Total Posts:29|Showing Posts:1-29
Jump to topic:

Pi.

Eitan_Zohar
Posts: 2,697
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 6:34:44 AM
Posted: 3 years ago
I debunk an age-old mathematical theorem.

No one cares.
"It is my ambition to say in ten sentences what others say in a whole book."
muzebreak
Posts: 2,781
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 6:38:16 AM
Posted: 3 years ago
Why is this in the philosophy section?
"Every kid starts out as a natural-born scientist, and then we beat it out of them. A few trickle through the system with their wonder and enthusiasm for science intact." - Carl Sagan

This is the response of the defenders of Sparta to the Commander of the Roman Army: "If you are a god, you will not hurt those who have never injured you. If you are a man, advance - you will find men equal to yourself. And women.
Eitan_Zohar
Posts: 2,697
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 6:47:45 AM
Posted: 3 years ago
At 5/27/2013 6:38:16 AM, muzebreak wrote:
Why is this in the philosophy section?

Philosophy is close to math. Besides, you have a better idea?
"It is my ambition to say in ten sentences what others say in a whole book."
muzebreak
Posts: 2,781
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 6:48:52 AM
Posted: 3 years ago
At 5/27/2013 6:47:45 AM, Eitan_Zohar wrote:
At 5/27/2013 6:38:16 AM, muzebreak wrote:
Why is this in the philosophy section?

Philosophy is close to math. Besides, you have a better idea?

miscellaneous
"Every kid starts out as a natural-born scientist, and then we beat it out of them. A few trickle through the system with their wonder and enthusiasm for science intact." - Carl Sagan

This is the response of the defenders of Sparta to the Commander of the Roman Army: "If you are a god, you will not hurt those who have never injured you. If you are a man, advance - you will find men equal to yourself. And women.
Eitan_Zohar
Posts: 2,697
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 8:48:20 AM
Posted: 3 years ago
At 5/27/2013 6:48:52 AM, muzebreak wrote:
At 5/27/2013 6:47:45 AM, Eitan_Zohar wrote:
At 5/27/2013 6:38:16 AM, muzebreak wrote:
Why is this in the philosophy section?

Philosophy is close to math. Besides, you have a better idea?

miscellaneous

....................../""/)
....................,/"../
.................../..../
............./""/'...'/"""`""
........../'/.../..../......./""\
........('(..."...".... "~/'...')
.........\.................'...../
..........'...\.......... _.""
............\..............(
..............\.............\...

Anyone have something constructive or relevant to say?
"It is my ambition to say in ten sentences what others say in a whole book."
Skepsikyma
Posts: 8,286
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 9:01:10 AM
Posted: 3 years ago
At 5/27/2013 6:34:44 AM, Eitan_Zohar wrote:
I debunk an age-old mathematical theorem.

No one cares.

No you didn't, because that isn't a valid way to determine circumference. Hence the blatantly wrong conclusion. I could make the same flawed argument about a square inscribed in a square to determine that the perimeter of the circumscribed square is equal to that of the inscribed square. This obviously isn't true, and this is because the method is flawed.
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
RoyLatham
Posts: 4,488
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 10:15:41 AM
Posted: 3 years ago
Look at the first approximation. The approximated circumference is 4, while the actual circumference is pi. As the steps are taken to make the approximate circumference "closer" to the real circumference, the error is not actually reduced because while the distance of the farthest point from the circle is reduced, the length of the approximating figure is not reduced.

The same type of "proof" can be set up to show that two points one-unit apart is more than their true distance. Draw a line between the two points, divide the line in half, and put a half circle on each each of the two segments. The combined length of half circles is pi/2, not 1. Keep subdividing, and the error in the length does not decrease.

The math message is that to get accurate convergence, the error in what you are trying to measure (e.g. distance) must go to zero, not some other metric (e.g. furthest distance).
AlbinoBunny
Posts: 3,781
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 11:01:57 AM
Posted: 3 years ago
At 5/27/2013 10:15:41 AM, RoyLatham wrote:
Look at the first approximation. The approximated circumference is 4, while the actual circumference is pi. As the steps are taken to make the approximate circumference "closer" to the real circumference, the error is not actually reduced because while the distance of the farthest point from the circle is reduced, the length of the approximating figure is not reduced.

