Добавил:
Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз: Предмет: Файл:
Доступний 3D-друк (теорія і практика 3D-друку).pdf
Скачиваний:
127
Добавлен:
12.05.2015
Размер:
15.1 Mб
Скачать

o E2)График области:

o E3)Поверхность Шерк-Коллинз64,котораяблизкак минимальнойповерхности:

oE4) Многогранная мозаика: Сейчас команды Mathematica "Транслировать" и "Повернуть" или "Масштабировать" производят STL-файлы, непригодные для печати. Требуется взять части объекта и собрать их вместе. Приведен пример наглядно доказывающий, что возможно заполнить пространство мозаикой из усеченныхвосьмигранников.

Ссылки

1.R. Netz. The Shaping of Deduction in Greek Mathematics: A study in Cognitive History. Cambridge University Press,1999.

2.M. Kline. Mathematical thought from ancient to modern times.The Clarendon Press, New York, 2.edition,1990.

3.E.R.Tufte.VisualExplanations.GraphicsPress, Cheshire,1997.

4.P. Bender. Noch einmal: Zur Rolle der Anschauung in formalen Beweisen. Studia Leibnitiana, 21(1):98-100,1989.

5.M.Levi.The MathematicalMechanic.PrincetonUniversityPress,2009.

6.G. Hanna and N. Sidoli. Visualisation and proof: a brief survey of philosophical perspectives. Math.Education,39:73-78,2007.

7.A.S.Posamentier.MathWonders,toinspireTeachersand Students.ASCD,2003.

8.R. S. Palais. The visualization of mathematics: Towards a mathematical exploratorium. Notices of the AMS,June/July 1999,1999.

9.E. Slavkovsky. Feasability study for teaching geometry and other topics using threedimensional printers. Harvard University, 2012. A thesis in the field of mathematics for teaching for the degreeofMaster ofLiberalArtsinExtensionStudies.

10.O. Knill and E. Slavkovsky. Thinking like Archimedes with a 3D printer. http://arxiv.org/abs/1301.5027,2013.

11.J.H.Conwayand R.K.Guy.Thebookofnumbers.Copernicus,1996.

12.C. Goodman-Strauss J. H. Conway, H. Burgiel. The Symmetries of Things. A.K. Peterse, Ltd., 2008.

13.Clifford A. Pickover. The Math book, From Pythagoras to the 57th dimension. 250 Milestones in theHistoryof Mathematics.Sterling,NewYork, 2009.

14.T.Jackson.An illustrated History of Numbers.Shelter Harbor Press,2012.

15.A. Fomenko. Visual Geometry and Topology. Springer-Verlag, Berlin, 1994. From the Russian by MariannaV.Tsaplina.

16.M.Berger.A PanoramicViewofRiemannianGeometry.Springer Verlag,Berlin,2003.

17.K. G. Cooper. Rapid Prototyping Technology, Selection and Application. Marcel Dekker, Inc, 2001.

18.C.S.LimC. K.Chua,K.F.Leong.Rapid Prototyping.World Scientific,second edition,2003.

19.A.Kamraniand E.A.Nasr.Rapid Prototyping,Theoryand Practice.Springer Verlag,2006.

20.M.Brain. How Stereolithography 3-D layering works. http://computer.howstuffworks.com/stereolith.htm/printable,2012.

21.D.RosenI.Gibsonand B.Stucker.AdditiveManufacturingTechnologies.Springer,2010.

22.J.Rifkin.The third industrialrevolution.Palgrave Macmillan,2011.

23.J. Rifkin. The third industrial revolution: How the internet, green electricity and 3d printing are ushering in a sustainable eraof distributed capitalism.World FinancialReview,2012.

24.Economist.The third industrialrevolution.Economist,Apr 21,2012,2012.

25.E. M. Rocha J. M. Borwein and J. F. Rodrigues. Communicating Mathematics in the Digital Era. A.K.Peters,2008.

26.H. Lipson. Printable 3d models for customized hands-on education. Paper presented at Mass

Customization and Personalization (MCPC) 2007, Cambridge, Massachusetts, United States of

America,2007.

27.J. M. Pearce, C.M. Blair, K. J. Kaciak, R. Andrews, A. Nosrat, and I. Zelenika-Zovko. 3-d printing of open source appropriate technologies for self-directed sustainable development. Journal of SustainableDevelopment,3(4):17-28,2010.

28.G.Lacey.3d printingbringsdesignstolife.techdirections.com,70(2):17-19,2010.

