12
https://plus.maths.org/content/issue/issue/12
en/issue12
https://plus.maths.org/content/issue12
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<span class="date-display-single">September 2000</span> </div>
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<p>In this issue Jim McElwaine explains how he combines his two passions, maths and mountaineering, into avalanche research. We also find out about applications of the harmonic series and how you should plan your finances for the future.</p>
12indexTue, 01 Jun 2010 12:21:27 +0000plusadmin5201 at https://plus.maths.org/contentDeath and statistics
https://plus.maths.org/content/death-and-statistics
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John Webb </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue12/features/annuities/icon.jpg?967762800" /> </div>
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Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. <strong>John Webb</strong> takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way. </div>
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<h2>Financial planning for the future</h2>
<p>With improving health, most of the population of Britain can expect to live many years after they take retirement from formal employment in their sixties. After that, they will have to live on a social security pension, or on a pension from their own investments and private pension funds. Planning for retirement is not usually top of somebody's list when they are starting their first job
straight out of school or university. But it is an important issue that cannot be ignored.<p><a href="https://plus.maths.org/content/death-and-statistics" target="_blank">read more</a></p>https://plus.maths.org/content/death-and-statistics#comments12actuarial mathematicsannuityarithmetic-geometric seriescompound interestmortality tablepensionprobabilityThu, 31 Aug 2000 23:00:00 +0000plusadmin2169 at https://plus.maths.org/contentFishy business
https://plus.maths.org/content/fishy-business
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John L. Casti </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue12/features/casti/icon.jpg?967762800" /> </div>
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'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.' <strong>John L. Casti</strong> tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the
shape of one organism to continuously transform it into other, physically similar organisms. </div>
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<p>Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers and what effect it would have had on the science of their times - and ours.<p><a href="https://plus.maths.org/content/fishy-business" target="_blank">read more</a></p>https://plus.maths.org/content/fishy-business#comments12catastrophe theorycomputer recognitionevolutioninvariant pointmathematics of growthThu, 31 Aug 2000 23:00:00 +0000plusadmin2170 at https://plus.maths.org/contentTake a break
https://plus.maths.org/content/take-break
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Emily Dixon </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="129" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue12/features/codes/icon.jpg?967762800" /> </div>
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There are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately. <strong>Emily Dixon</strong> takes a break and discovers that codes are not just for sleuths. </div>
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<div class="pub_date">September 2000</div>
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<p><a href="https://plus.maths.org/content/take-break" target="_blank">read more</a></p>https://plus.maths.org/content/take-break#comments12barcodeerror-correcting codeISBNmodular arithmeticnon-commutativitypermutationThu, 31 Aug 2000 23:00:00 +0000plusadmin2171 at https://plus.maths.org/contentIn perfect harmony
https://plus.maths.org/content/perfect-harmony
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John Webb </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue12/features/harmonic/icon.jpg?967762800" /> </div>
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The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. <b>John Webb</b> applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way. </div>
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<h2>Introduction</h2>
<p>Two elementary series are studied in school mathematics:</p>
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<li>arithmetic series, such as <img src="/MI/3e35c3a6a00638f7c180b293c8e21feb/images/img-0001.png" alt="$1+2+3+\dots +n$" style="vertical-align:-2px;
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<p>and</p><p><a href="https://plus.maths.org/content/perfect-harmony" target="_blank">read more</a></p>https://plus.maths.org/content/perfect-harmony#comments12arithmetic seriesconvergencedivergencegeometric seriesharmonic serieslogarithmThu, 31 Aug 2000 23:00:00 +0000plusadmin2172 at https://plus.maths.org/contentCareer interview: Avalanche researcher
https://plus.maths.org/content/career-interview-avalanche-researcher
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Danielle Stretch </div>
