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https://plus.maths.org/content/taxonomy/term/935
enExtracting beauty from chaos
https://plus.maths.org/content/extracting-beauty-chaos
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Andy Burbanks </div>
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<img class="imagefield imagefield-field_abs_img" width="110" height="110" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue9/features/lyapunov/icon.jpg?936140400" /> </div>
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Images based on Lyapunov Exponent fractals are very striking. <b>Andy Burbanks</b> explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos <em>really</em> is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics. </div>
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<div class="pub_date">September 1999</div>
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<p>There are any number of sites on the World Wide Web dedicated to galleries of computer-generated fractal images. Pictures based on Lyapunov Exponent fractals, such as the one pictured above, are some of the most striking and unusual.</p><p><a href="https://plus.maths.org/content/extracting-beauty-chaos" target="_blank">read more</a></p>https://plus.maths.org/content/extracting-beauty-chaos#comments9bifurcationchaosdynamical systemerrorfractaliterationlogistic mapLyapunov Exponentmathematics and artorbitTue, 31 Aug 1999 23:00:00 +0000plusadmin2392 at https://plus.maths.org/contentThe origins of proof II : Kepler's proofs
https://plus.maths.org/content/origins-proof-ii-keplers-proofs
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J.V. Field </div>
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<img class="imagefield imagefield-field_abs_img" width="109" height="110" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue8/features/proof2/icon.jpg?925513200" /> </div>
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Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. <b>J.V. Field</b> continues our series on the origins of proof with an examination of Kepler's astronomy. </div>
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<div class="pub_date">May 1999</div>
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<p>As we explained in <a href="/issue7/features/proof1/index.html">The Origins of Proof, Part I</a> in <a href="https://plus.maths.org/content/issue/7">Issue 7</a> of PASS Maths, the concept of a "proof" was developed in the field of geometry by the Greeks. The Pythagoreans and Euclid were among the mathematicians who developed the idea of abstract deduction. But during the Renaissance the philosophy
of nature increasingly came to rely upon mathematics to help to explain the Universe and its workings.</p><p><a href="https://plus.maths.org/content/origins-proof-ii-keplers-proofs" target="_blank">read more</a></p>https://plus.maths.org/content/origins-proof-ii-keplers-proofs#comments8astronomyellipseerrorgeometrygravityhistory of mathematicsKepler's three laws of planetary motionproofFri, 30 Apr 1999 23:00:00 +0000plusadmin2389 at https://plus.maths.org/content