The same type of "proof" can be set up to show that two points one-unit apart is more than their true distance. Draw a line between the two points, divide the line in half, and put a half circle on each each of the two segments. The combined length of half circles is pi/2, not 1. Keep subdividing, and the error in the length does not decrease.

The math message is that to get accurate convergence, the error in what you are trying to measure (e.g. distance) must go to zero, not some other metric (e.g. furthest distance).

I don't understand what's happening, but when I do, I'll return and study this (seemingly) valuable perspective. I'm sure I won't be disappointed.
bladerunner060 | bsh1 , 2014! Presidency campaign!

http://www.debate.org...
http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

May the best man win!
drafterman
Posts: 18,870
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 12:29:51 PM
Posted: 3 years ago
At 5/27/2013 8:48:20 AM, Eitan_Zohar wrote:
At 5/27/2013 6:48:52 AM, muzebreak wrote:
At 5/27/2013 6:47:45 AM, Eitan_Zohar wrote:
At 5/27/2013 6:38:16 AM, muzebreak wrote:
Why is this in the philosophy section?

Philosophy is close to math. Besides, you have a better idea?

miscellaneous

....................../""/)
....................,/"../
.................../..../
............./""/'...'/"""`""
........../'/.../..../......./""\
........('(..."...".... "~/'...')
.........\.................'...../
..........'...\.......... _.""
............\..............(
..............\.............\...

Anyone have something constructive or relevant to say?

Yes, the limit of that series is not the circumference of the circle.
TheElderScroll
Posts: 643
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 2:02:56 PM
Posted: 3 years ago
At 5/27/2013 6:47:45 AM, Eitan_Zohar wrote:
At 5/27/2013 6:38:16 AM, muzebreak wrote:
Why is this in the philosophy section?

Philosophy is close to math. Besides, you have a better idea?

Science perhaps? Math is said to the queen of science.
AlbinoBunny
Posts: 3,781
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 2:06:22 PM
Posted: 3 years ago
Worked it out. In reality, you'll have billions of lines on the surface of the circle going out and then back to the surface repeatedly. If the lengths are in meters, this will add just over 858.407 mm to the circumference.
bladerunner060 | bsh1 , 2014! Presidency campaign!

http://www.debate.org...
http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

May the best man win!
medv4380
Posts: 200
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 4:55:18 PM
Posted: 3 years ago
At 5/27/2013 6:34:44 AM, Eitan_Zohar wrote:
I debunk an age-old mathematical theorem.

No one cares.

Maybe you should learn to show your actual work. I've done the same thing using a polygon on the inside and pi definitely doesn't equal 4.
Lordknukle
Posts: 12,788
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 5:30:59 PM
Posted: 3 years ago
How exactly do you repeat something an infinite amount of times? Hmm?
"Easy is the descent to Avernus, for the door to the Underworld lies upon both day and night. But to retrace your steps and return to the breezes above- that's the task, that's the toil."
Eitan_Zohar
Posts: 2,697
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 8:49:54 PM
Posted: 3 years ago
At 5/27/2013 5:30:59 PM, Lordknukle wrote:
How exactly do you repeat something an infinite amount of times? Hmm?

You'll have to ask the guy who made it. Besides, math doesn't deal in things that are strictly metaphysically possible.

Anyway, this is where I got it from: http://qntm.org...
"It is my ambition to say in ten sentences what others say in a whole book."
ConservativePolitico
Posts: 8,210
Add as Friend
Challenge to a Debate
Send a Message
5/27/2013 9:05:10 PM
Posted: 3 years ago
At 5/27/2013 8:49:54 PM, Eitan_Zohar wrote:
At 5/27/2013 5:30:59 PM, Lordknukle wrote:
How exactly do you repeat something an infinite amount of times? Hmm?

You'll have to ask the guy who made it. Besides, math doesn't deal in things that are strictly metaphysically possible.

Anyway, this is where I got it from: http://qntm.org...

The issue here is the poster's misunderstanding of limits and series...
AlbinoBunny
Posts: 3,781
Add as Friend
Challenge to a Debate
Send a Message
5/28/2013 7:14:59 AM
Posted: 3 years ago
At 5/27/2013 9:05:10 PM, ConservativePolitico wrote:
At 5/27/2013 8:49:54 PM, Eitan_Zohar wrote:
At 5/27/2013 5:30:59 PM, Lordknukle wrote:
How exactly do you repeat something an infinite amount of times? Hmm?

