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PhantomTurkey

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I don't understand what about that is meant to be paradoxical? It fits into standard logic.

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I was wondering the same thing :scratchhead:

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just a page i came across on stumbleupon - called the paradox of the infinite circle - heres the link - easier than copy-pasting or translating into my own words !

http://www.stumbleupon.com/su/2hSU3W/www.ponderabout.com/archives/706/the-paradox-of-the-infinite-circle/

( isnt it a paradox to say if an infinitely large circle was constructed from a straight line it could not possibly form a circle - then again on second thoughts perhaps i am wrong :P - it happens :) ? )

Edited by tipz

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There are a couple of obvious fallacies there. Firstly, if the problem with a circle of infinite radius is that a circle has no ends but a straight line does, then the simple response to that is that an infinite straight line also has no ends. The other fallacy is with the concept of infinity. This holds even if you don't buy the first explanation. When mathematicians say "at infinity", they actually mean "the limit as (insert variable) approaches infinity". Infinity is not a point in itself. It is only something that can be approached. So if you take a circle and increase its radius towards infinity, its curvature will approach zero. If you stop increasing the radius at some point, the curvature will still be greater than zero. But if you choose an arbitrarily large radius, you can always smoothly increase the radius to above that chosen. It is a limiting process.

Mathematically, one would say that the limit of 1/r as r approaches infinity is zero, where r is the radius and 1/r is the curvature.

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I think the biggest flaw in the "paradoxical circle" is that in point one from the link, we're discussing the "curvature of a given length of its circumference".

In the the final point, we seem to have totally forgotten that we were originally talking about a given length of the circle's circumference and now assume that the same thing that appears to happen to a "given length" will happen to the total circle.

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There are some chronically funny pictures in this thread.

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love the "wheres wally" one. mate that made my night haha

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1-jupiterbound.jpg

This image of Earth (on the left) and the moon (on the right) was taken by NASA's Juno spacecraft on Aug. 26, 2011, when the spacecraft was about 6 million miles (9.66 million kilometers) away. It was taken by the spacecraft's onboard camera, JunoCam. The solar-powered Juno spacecraft lifted off from Cape Canaveral Air Force Station in Florida on Aug. 5 to begin a five-year journey to Jupiter. Image credit: NASA/JPL-Caltech

Edited by qualia

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^^

that was part of a much bigger animation wasn't it? i remember seeing something very similar a few years ago, maybe it was in spain?

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i think you're thinking of blu

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cool vid...

Edited by Ulca

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^^

aye thats it. cool stuff that

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tumblr_ksnpi8BC6I1qz6f9yo1_500.jpg

b8799b5111fe3f24b6c724c587151d1edf3bfa78_m.jpg

629a9643dfd9cdca4dd1c5f6689ef18f40c78d0a_m.jpg

001d3332368db2113d3ff82f07b6a7155663fc3d_m.jpg

tumblr_l3eqyhMLTJ1qz9qooo1_500.jpg

yep definitely cross her out :rolleyes:

tumblr_l3k523rsTm1qz6f9yo1_500.jpg

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3ff5149c2cea9b09bc7a69d7539205f4475fd415_m.jpg

Edited by bulls on parade

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Yeah, good old David Thorne. :lol: Kates party was epic.

Edited by Evil Genius

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wow i just realised the person in the foreground is nowhere near the tree. that is one massive spider tree and i'm sure it has fueled some very productive spider runs. villages need a good supply of spiders because, among other reasons, children need lots of spider pie to grow up healthy.

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