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  1. Imitating Soap Bubbles (Judith Haemmerle) 10/09/96
    Looking for a well-defined algorithm: Create the shortest path that connects n points. [one-dimensional soap films]

  2. Lobochevskian (hyperbolic) Geometry (Richard Stigels) 06/17/96
    In Hyperbolic (or Lobochevskian) Geometry: Given ANY two triangles; the one with the greater sum of its sides has a lesser sum of its angles than the other one (which leads to that two triangles of totally different shapes but with the same side-sum also have the same angle-sum). True or false?

  3. Points on the Earth (Judith Haemmerle) 01/19/96
    I need a formula to calculate the distance between two points on the Earth's surface, knowing the latitudes and longitudes of the points. Also needed is a formula to calculate the direction from one point to the other.

  4. A banana is more convex than a cup (Tim Poston) 01/10/96
    A discussion on the topological convexity of a banana. [Gromov "Hyberbolic manifolds, groups and actions," Annals of Mathematics Studies; Chai, "A geometric inequality for certain types of compact sets in R^n," Amer. Journal of Math.]


  1. Fractals and Fractional Dimensions (Judith Haemmerle) 11/26/95
    I have to write an essay on whether a fractal really is a fractional dimension or not. I managed to find something on the relationship between topological dimensions, which I understand, and Hausdorff dimensions, which I don't. Can anyone out there help me with this or direct me to something simple and readable?

  2. Neutral Geometries (Name withheld by request) 11/01/95
    How many different kinds of neutral geometry are there? If a neutral geometry is one which shares all the other postulates except the parallel postulate, then does neutral geometry, n1, posess the Euclidean postulates and possibly some other, n2, would possess the Euclidean postulates and different others, etc.?

  3. Extra credit geometry proof (Steve Heintz) 10/29/95
    Given: Rectangle ABCD with P any point on line AB. line PE is perpendicular to line BD, line PM is perpendicular to line AC, line AN is perpendicular to line BD. Prove: PE+PM=AN.

  4. Schoolteacher Follies (Richard Mateosian) 10/13/95
    Public school education now and in the past; press reports of schooling.

  5. Defining a rectangle (Patricia) 10/12/95
    I learned in California that a rectangle was defined by having four sides and four right angles, making a square a type of rectangle. Now that I am teaching for a year in Scotland my students are insisting that a rectangle must have two sides which are longer. The dictionaries which we looked at have definitions to justify either claim. Can anyone help us out?

  6. Standard Math Symbols in ASCII (Gerald D. Brown) 10/10/95
    Does anybody know of a list of recognized ASCII character strings used to denote standard math symbols?

  7. Pythagorean Theory and a President (Matt Bradbury) 09/26/95
    I have a question that has our H.S. History of Math class stumped. We have to find people that were significant in mathematical history, and one of the questions is: Discovered proof of Pythagorean Theorem, and a U.S. President. [Congressman Garfield]

  8. Quaternions (DELBECQUE Yannick) 09/23/95
    I am looking for interesting facts about quaternions for a music composer who wishes to use them to compose. Geometrical interpretations of some proprieties of quaternions are the best things I can bring him, since they are simple to understand and visualise and they can be "put into music" more easily. [Kantor, I.L. and A.S. Solodovnikov. _Hypercomplex Numbers: An Elementary Introduction to Algebras_. Iannis Xenakis, Formal Music. Ebbinghaus, H.-D. et al. _Numbers_. Readings in Mathematics, Graduate Texts in Mathematics]

  9. Request for advice - Independent HS project (Mark Jaffee) 09/08/95
    Request for advice on teaching high school with Sketchpad and limited numbers of computers, and for a student's independent math project on "Philosophy of Mathematics." [Carl Boyer, Morris Kline, Phillip Kitcher]

  10. Polyhedra Database (Andrew Hume) 08/30/95
    Request for a volunteer to take over a polyhedra database and introduce it to the WWW. [offer to work with such a volunteer on polyhedra nomenclature]

  11. 3D: Tetrahedra colliding? (Enno Rehling) 07/19/95
    Given 2 Tetrahedra, determine whether they intersect or not. It's not sufficient to test for one of the corners being inside the other tetrahedron. I'd like to know the fastest way to calculate this.

  12. Geometric Orthodontics Questions (Paulo Jorge Santos) 07/19/95
    How calculate a perpendicular if you have only 3 points (A,B and C)? How calculate the distance between C and the line AB? (the point C must be perpendicular to AB). If you have two lines (and the respective linear equations), how calculate the interception points (x and y)?

