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020 _a9783034805544
_9978-3-0348-0554-4
024 7 _a10.1007/978-3-0348-0554-4
_2doi
035 _ato000541794
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA166-166.247
072 7 _aPBV
_2bicssc
072 7 _aMAT013000
_2bisacsh
082 0 4 _a511.5
_223
100 1 _aJohnson, Tom.
_eauthor.
_9447657
245 1 0 _aLooking at Numbers
_helectronic resource
_cby Tom Johnson, Franck Jedrzejewski.
260 _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
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.
_9566183
650 1 4 _aMathematics.
_9566184
650 2 4 _aGraph Theory.
_9412136
650 2 4 _aMathematics, general.
_9304764
650 2 4 _aMathematics in Music.
_9445568
700 1 _aJedrzejewski, Franck.
_eauthor.
_9318850
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0554-4
912 _aZDB-2-SMA
999 _c399717