Pi explained • Hacker News Board

Re: Pi explained

#21

Post by ars » Fri, Jun 17, 2011, 11:23 PM UTC

fexl wrote: post #19

joejohnson wrote: post #13

Earlier quoted context omitted.

I think something could be two units long. Two is discrete, and at a microscopic level, things can be exactly discrete values (i.e. two angstroms...). I think asking if something could be exactly pi long is a different question.

Yeah I gotta think about that one. If we assume that there is some smallest discrete base unit of space (which I think is plausible), then all string lengths could only be some integer multiple of that base unit. Therefore length pi is out of the question. Now presumably 1 meter will be equivalent to some integer multiple of base units, though that may turn out not to be the case. Perhaps the current definition of a…

See my reply here: http://news.ycombinator.com/item?id=2667461

There is no discrete base unit of space, and on top of that objects do not have determinate sizes.

Re: Pi explained

#22

Post by chrisedge » Fri, Jun 17, 2011, 11:26 PM UTC

hugh3 wrote: post #2

While I doubt this would actually explain pi to anyone who didn't already understand it, it is nonetheless kinda neat.

I agree that it is very neat and could be used for students that just can't quite grasp the concept of what pi really means. One of my teachers used something very similar to this to explain pi to students that did not quite understand the textbook definition.

Re: Pi explained

#23

Post by petercooper » Fri, Jun 17, 2011, 11:40 PM UTC

You can also calculate pi by throwing frozen hot dogs: http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-D...

Re: Pi explained

#24

Post by grannyg00se » Sat, Jun 18, 2011, 12:11 AM UTC

grantismo wrote: post #14

ianterrell wrote: post #11

Pi is the wrong constant. That animation looks great, but it's misleading: the fundamental measurement of the circle is the radius, not the diameter. Measured with a unit radius, we'd see 2*pi for a full "turn" of the wheel. Twice pi, or tau, is the magic number. See http://tauday.com/ for details.

>Pi is the wrong constant. Seems a bit pedantic. The post was about illustrating pi after all. I do enjoy the argument for tau though.

Actually I found that the animation showed a clear example demonstrating that pi is wrong. I don't know about you, but when I looked at it I immediately recognized the blue arrow and the centre of the wheel. That's a radius. There's no easy way to determine that a diameter was in the picture. As it rolls over the circumference, it's the radius line we follow. Therefore, I agree that pi is truly the wrong constant to show here. And it is wrong in a greater sense than what is presented at tauday. It's actually downright confusing or even misleading to highlight a radius and a circumference, and then talk about pi.

Re: Pi explained

#25

Post by jerf » Sat, Jun 18, 2011, 12:37 AM UTC

granite_scones wrote: post #16

phillmv wrote: post #8

Earlier quoted context omitted.

Sure. Take any circle made with a piece of string and declare it to be your reference unit circle. Blammo! Its diameter is 1 and its length is now pi ;).

That just pushes the problem back to whether perfect circles can exist in reality.

In which case, problem solved: They can't.

Re: Pi explained

#26

Post by tschill » Sat, Jun 18, 2011, 1:24 AM UTC

Kinda neat. But I was always more intrigued by the Monte Carlo approximation for thinking about pi. http://www.eveandersson.com/pi/monte-carlo-demo. Although it does take alot of iterations to converge to a decent estimate of pi.

Re: Pi explained

#27

Post by eternalmatt » Sat, Jun 18, 2011, 1:43 AM UTC

jerf wrote: post #25

granite_scones wrote: post #16

Earlier quoted context omitted.

That just pushes the problem back to whether perfect circles can exist in reality.

In which case, problem solved: They can't.

And neither can perfectly straight lines.

Re: Pi explained

#28

Post by DannoHung » Sat, Jun 18, 2011, 2:44 AM UTC

ianterrell wrote: post #11

Pi is the wrong constant. That animation looks great, but it's misleading: the fundamental measurement of the circle is the radius, not the diameter. Measured with a unit radius, we'd see 2*pi for a full "turn" of the wheel. Twice pi, or tau, is the magic number. See http://tauday.com/ for details.

Pi is the right unit because it represents the largest irreducible radian size. It is the fundamental unit of 2 dimensional angles.

Re: Pi explained

#29

Post by 16BitTons » Sat, Jun 18, 2011, 3:22 AM UTC

m_myers wrote: post #6

Next question: Is it possible for a piece of string to be pi units long? How do transcendental numbers translate to the real world?

Transcendental numbers translate into the real world just as well as any other Real number.[1]

You can't fabricate a string that is exactly Pi long anymore than you can fabricate a string that is exactly One long. But you can get as close to a transcendental number as you can to an algebraic number.

[1] I'm ignoring the trivial case.

Re: Pi explained

#30

Post by fexl » Sat, Jun 18, 2011, 3:23 AM UTC

ars wrote: post #21

fexl wrote: post #19

Earlier quoted context omitted.

Yeah I gotta think about that one. If we assume that there is some smallest discrete base unit of space (which I think is plausible), then all string lengths could only be some integer multiple of that base unit. Therefore length pi is out of the question. Now presumably 1 meter will be equivalent to some integer multiple of base units, though that may turn out not to be the case. Perhaps the current definition of a…

See my reply here: http://news.ycombinator.com/item?id=2667461 There is no discrete base unit of space, and on top of that objects do not have determinate sizes.

I was just taking the gambit and running with it. Certainly when you start zeroing in on the end of the string, things start to get very fuzzy indeed.