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Latest news from Plus magazine! - http://plus.maths.org In this newsletter: * Latest news - cut your cake and eat it too * Browse with Plus - the sound of mathematics * Mathematical moments - the mathematical Bernoullis * Live maths - maths meets music ********** Latest news Better ways to cut a cake The maths of fair division http://plus.maths.org/latestnews/sep-dec06/sharing/index.html Travel-time maps - transforming our view of transport A new way to use old data can help you assess your travel options http://plus.maths.org/latestnews/sep-dec06/traveltime/index.html Body count A statistical study into Iraq war deaths sparks controversy http://plus.maths.org/latestnews/sep-dec06/iraq/index.html Plus ... more news from the world of maths in the Plus blog Plus new writers award - the entries are in! http://plus.maths.org/blog/index.html ********** Browse with Plus The Sound of Mathematics - Plus has long been interested in the interplay between mathematics and music, but now we have had the pleasure of listening to it. Daniel Cummerow's site is filled with fantastic examples of "algorithmic music determined by mathematics and the musical preferences of a human". The current featured piece, "pi - four parts in A harmonic minor", is very lovely and reminiscent of a classical harpsichord work, while "The Sierpinski Triangle" is more ambient in sound. The pieces are based on some well-known and some more obscure mathematical constants, functions and sequences, and are accompanied by Daniel's explanations on how he translated the mathematics into music. http://www.geocities.com/Vienna/9349/ And you can read more about music and maths on Plus: http://plus.maths.org/indices/keyword_urls.html#MATHEMATICS%20AND%20MUSIC ********** Mathematical moments The Mathematical Bernoullis from Basle Brothers Jacob I (1654-1705) and Johann I (1667-1748) Their nephew Nikolaus I (1687-1759) Johann's sons Nikolaus II (1695-1726), Daniel (1700-1782) and Johann II (1710-1790) And Johann II's sons Johann III (1744-1807) and Jacob II (1759-1789) The famous mathematical family, the Bernoullis, produced an astounding eight mathematicians over three generations. The sheer number of them, and the family habit of using the same first names, required the numbering system you see above to keep track of them all. And given the family's mathematical success, you would think that each generation was actively encouraged to study the subject. But instead the mathematical members of the family often had to study mathematics and astronomy against the wishes of their parents. Indeed there were enough quarrels, backstabbing and even untimely deaths among the Bernoullis to script a soap opera. Jacob (I) Bernoulli was the first member of the family to study maths, and taught his brother Johann (I) who had been forced to study medicine. The brothers worked on similar topics, such as calculus (Jacob was the first mathematician to use the term 'integral') and studying families of curves such as the catenary, the curve of a suspended string. However, in what would prove to be typical behaviour in the family, the brothers soon went from collaborators to rivals, publicly criticising each other's intellect and competing to solve the same mathematical problems. Jacob and Johann taught their nephew, Nikolaus I, mathematics, and Nikolaus assisted his uncle, Jacob, in publishing his works. Nikolaus is known for posing the probability problem the "St Petersburg paradox", which describes a gambling game that no-one would reasonably play, despite a possibly infinite prize. Nikolaus's cousin Daniel (son of Johann) provided an explanation of the St Petersburg paradox. Daniel, probably the most famous mathematician of the family, did his most important work on fluid dynamics, and gave the Bernoulli principle. However, continuing the family's bitter history, Daniel had a difficult relationship with his father Johann, who did not want him as a mathematical competitor. Johann tried to stop Daniel from studying mathematics, and even attempted to plagiarise Daniel's greatest work, "Hydrodynamica". Johann I's other two sons were also mathematicians. His favourite Nikolaus II worked on the problem of trajectories, and the mathematical arguments behind Newton and Leibniz's dispute over who had invented calculus. Johann II worked in mathematical physics. Johann II also had two mathematical sons. Johann III was a child prodigy, and was just 19 years old when he was appointed to the Berlin Academy. He produced work in astronomy and probability, but his accounts of his travels in Germany had a greater impact historically. Jacob II worked on mathematical physics at the St Petersburg Academy of Sciences, and married Euler's granddaughter. Sadly he drowned in the Neva River when he was only 29 years old. The Bernoulli family, despite its infighting and bitterness, dominated mathematics in the 17th and 18th centuries. Together with their contemporaries Newton, Leibniz, Euler and Lagrange, they laid many of the foundations of mathematics and physics that we still use today. "There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician." - Daniel Bernoulli Read more about the Bernoulli clan in: MacTutor History of Mathematics Archive... http: //www-history.mcs.st-andrews.ac.uk/history/Biographies/Bernoulli_Jacob.html http: //www-history.mcs.st-andrews.ac.uk/history/Biographies/Bernoulli_Johann.html http: //www-history.mcs.st-andrews.ac.uk/history/Biographies/Bernoulli_Daniel.html And about the Bernoullis, the St Petersburg Paradox and the Bernoulli principle on Plus... http: //plus.maths.org/issue22/xfile/index.html http: //plus.maths.org/issue1/bern/index.html http: //plus.maths.org/issue1/turb/ http: //plus.maths.org/issue2/bottle/index.html ********** Live maths YEA, WHY TRY HER RAW WET HAT? - Due to overwhelming demand, Robin Wilson's lecture at the 2006 Cambridge Music Festival is being repeated. This illustrated lecture features music ranging from Tallis and Bach to Bartok and Hindemith, and answers such questions as: Why are pianos always out of tune? Can music have a 'geometry'? Why are there seven colours in the rainbow? and What is the meaning of the title of this talk? When: Thursday 16th November 2006, 2.30 - 3.30 pm Where: Centre for Mathematical Sciences, Clarkson Road, Cambridge Tickets: For tickets and more information visit the festival website, http://www.cammusic.co.uk/ The Poincare Conjecture on BBC Radio 4 Last week, Melvyn Bragg teamed up with mathematicians Ian Steward, Marcus de Sautoy and June Barrow-Green on his programme In Our Time to discuss Henri Poincare and his famous conjecture which is now, it seems, a theorem. You can listen to the episode on the BBC website http://www.bbc.co.uk/radio4/history/inourtime/inourtime.shtml Happy reading from the Plus team! ********** If you received this message you have subscribed yourself to the PLUS-ANNOUNCE mailing list via our website. If you do not wish to remain on the list please visit http://www.jiscmail.ac.uk/cgi-bin/wa.exe?SUBED1=plus-announce&A=1 and follow the instructions to leave the list. If you have any comments on this newsletter, or Plus Magazine, please contact us at [log in to unmask] - we are always happy to hear from our readers! Feel free to forward this email to anyone you think might be interested.