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Math Related Websites:
For very extensive listings of such things see:
- George Hart's site
- The Geometry Junkyard
Math Related Books and Articles:
Most of the references below can be found at
George Hart's mammoth reference list, or the bibliography of Peter
Cromwell's book Polyhedra. The ones below are ones that I have seen or
Clifford W. Ashley, The Ashley Book of Knots, Doubleday 1944
---Contains illustrations, tips for tying, and historical information
of about 3800 different knots. Essential for anyone who wants to
practice binding arbitration.
W.W.Rouse Ball, H.S.M. Coxeter, Mathematical Recreations and Essays,
Martin Berman, "Regular-faced Convex Polyhedra," Journal of the Franklin
Institute, vol 291, no. 5, p329-352, 1971
---Gives nets and photos and values for surface area and volume for all
the regular faced convex polyhedra, other than the prisms. Apparently, several
of the volumes listed are incorrect. You can find corrected (unverified by me though!)
volume numbers at a page from
Lewis Carroll (Charles L. Dodgson, M.A.), Euclid and His Modern Rivals,
Macmillan and Co. 1885, Dover 1973
---Highly praises Euclid's Elements by comparing it favorably in
dramatic form to many other geometry book writers of Carroll's
time. He has a point.
Stuart Coffin, The Puzzling World of Polyhedral Dissections, Oxford
University Press 1990
---Pretty neat book which contains a whole lot of information about
making puzzles from wood. Most are constructible from cutting up
square sticks in various ways.
H.S.M. Coxeter, Introduction to Geometry, John Wiley and Sons Inc. 1961, 1969
Regular Polytopes, Dover, 1973
Regular Complex Polytopes, Cambridge Univ. Press 1974, 1991
---These are a very good start for the mathematics of polyhedra.
H.S.M. Coxeter, P. Duval, H.T. Flather, J.F. Petrie, The 59 Icosahedra,
---Contains excellent drawings and related math info about the 59
stellations of the icosahedron.
H.S.M. Coxeter, Michele Emmer, Roger Penrose, M. Teuber (editors),
M.C. Escher, Art and Science, North-Holland 1986,1987
---This is a book of articles from many different fields from a
conference on M.C. Escher in 1986
H.S.M. Coxeter, M.S. Longuet-Higgins, J.C.P. Miller, "Uniform Polyhedra,"
Philosophical Transactions of the Royal Society, Series A, vol 246, p401-449, 1954
---The first complete enumeration of all the uniform polyhedra. Good
solid discussion, lots of geometric properties,
and lots of pictures.
Peter Cromwell, Polyhedra, Cambridge University Press 1997
---Informative and even useful overview of the multifaceted history
and nature of polyhedra. Lots of diagrams and references. Admirable
at least for its weight.
H. Martin Cundy, A.P. Rollet, Mathematical Models, Oxford Univ. Press 1961
---A very good book, which I highly recommend for the math model maker.
Info about polyhedra, tools for drawing math curve, gears, and more.
Salvador Dali, 50 Secrets of Magic Craftsmanship, Dover 1992
---Among other things, here he advises living around geometric objects
as a way of life.
Albrecht Durer, Unterwyseng, 1525
Aniela Ehrenfucht, The Cube Made Interesting, Pergamon Press 1964
---And what better way than with blue and red 3-d pictures
Michele Emmer (editor), The Visual Mind, MIT Press 1993
---Several articles by mathematicians and artists about the place and
practice of math in art and vice versa.
M.C. Escher, His Life and Complete Graphic Work, Abradale Press 1992
Euclid, The Thirteen Books of the Elements, written long ago, Dover 1965
---A very sturdy math book
R. Buckminster Fuller, Synergetics, Macmillan Publishing Company Inc. 1975
--Synergetics 2, Macmillan Pub. Co. Inc. 1979
---Be prepared to wade through page after page of boyish philosophical
entanglement to distill the pertinent information.
Isvan and Magdolna Hargittai, Symmetry, Shelter Publications Inc. 1994
--Symmetry Through the Eyes of a Chemist, 2nd. edition, Plenum Press, 1995
---These are filled with pictures of symmetry from around the world.
Alan Holden, Shapes, Space, and Symmetry, Dover 1971
--Orderly Tangles, Columbia University Press 1983
---Tangles is a very interesting exploration of constructions with
dowels. Each is well illustrated with photos.
Leopold Infeld, Whom the Gods Love, National Council of Teachers of Mathematics, 1948
---A somewhat novelized account of the life and times of Evariste
Galois. Contains some pretty good dialogue.
Johannes Kepler, Harmonicus Mundi, 1625, book 2 about polyhedra and tiling
is translated by J.V.Field, "Kepler's Star Polyhedra," Vistas in Astronomy,
Vol 23, p109-141
Felix Klein, Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, Dover 1956
L. Lines, Solid Geometry, Dover 1965
---Contains many useful theorems, plus a big section on polyhedra.
Koji Miyazaki, An Adventure in Multidimensional Space, Asakura Publishing
Company Ltd. 1983 (japanese), John Wiley & Sons 1988 (english)
---Photos of many hundreds of polyhedra, lots of historical asides,
and introductions by Fuller and Coxeter.
Hiroshi Ogawa, Forms of Paper, Van Nostrand Reinhold Company, NY 1971
---Paper lanters, wavy columns, ripples and more.
Sundara Row, Geometric Excercises in Paper Folding, Open Court Publishing Co. 1958
---Many interesting constructions by only folding paper.
Marjorie Sinethal, George Fleck (editors), Shaping Space, Birkhauser Boston Inc. 1998
---This book grew from a polyhedra conference held at Smith College
in 1984. Contains many articles from many viewpoints.
Simon Singh, Fermat's Enigma, Walker and Company 1997
---Many tales of adventures of math and mathematicians,
centered around Fermat's Last Theorem.
J.Skilling, "The Complete Set of Uniform Polyhedra," Philosophical Transactions
of the Royal Society, Series A, vol 278, p111-135, 1975
---Presents the computer assisted proof that the list of uniform
polyhedra presented by Coxeter, et al is complete.
S. Vajda, Fibonacci & Lucas Numbers and the Golden Section, Ellis Horwood Limited,
W.C. Waterhouse, "The Discovery of the Regular Solids," Archive for the History of Exact Sciences, vol 9 (1972-3) p212-221
---Discusses speculations about the references to the discovery of
the regular solids. Summed up in Cromwell's Polyhedra.
Magnus J. Wenninger, Polyhedron Models, Cambridge University Press 1973
Spherical Models, Cambridge 1979
Dual Models, Cambridge 1983
---If nothing else, you will learn complication from these. A large
number of very complicated polyhedra presented with construction
tips and diagrams.
Robert Williams, The Geometric Foundation of Natural Structure, Dover 1979
---Has a table of numerical properties of Platonic and Archimedean
solids and their duals, plus a lot about aggregations.
Viktor Zalgallar, Convex Polyhedra with Regular Faces, Consultants Bureau, NY 1969
---A proof that all the convex regular faced solids can be built from
28 basic polyhedra, plus the prisms and antiprisms.