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
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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
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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
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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
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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!
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