You'll have to ask the guy who made it. Besides, math doesn't deal in things that are strictly metaphysically possible.

Anyway, this is where I got it from: http://qntm.org...

The issue here is the poster's misunderstanding of limits and series...

Divide by 0?
bladerunner060 | bsh1 , 2014! Presidency campaign!

http://www.debate.org...
http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

May the best man win!
medv4380
Posts: 200
Add as Friend
Challenge to a Debate
Send a Message
5/28/2013 10:44:44 AM
Posted: 3 years ago
At 5/28/2013 7:14:59 AM, AlbinoBunny wrote:
At 5/27/2013 9:05:10 PM, ConservativePolitico wrote:
At 5/27/2013 8:49:54 PM, Eitan_Zohar wrote:
At 5/27/2013 5:30:59 PM, Lordknukle wrote:
How exactly do you repeat something an infinite amount of times? Hmm?

You'll have to ask the guy who made it. Besides, math doesn't deal in things that are strictly metaphysically possible.

Anyway, this is where I got it from: http://qntm.org...

The issue here is the poster's misunderstanding of limits and series...

Divide by 0?

Placing a circle in a square defines the upper limit of pi at 4. Placing a pentagram inside the circle establishes the lower limit of pi at 3.

Because he didn't show his work he can't prove he's right through an alternate method. I'd use Area. If he was right then using the area to show what Pi is would also be 4. However, it wont be because the area is decreasing at each step, and is approaching the area of a circle.

Chucking away squares might look right, but it isn't. If he had used triangles it would have worked. The problem is his 90 degree angle isn't approaching the angle of the circle. Even at infinite he'd be left with an infinite number of 90 degree angles, and that isn't a circle, but because of his error it will never actually meet the area of the circle at infinite. Just slightly larger than that.

When you use a triangle properly the angle of the triangles changes each time. At infinite you have a triangle with the angles at 90, 90, and 0. Which is a line, and not a triangle anymore. All a circle is, is a line extended at the radius and used to create a infinite number of points at the distance away from the radius.
Sidewalker
Posts: 3,713
Add as Friend
Challenge to a Debate
Send a Message
5/28/2013 1:26:13 PM
Posted: 3 years ago
At 5/27/2013 8:49:54 PM, Eitan_Zohar wrote:
At 5/27/2013 5:30:59 PM, Lordknukle wrote:
How exactly do you repeat something an infinite amount of times? Hmm?

You'll have to ask the guy who made it. Besides, math doesn't deal in things that are strictly metaphysically possible.

Math doesn't deal in bad geometry or "proofs" with false reasoning either. Drawing a square around a circle and then removing corners an infinite number of times doesn't change the fact that you are applying the limit calculations to the circumference of the square, not the circumference of the circle.

There's a reason t's called "Troll" Pi.

Anyway, this is where I got it from: http://qntm.org...
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
AlbinoBunny
Posts: 3,781
Add as Friend
Challenge to a Debate
Send a Message
5/28/2013 2:19:20 PM
Posted: 3 years ago
At 5/28/2013 10:44:44 AM, medv4380 wrote:

Placing a circle in a square defines the upper limit of pi at 4. Placing a pentagram inside the circle establishes the lower limit of pi at 3.

Because he didn't show his work he can't prove he's right through an alternate method. I'd use Area. If he was right then using the area to show what Pi is would also be 4. However, it wont be because the area is decreasing at each step, and is approaching the area of a circle.

Chucking away squares might look right, but it isn't. If he had used triangles it would have worked. The problem is his 90 degree angle isn't approaching the angle of the circle. Even at infinite he'd be left with an infinite number of 90 degree angles, and that isn't a circle, but because of his error it will never actually meet the area of the circle at infinite. Just slightly larger than that.

When you use a triangle properly the angle of the triangles changes each time. At infinite you have a triangle with the angles at 90, 90, and 0. Which is a line, and not a triangle anymore. All a circle is, is a line extended at the radius and used to create a infinite number of points at the distance away from the radius.

The area might decrease, but the circumference doesn't. I know it would be lines going in and out, many of them, which would add to the circumference. You could say something similar about a perfect cube. You can take little cubes out of it and increase the surface area, but decrease the volume. In this case, the closer the line gets to the circle, the more in and out lines there are. It might get incredibly close to the circle, but there'd also be incredibly many "bumps".