29.R. Q. Berry, G. Bull, C. Browning, D. D. Thomas, K. Starkweather, and J. H. Aylor. Preliminary considerations regarding use of digital fabrication to incorporate engineering design principles in elementary mathematics education. Contemporary Issues in Technology and Teacher Education,10(2):167-172,2010.

30.D. Cliff, C. O'Malley, and J. Taylor. Future issues in socio-technical change for uk education. BeyondCurrentHorizons,pages1-25,2008. Briefingpaper.

31.G. Bull and J. Groves. The democratization of production. Learning and Leading with Technology,37:36-37,2009.

32.B.Evans.Practical3DPrinters.TechnologyinAction.Apress,2012.

33.S.Singh. BeginningGoogle SketchUpfor 3Dprinting.Apress,2010.

34.J. F. Kelly and P. Hood-Daniel. Printing in Plastic, build your own 3D printer. Technology in Action.Apress,2011.

35.M. P. Skerritt J. M. Borwein. An Introduction to Modern Mathematical Computing. With Mathematica.SUMAT.Springer,2012.

36.M.Trott.TheMathematicaGuidebook.SpringerVerlag,2004.

37.S.Wagon.Mathematicain Action.Springer,thirdedition edition,2010.

38.R.E.Maeder.ComputerSciencewithMathematica.CambridgeUniversityPress,2000.

39.S. Kamin P. Wellin and R. Gaylord. An Introduction to Programming with Mathematica.

Cambridge University Press, 2005.

40.J. H. Conway and N. J. A. Sloane. Sphere packings, Lattices and Groups, volume 290 of A series of Comprehensive Studies in Mathematics. Springer Verlag, New York, 2.nd edition edition, 1993.

41.J.Leech.Theproblemofthethirteenspheres.Math.,Gazette,40:22-23, 1956.

42.A.VanOosteromandJ.Strackee.Thesolid angleofaplanetriangle.IEEETrans.Biom.Eng., 30(2):125-126,1983.

43.C.Olah.STLsuppportinSAGE.DiscussioninGooglegroupsin2009.

44.G.Hart.GeometricsculpturesbyGeorgeHart.http://www.georgehart.com

45.Makerbot.Thingiverse.http://www.thingiverse.com.

46.O.Knill.A discreteGauss-Bonnettypetheorem.ElementederMathematik,67:1-17,2012.

47.T. L. Heath. A history of Greek Mathematics, Volume II, From Aristarchus to Diophantus. Dover, NewYork,1981.

48.T.L.Heath.A ManualofGreekMathematics.Dover,2003(republished).

49.I. Thomas. Selections illustrating the history of Greek Mathematics. Harvard University Press, third edition,1957.

50.T. M. Apostol and M. A. Mnatsakanian. A fresh look at the method of Archimedes. American Math.Monthly,111:496-508,2004.

51.R.Netzand W.Noel.TheArchimedesCodex.DaCapoPress,2007.

52.C. Sparrow. The Lorenz equations: bifurcations, chaos, and strange attractors, volume 41 of Applied MathematicalSciences.Springer-Verlag,NewYork,1982.

53.G.Francis.A topological picturebook.Springer Verlag,2007.

54.M. Aigner and G.M. Ziegler. Proofs from the book. Springer Verlag, Berlin, 2. edition edition, 2010.Chapter 29.

55.O.Knill.Onnonconvex causticsofconvex billiards.Elementeder Mathematik,53:89-106,1998.

56.O.Knill.The McKean-Singer FormulainGraphTheory.http://arxiv.org/abs/1301.1408,2012.

57.A. Gray. Modern Differential Geometry of Curves and Surfaces with Mathematica. CRC Press, 2 edition,1997.

58.H-O. Peitgen and D. Saupe. The Science of Fractal Images. Springer-Verlag New York Berlin Heidelberg,1988.

59.H. Eves. Great moments in mathematics (I and II). The Dolciani Mathematical Expositions. MathematicalAssociationofAmerica,Washington,D.C.,1981.

60.W.Feller.An introduction toprobabilitytheoryand itsapplications.John Wileyand Sons,1968.

61.P.Deane.Thefirstindustrialrevolution.CambridgeUniversityPress,second edition,1979.

62.M. Levin, S. Forgan, M. Hessler, R. Hargon, andM. Low. Urban Modernity, Cultural Innovation in theSecond IndustrialRevolution.MIT Press,2010.

63.S.Weinzierl.Computer algebrain particlephysics.http://www.arxiv.org/hep-ph/0209234,2002

64.B.

Collins.

Sculptures

of

mathematical

surfaces.

http://www.cs.berkeley.edu/sequin/SCULPTS/collins.html.

Переводчики:Woolpit,alex_itz