paradox
https://plus.maths.org/content/taxonomy/term/706
enVisual curiosities and mathematical paradoxes
https://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="https://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="https://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes" target="_blank">read more</a></p>https://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 https://plus.maths.org/contentAll about averages
https://plus.maths.org/content/all-about-averages
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Andrew Stickland </div>
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Did you know that you can't average averages? Or that Paris is rainier than London ... but it rains more in London than in Paris? <b>Andrew Stickland</b> explores the dangers that face the unwary when using a single number to summarise complex data. </div>
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<div class="pub_date">January 2005</div>
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<p>Another rainy day in London</p><p><a href="https://plus.maths.org/content/all-about-averages" target="_blank">read more</a></p>https://plus.maths.org/content/all-about-averages#comments33averagecorrelationmeanmedianoutlierparadoxprobabilitySimpson's ParadoxstatisticsSat, 01 Jan 2005 00:00:00 +0000plusadmin2261 at https://plus.maths.org/contentA postcard from Italy
https://plus.maths.org/content/postcard-italy
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Eugen Jost </div>
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<strong>Eugen Jost</strong> is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it. </div>
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<div class="pub_date">September 1999</div>
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<p><em><a href="http://www.datacomm.ch/jostechk/">Eugen Jost</a> is a Swiss artist, born in Zürich, whose work is strongly influenced by mathematics.</em></p>
<p><em>His early career was a technical one: after taking an apprenticeship with Siemens-Albis Telecommunications and working as a technical designer at Bobst et fils in Lausanne, he went on to Teacher Training College in Bern, later becoming a teacher and an instructor in Matten/Interlaken and Spiez.</em></p><p><a href="https://plus.maths.org/content/postcard-italy" target="_blank">read more</a></p>https://plus.maths.org/content/postcard-italy#comments9Fibonacci numberinfinitypalindromeparadoxpuzzlesundialsymmetrytrigonometryTue, 31 Aug 1999 23:00:00 +0000plusadmin2390 at https://plus.maths.org/contentThe origins of proof III: Proof and puzzles through the ages
https://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages
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Jon Walthoe </div>
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For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. <strong>Jon Walthoe</strong> explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems. </div>
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<div class="pub_date">September 1999</div>
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<p>In the Millennia since Euclid, people's conceptions of mathematical proof have been revolutionised. From the discovery of Calculus and the rise of abstract mathematics, to Gödel's amazing discovery. There have been many changes and a few surprises along the way.</p><p><a href="https://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages" target="_blank">read more</a></p>https://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages#comments9axiomcalculusdeductionGödel's Incompleteness Theoreminductionirrational numberparadoxproofrational numberRussell's ParadoxTue, 31 Aug 1999 23:00:00 +0000plusadmin2394 at https://plus.maths.org/content