And as usual infinity makes no sense, parallel lines never meet, and infinity never ends, so where do parallel lines meet? :P
bladerunner060 | bsh1 , 2014! Presidency campaign!

http://www.debate.org...
http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

May the best man win!
medv4380
Posts: 200
Add as Friend
Challenge to a Debate
Send a Message
5/28/2013 2:43:52 PM
Posted: 3 years ago
At 5/28/2013 2:19:20 PM, AlbinoBunny wrote:
And as usual infinity makes no sense, parallel lines never meet, and infinity never ends, so where do parallel lines meet? :P

At the north and south pole.
RoyLatham
Posts: 4,488
Add as Friend
Challenge to a Debate
Send a Message
5/30/2013 1:23:40 PM
Posted: 3 years ago
I addressed this in detail in another thread. The error in the "proof" is that it uses the infinite sequence to converge on the area of the circle while not converging on the circumference of the circle. A similar pseudo-proof can be used to "prove" that a straight line is longer than it really is. to converge on the correct answer, the error in the desired quantity, not some other quantity.
1Devilsadvocate
Posts: 1,518
Add as Friend
Challenge to a Debate
Send a Message
5/30/2013 3:11:39 PM
Posted: 3 years ago
Roy nailed it. I especially liked the comparison to using semi circles to measure a strait line.

I would add another way of looking at it is as follows:
What is attempting to be done here is reduce the distance from the outer figure to circle this is being done breaking up the corner an infinite number of times thus reducing the distance. The problem is that the actual combined area of the space remains the same, it's just divided up into an infinite number of spaces. so you end up with an infinitely small distance, but you have an infinity of them, thus they cancel out, and nothing has been accomplished.

Another way of looking at it is, that what is attempting to be done is reduce the excess perimeter of the square by reducing the distance that the "square" moves away from the circle, again this is being done successfully, but the problem is that it is done an infinite number of times, thus canceling out any change in perimeter.

Basically, it all boils down to the fact that the shortest path between 2 points is a strait line. Instead of getting trying to get closer to the square by creating an infinite number of these "^", which creates a lot of little excess space/perimeter & accomplishes nothing, we need an infinite number of infinitely small strait lines, which cuts the excess perimeter/area of space in between, which will get PI.
I hope this is somewhat understandable, it's easier to explain graphically.
& I really should get off here and study for my Calc. final.
I cannot write in English, because of the treacherous spelling. When I am reading, I only hear it and am unable to remember what the written word looks like."
"Albert Einstein

http://www.twainquotes.com... , http://thewritecorner.wordpress.com... , http://www.onlinecollegecourses.com...
AlbinoBunny
Posts: 3,781
Add as Friend
Challenge to a Debate
Send a Message
5/30/2013 6:17:06 PM
Posted: 3 years ago
So basically infinity is giving us the finger, as usual.
bladerunner060 | bsh1 , 2014! Presidency campaign!

http://www.debate.org...
http://www.debate.org... - Running for president.
http://www.debate.org... - Running as his vice president.

May the best man win!
wiploc
Posts: 1,485
Add as Friend
Challenge to a Debate
Send a Message
6/2/2013 9:46:23 AM
Posted: 3 years ago
At 5/27/2013 6:34:44 AM, Eitan_Zohar wrote:
I debunk an age-old mathematical theorem.

No one cares.

It is polite to make it clear what your topic is in the thread title. Failing that, you should make your subject clear in the opening post. Failing that, yes, no one cares.
v3nesl
Posts: 4,505
Add as Friend
Challenge to a Debate
Send a Message
6/4/2013 12:00:34 PM
Posted: 3 years ago
At 5/27/2013 5:30:59 PM, Lordknukle wrote:
How exactly do you repeat something an infinite amount of times? Hmm?

Well, that is the basis of calculus. To get the area under a curve, for instance, you sum an infinite number of rectangles (bordering on the curve) of infinitely small width. So the 'proof' is a clever take off on that technique. I wonder, can the final step "repeat to infinity" be expressed as an equation? Can there be a formula for all squares as number-of-squares approaches infinity?

Escher would be proud, I bet. Fun stuff.
This space for rent.