Mathematics and LCSR:
Differences and Challenges

  1. Differences (from much of humanities, arts, social sciences), and common to other "hard sciences": no need for "only formulas" but can't omit formulas entirely, either.

  2. Insufficient Mathematics in the LCSR Volumes

    Possible Remedies:

    (a) See suggested additions, below
    (b) Allowing bending of one-third/two-thirds rule.

  3. Much of classics are unreadable (analogy: Old English)

    Possible Remedies: carefully chosen texts and excerpts from (rather than whole) texts.

  4. Finding "Great Ideas of Mathematics" that are understandable by undergraduates (let alone non-majors): challenging but possible (and rewarding!)

  5. Unlike the author, most American mathematics teachers do not have much if any experience with reading/writing assignments in mathematics.

    Possible LCSR/HONR Course

    Title: "The Shape of Space"

    Using portions of Part V of [FAPP] such as "Growth and Form", "Geometric Growth", "Inaccessible Distances", "Reflecting the Universe", Symmetry/Patterns/Tilings, and "New Geometries for a New Universe"; parts of [EG], [F], [SOS], and [GI]. There is enough material here for at least 4 or 5 semesters each with a somewhat different "flavor" of the types of geometry/topology presented!

    Other Possible Courses

  6. Part of [GEB] are useful for studying Mathematical Logic, although additional sources would need to be added.

  7. A course on the history and development of Geometry might use [E], in particular the online versions, as well as parts of [FAPP] such as "Inaccessible Distances".

  8. Math other possibilities exist, but (significant) time would be required to "dig up" additional sources appropriate to other types of mathematics courses. Other "gem" books include Excursions into Mathematics by Anatoli Beck et al.

Bibliography

Possible Sources for 'Mathematical Classics'

  • [E] Elements by Euclid.

  • Euclid's Elements online and a nicer version
    (PT implies PP
  • Nice short plato dialogue w/slave boy on a theorem on squares

  • [EG] Experiencing Geometry on Plane and Sphere [EG1]and Experiencing Geometry in Euclidean, Spherical, and Hyperbolic Spaces [EG2] by David W. Henderson.

    See http://math.cornell.edu/~dwh

  • [F] Flatland by Edwin A. Abbott (2nd revised edition, 1884).

    Resources:

    Best online version (best illustrations):
    http://www.geom.umn.edu/~banchoff/Flatland/

    Version at UNC:
    ftp://sunsite.unc.edu/pub/docs/books/gutenberg/etext95/flat10a.txt

    Version at UK site:
    ftp://src.doc.ic.ac.uk/media/literary/collections/project_gutenberg/gutenberg/etext95/flat10a.txt

  • [SOS] The Space of Space. By Jeff Weeks. Marcel Dekker, 1985.

    Related Curricular Materials

    The South-West-North paradox:

    http://www.cut-the-knot.com/triangle/pythpar/NonEuclid.html

    Properties of Shapes
    http://www.stg.brown.edu/projects/classes/ma8/papers/leckstein/Cosmo/properties.htmland following links, particularly the hypersphere.

    On the Shape of Space, Flatland, and Ourland:

    http://math.rice.edu/~joel/NonEuclid/space.html

  • [FAPP] For All Practical Purposes. Introduction to Contemporary by COMAP, the Consortium for Mathematics and Its Applications, third edition. Mathematics

  • [GEB] Godel, Escher, Bach. An Eternal Golder Braid. By Douglas Hofstatder.

  • [GI] Geometry and the Imagination by D. Hilbert and S. Cohn-Vossen.
  • Geometry and the Imagination by Thurston et al, (online)
  • Henderson's book

    Miscellaneous

  • Pyth Thm animated pf

  • virtual polyhedra

  • 4-D analog/followup to flatland

  • strange philosophical-physics essay

    Harel Barzilai, May 1999.