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024 7 $a10.1007/978-3-0348-0554-4
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100   $a20131127d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aLooking at Numbers /$fby Tom Johnson, Franck Jedrzejewski
205   $a1st ed. 2014.
210  1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014.
215   $a1 online resource (126 p.)
300   $aDescription based upon print version of record.
311   $a3-0348-0553-5 
320   $aIncludes bibliographical references and index.
327   $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.
330   $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.
606   $aGraph theory
606   $aMathematics
606   $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020
606   $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009
606   $aMathematics in Music$3https://scigraph.springernature.com/ontologies/product-market-codes/M33000
615  0$aGraph theory.
615  0$aMathematics.
615 14$aGraph Theory.
615 24$aMathematics, general.
615 24$aMathematics in Music.
676   $a513.5
700   $aJohnson$b Tom$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721690
702   $aJedrzejewski$b Franck$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910768441703321
996   $aLooking at Numbers$93658079
997   $aUNINA