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Erronius

Erronius

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Fucking Amod Amod what the fuck is this shit.

Is this really a... <checks notes> ...Math Playground bot?
 
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