000			03164nam a22004335i 4500
001			978-3-0348-0554-4
003			DE-He213
005			20140220082506.0
007			cr nn 008mamaa
008			131127s2014 sz | s |||| 0|eng d
020			_a9783034805544 _9978-3-0348-0554-4
024	7		_a10.1007/978-3-0348-0554-4 _2doi
050		4	_aQA166-166.247
072		7	_aPBV _2bicssc
072		7	_aMAT013000 _2bisacsh
082	0	4	_a511.5 _223
100	1		_aJohnson, Tom. _eauthor.
245	1	0	_aLooking at Numbers _h[electronic resource] / _cby Tom Johnson, Franck Jedrzejewski.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2014.
300			_aXVII, 120 p. 139 illus., 1 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aIntroduction -- 1. Permutations -- 1.1 Symmetric Group -- 1.2 Bruhat Order -- 1.3 Euler Characteristic -- 1.4 Group Action -- 1.5 Permutohedra and Cayley Graphs -- 1.6 Coxeter Groups -- 1.7 Homometric Sets -- 2. Sums -- 2.1 Integer Partitions -- References -- 3. Subsets -- 3.1 Combinatorial Designs -- 4 Kirkman’s Ladies, a Combinatorial Design -- 4.1 Steiner and Kirkman Systems -- 5. Twelve -- 5.1 (12,4,3) -- 6. (9,4,3) -- 6.1 Decomposition of Block Designs -- 7. 55 Chords -- 7.1 Chords and Designs.-8. Clarinet Trio -- 8.1 Strange Fractal Sequences -- 9. Loops -- 9.1 Self-Replicating Melodies -- 9.2 Rhythmic Canons.-10. Juggling -- 10.1 Juggling, Groups, and Braids -- 11. Unclassified -- 11.1 Some Other Designs -- A Figures -- References.
520			_aGalileo Galilei said he was “reading the book of nature” as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and out of the hands of good jugglers. Numbers are, after all, a part of nature. As such, looking at and thinking about them is a way of understanding our relationship to nature. But when we do so in a technical, professional way, we tend to overlook their basic attributes, the things we can understand by simply “looking at numbers.” Tom Johnson is a composer who uses logic and mathematical models, such as combinatorics of numbers, in his music. The patterns he finds while “looking at numbers” can also be explored in drawings. This book focuses on such drawings, their beauty and their mathematical meaning. The accompanying comments were written in collaboration with the mathematician Franck Jedrzejewski.
650		0	_aMathematics.
650	1	4	_aMathematics.
650	2	4	_aGraph Theory.
650	2	4	_aMathematics, general.
650	2	4	_aMathematics in Music.
700	1		_aJedrzejewski, Franck. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034805537
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0554-4
912			_aZDB-2-SMA
999			_c92440 _d92440