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<p><i>Plus</i> caught up with jet-lagged avalanche researcher, <a href="http://www%20duvel.lowtem.hokudai.ac.jp/~jim/index.html">Jim McElwaine</a>, who had just flown back from Japan to begin a new job in Cambridge. Jim completed a mathematics degree at <a href="http://www.cam.ac.uk">Cambridge University</a> and then went on to do research for a PhD in quantum mechanics.<p><a href="https://plus.maths.org/content/career-interview-avalanche-researcher" target="_blank">read more</a></p>https://plus.maths.org/content/career-interview-avalanche-researcher#comments12avalanchecareer interviewEnvironmentgranular flowmathematical modellingScience & EngineeringsimulationThu, 31 Aug 2000 23:00:00 +0000plusadmin2397 at https://plus.maths.org/contentPuzzle page
https://plus.maths.org/content/puzzle-page-2
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Solve the puzzle and eat the nuts! </div>
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<div class="pub_date">September 2000</div>
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<h2>Monkey Nut Puzzle</h2>
<p>Here's a seemingly simple challenge...</p>
<p>You have a chessboard, which can be as large as you like, and on the bottom left square there is a monkey-nut. All other squares are empty.</p>
<p>At any time, you may remove a monkey-nut, and replace it with two more: one on the square above the removed nut, and one on the square to the right of the removed nut. But only if both these squares are empty to start with.</p><p><a href="https://plus.maths.org/content/puzzle-page-2" target="_blank">read more</a></p>https://plus.maths.org/content/puzzle-page-2#comments12Thu, 31 Aug 2000 23:00:00 +0000plusadmin2837 at https://plus.maths.org/content'The Cogwheel Brain'
https://plus.maths.org/content/cogwheel-brain
<div class="pub_date">September 2000</div>
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<h2><a name="book3" id="book3"><i>The Cogwheel Brain: Charles Babbage and the quest to build the first computer</i></a></h2>
by Doron Swade<br />
<p>Reviewed by Helen Joyce</p>
<p><i>I wish to God these calculations had been executed by steam."</i></p><p><a href="https://plus.maths.org/content/cogwheel-brain" target="_blank">read more</a></p>https://plus.maths.org/content/cogwheel-brain#comments12book reviewThu, 31 Aug 2000 23:00:00 +0000plusadmin3294 at https://plus.maths.org/content'Ingenious Pursuits'
https://plus.maths.org/content/ingenious-pursuits
<div class="pub_date">September 2000</div>
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<h2><a name="book2" id="book2"><i>Ingenious Pursuits: Building the scientific revolution</i></a></h2>
by Lisa Jardine<br />
<p>Reviewed by Julia Hawkins (Millennium Mathematics Project)</p><p><a href="https://plus.maths.org/content/ingenious-pursuits" target="_blank">read more</a></p>https://plus.maths.org/content/ingenious-pursuits#comments12book reviewThu, 31 Aug 2000 23:00:00 +0000plusadmin3295 at https://plus.maths.org/content'The Maths Gene'
https://plus.maths.org/content/maths-gene
<div class="pub_date">September 2000</div>
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<h2><a name="book1" id="book1"><i>The Maths Gene: Why everyone has it, but most people don't use it</i></a></h2>
by Keith Devlin<br />
<p>Reviewed by Helen Joyce (Plus editorial team)</p><p><a href="https://plus.maths.org/content/maths-gene" target="_blank">read more</a></p>https://plus.maths.org/content/maths-gene#comments12book reviewThu, 31 Aug 2000 23:00:00 +0000plusadmin3296 at https://plus.maths.org/contentMathematical mysteries: The Solitaire Advance
https://plus.maths.org/content/mathematical-mysteries-solitaire-advance
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<p>Solitaire is a game played with pegs in a rectangular grid. A peg may jump horizontally or vertically, but not diagonally, over a peg in an adjacent square into a vacant square immediately beyond. The peg which was jumped over is then removed.</p>
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<div class="pub_date">September 2000</div>
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<p>Solitaire is a game played with pegs in a rectangular grid. A peg may jump horizontally or vertically, but not diagonally, over a peg in an adjacent square into a vacant square immediately beyond. The peg which was jumped over is then removed.</p><p><a href="https://plus.maths.org/content/mathematical-mysteries-solitaire-advance" target="_blank">read more</a></p>https://plus.maths.org/content/mathematical-mysteries-solitaire-advance#comments12Mathematical mysteriesThu, 31 Aug 2000 23:00:00 +0000plusadmin4745 at https://plus.maths.org/contentOpinion
https://plus.maths.org/content/opinion
<p><a href="https://plus.maths.org/content/opinion" target="_blank">read more</a></p>12editorialmathematics educationpublic image of mathematicsregression to the meanusefulness of mathematicsThu, 31 Aug 2000 23:00:00 +0000plusadmin4862 at https://plus.maths.org/contentLetters
https://plus.maths.org/content/letters-1
<p><a href="https://plus.maths.org/content/letters-1" target="_blank">read more</a></p>12editorialThu, 31 Aug 2000 23:00:00 +0000plusadmin4920 at https://plus.maths.org/contentHamming codes
https://plus.maths.org/content/hamming-codes
<p><a href="https://plus.maths.org/content/hamming-codes" target="_blank">read more</a></p>12editorialThu, 31 Aug 2000 23:00:00 +0000plusadmin4953 at https://plus.maths.org/contentPlus Magazine
https://plus.maths.org/content/plus-magazine-18
<p><a href="https://plus.maths.org/content/plus-magazine-18" target="_blank">read more</a></p>12editorialThu, 31 Aug 2000 23:00:00 +0000plusadmin5099 at https://plus.maths.org/content