Banach-Tarski paradox
http://plus.maths.org/content/taxonomy/term/458
enVisual curiosities and mathematical paradoxes
http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes
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Linda Becerra and Ron Barnes </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/21%20Oct%202010%20-%2016%3A38/icon.jpg?1287675519" /> </div>
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<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.</p>
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<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions; appear to be true but in actual fact are self-contradictory; or appear contradictory, even absurd, but in fact may be true. Here again it is up to your brain to make sense of these situations. Again, your brain may get it wrong. These situations are referred to as paradoxes.<p><a href="http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes" target="_blank">read more</a></p>http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes#commentsarchitectureBanach-Tarski paradoxBarber's Paradoxeschergeometryimpossible objectoptical illusionparadoxPenrose staircasePenrose triangleperspectiveRussell's ParadoxWed, 17 Nov 2010 14:06:13 +0000mf3445337 at http://plus.maths.org/contentMeasure for measure
http://plus.maths.org/content/measure-measure
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Andrew Davies </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/issue17/features/measure/icon.jpg?975628800" /> </div>
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Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. <strong>Andrew Davies</strong> gives us an introduction to Measure Theory. </div>
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<div class="pub_date">Nov 2001</div>
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<h3>Measure for Measure, or, How to make a carpet out of nothing.</h3>
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<h3>"How long is a piece of string?" [<a href="#quote1">1</a>]</h3>
<p>As long as you want it to be, of course! But when someone has asked that, either as a joke or to make a point in a conversation, did you ever stop to think that you were taking something very important for granted? Was it a question that worried you? Are you sure?</p><p><a href="http://plus.maths.org/content/measure-measure" target="_blank">read more</a></p>http://plus.maths.org/content/measure-measure#comments17Banach-Tarski paradoxCantor dustCantor setfractalLebesgue integrationmeasurabilitymeasure theoryRiemann integrationSierpinski's CarpetFri, 01 Dec 2000 00:00:00 +0000plusadmin2192 at http://plus.maths.org/content