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001			on1066741225
003			OCoLC
005			20220908100150.0
006			m o d
007			cr cnu|||unuuu
008			181121s2019 nju ob 001 0 eng d
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019			_a1096512940
020			_a9780691188997 _q(electronic bk.)
020			_a0691188998 _q(electronic bk.)
020			_z9780691181370
020			_z0691181373
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035			_a(OCoLC)1066741225 _z(OCoLC)1096512940
037			_a22573/ctv5rnhk3 _bJSTOR
037			_a9452377 _bIEEE
050		4	_aQA614.8 _b.S39 2019
050		4	_aQA853 _b.S39 2019
072		7	_aMAT _x039000 _2bisacsh
072		7	_aMAT _x023000 _2bisacsh
072		7	_aMAT _x026000 _2bisacsh
072		7	_aMAT _x012000 _2bisacsh
072		7	_aMAT _x022000 _2bisacsh
072		7	_aMAT _x036000 _2bisacsh
082	0	4	_a515/.39 _223
049			_aMAIN
100	1		_aSchwartz, Richard Evan, _eauthor. _965242
245	1	4	_aThe plaid model / _cRichard Evan Schwartz.
264		1	_aPrinceton, New Jersey : _bPrinceton University Press, _c[2019]
264		4	_c�2019
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aAnnals of mathematics studies ; _vNumber 198
504			_aIncludes bibliographical references and index.
588	0		_aVendor-supplied metadata.
505	0	0	_gFrontmatter -- Contents -- Preface -- Introduction -- Part 1. _tThe plaid model -- _gChapter 1. _tDefinition of the plaid model -- _gChapter 2. _tProperties of the model -- _gChapter 3. _tUsing the model -- _gChapter 4. _tParticles and spacetime diagrams -- _gChapter 5. _tThree-dimensional interpretation -- _gChapter 6. _tPixellation and curve turning -- _gChapter 7. _tConnection to the Truchet tile system -- _gPart 2. _tThe plaid PET -- _gChapter 8. _tThe plaid master picture theorem -- _gChapter 9. _tThe segment lemma -- _gChapter 10. _tThe vertical lemma -- _gChapter 11. _tThe horizontal lemma -- _gChapter 12. _tProof of the main result -- _gPart 3. _tThe graph PET -- _gChapter 13. _tGraph master picture theorem -- _gChapter 14. _tPinwheels and quarter turns -- _gChapter 15. _tQuarter turn compositions and PETs -- _gChapter 16. _tThe nature of the compactification -- _gPart 4. _tThe plaid-graph correspondence -- _gChapter 17. _tThe orbit equivalence theorem -- _gChapter 18. _tThe quasi-isomorphism theorem -- _gChapter 19. _tGeometry of the graph grid -- _gChapter 20. _tThe intertwining lemma -- _gPart 5. _tThe distribution of orbits -- _gChapter 21. _tExistence of infinite orbits -- _gChapter 22. _tExistence of many large orbits -- _gChapter 23. _tInfinite orbits revisited -- _gChapter 24. _tSome elementary number theory -- _gChapter 25. _tThe weak and strong case -- _gChapter 26. _tThe core case -- _gReferences -- Index.
520	8		_aOuter billiards provides a toy model for planetary motion and exhibits intricate and mysterious behaviour even for simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of billiards. 'The Plaid Model', which is a self-contained sequel to Schwartz's 'Outer Billiards on Kites', provides a combinatorial model for orbits of outer billiards on kites. The combinatorial model, called 'the plaid model', has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be very difficult to reach through traditional maths. The work includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.
590			_aIEEE _bIEEE Xplore Princeton University Press eBooks Library
650		0	_aDifferentiable dynamical systems. _920832
650		0	_aCombinatorial dynamics. _965243
650		0	_aGeometry. _921224
650		0	_aNumber theory. _913208
650		6	_aDynamique diff�erentiable. _963691
650		6	_aOrbites p�eriodiques (Math�ematiques) _965244
650		6	_aG�eom�etrie. _965245
650		6	_aTh�eorie des nombres. _964750
650		7	_ageometry. _2aat _921224
650		7	_aMATHEMATICS _xEssays. _2bisacsh _964120
650		7	_aMATHEMATICS _xPre-Calculus. _2bisacsh _964121
650		7	_aMATHEMATICS _xReference. _2bisacsh _964122
650		7	_aMATHEMATICS _xGeometry _xGeneral. _2bisacsh _97661
650		7	_aNumber theory. _2fast _0(OCoLC)fst01041214 _913208
650		7	_aGeometry. _2fast _0(OCoLC)fst00940864 _921224
650		7	_aDifferentiable dynamical systems. _2fast _0(OCoLC)fst00893426 _920832
650		7	_aCombinatorial dynamics. _2fast _0(OCoLC)fst00868969 _965243
650		7	_aMathematics. _2fast _0(OCoLC)fst01012163 _911584
655		4	_aElectronic books. _93294
776	0	8	_iPrint version: _aSchwartz, Richard Evan. _tPlaid model. _dPrinceton, New Jersey : Princeton University Press, [2019] _z9780691181370 _z0691181373 _w(OCoLC)1051133975
830		0	_aAnnals of mathematics studies ; _vno. 198. _965246
856	4	0	_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452377
938			_aAskews and Holts Library Services _bASKH _nAH35690461
938			_aProQuest Ebook Central _bEBLB _nEBL5598243
938			_aEBSCOhost _bEBSC _n1898630
938			_aOxford University Press USA _bOUPR _nEDZ0002090788
938			_aYBP Library Services _bYANK _n15818264
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