  13. Geometry on a Graphing Calculator (Suzanne Ewing) 07/19/95
    I am interested in finding lesson ideas for geometry dealing with the graphing calculator. I would prefer ideas that deal with circles, triangles, quadrilaterals, etc., but any ideas would be helpful. [suggestions for newsgroup posts and Cabri Geometry II]

  14. Geometry Textbook (Gary Wang) 07/14/95
    Since I began my studies in math education, I've become more and more interested in the use of computer software designed for geometry. I've seen a lot of activities, as well as activity books. However, I was wondering if there's been a geometry textbook written in conjunction with one of the software packages, such as Cabri Geometre or Geometer's Sketchpad? [_Machine Proofs in Geometry_, _Discovering Geometry_ (Serra)]

  15. Toblerone chocolate box shape (Steven Kirshner) 06/26/95
    Is anyone familiar with the chocolate Toblerone? What do you call the shape of the box it comes in? [prism]

  16. Sphere packing (Ed Dickey) 03/23/95
    Can someone (Prof. Conway?) provide an update on the sphere packing problem? Has Hsiang's proof held up or is this still an open question? Similarly, has the 4-D kissing number problem (24 or 25) been settled? - The sphere packing problem is to find the greatest proportion of a fixed space filled by identical spheres. To quote Conway and Sloane who quote Rogers "many mathematicians believe, and all physicists know" that the correct proportion is pi/sqrt(18) or 0.7405 ... . Hsiang offered a proof in 1991. - The kissing number problem is to find the greatest number of "spheres," all the same size, that can be arranged around another sphere. In two dimensions, the answer is six (six circles around another circle). In three dimensions, it's 12 (try it with tennis or billiard balls); proving it is another matter. In 4-D, it's 24 or 25 (unless the question has been settled).

  17. Plane Symmetry and TesselMania (PatsyJMJ) 02/13/95
    Some years ago in Creative computing magazine, there was a listing for a BASIC program that used the 17 types of plane symmetry for simple drawing with the cursor, to form Escher-like pictures. As an artist and quiltmaker by avocation, I would like to know where to find some similar program using VGA or better screens. - TesselMania.

  18. Morgan's Theorem (Minchbear) 02/02/95
    Ryan Morgan is a high school student in Baltimore. He has made an interesting discovery that is an extension of Marion's Theorem. If you are like me, I didn't know what Marion's Theorem was until a few weeks ago. The whole topic is explained quite well on p.726 of the December, 1994, issue of the Mathematics Teacher. More information also given in this thread.

  19. Penrose and Quasiperiodic Tilings (Margaret Sinclair) 01/20/95
    Does anyone know of a supplier of Penrose tiles (i.e. cardboard or plastic "kites" and "darts")? Alternatively, has anyone come up with a method for making them at home? I got interested in these tiles because of an article in Discover magazine, February 1990. Does anyone have any other articles or books to recommend? I would like to know what Steinhardt's procedures are for building Penrose tilings with strictly local rules and to find out if there has been any success at finding a related procedure for three dimensions. [Martin Gardner, 1971 / Conway in "Tilings", Grunbaum & Shephard / rhombic tiles / matching conditions / Petra Gummelt of Greifswald and the "Cartwheel decagon" / dart and kite rhombs / tesselations / Socolar comment: physics, 2D tilings and symmetry / non-repeating patterns and crinkly surfaces / Wieringa roof]


  1. Where is GSP? (John Olive) 08/24/94
    Is the Forum going to start a special section for users of Sketchpad and Cabri Geometer? [Current organization of the Forum / possibility of new newsgroup / demo versions of Sketchpad and Cabri from Forum archives]

  2. Integrating Geometry and Biology (Deobra Ray) 07/21/94
    A teacber asks for suggestions about a 3-hour Geometry/Biology class. [books: By Nature's Design, Connections / Mathematics in Medicine and the Life Sciences/ game of life]

  3. Internet access for teachers (Michelle Manes) 06/08/94
    June 1994 listing of ways teachers in various states of the U.S. get email and/or full Internet access, by state.

  4. The Forum Newsreader Plans (Helen Plotkin) 04/05/94
    A newsreading module designed for use with a World Wide Web browser like Mosaic. The general idea, how the URLs will work. [what about speed? / batch fetching desirable / how to cope with a move? / .newsrc formats don't keep message-id's]

  5. Visual Basic (Ben Preddy) 03/27/94
    What is Visual Basic--how does it differ from 'regular' basic? [Microsoft's Basic for Windows / first draw needed objects, then write event-driven code / Dynamic Link Libraries]

  6. Question Concerning Buddhism (Lee Rudolph) 02/09/94
    Is it possible to think without language? Reason (thought) is only possible by manipulating symbols representing the world. [geometers thinking symbolically/non-symbolically / a wordless movie of a proof (intersection of a plane with a right circular cylinder is an ellipse / mathematics is a language / visualizing geometric figures / first gain an awareness or intuition of aspects of geometry, then assert the result in language / Einstein on 'visual thinking' / power of being able to name things / not essential to name things before thinking about them / solving puzzles without words / unprofitable discussion?]

  7. Karl Menger (Mike Mortenson) 02/07/94
    Looking for biographical information on the creator of the 'Menger sponge', "one of those pre-fractal geometric objects that mathematicians once called 'monsters'." [combinatorial and set-theoretic work / 'distance geometry' / book Menger wrote published by Chicago science museum]

  8. Geometry Programs for Dos/Windows (Seth Delackner) 01/18/94
    Request for info about a good geometry program for Dos/Windows. [Sketchpad for Windows / demo available from Forum / 800 numbers for Sketchpad and Cabri / no Windows version of Cabri]


  1. Posting Pictures? (Tom McDougal) 09/14/93
    Is anyone working on a system to allow postings of pictures? [Sander articles with figures in Forum directory / Forum newsreader being written / why not build on Nuntius? / interface confusing to novice users]

  2. Unit Volume in 4D or higher... (Djamal Bouzida) 08/31/93
    Request for formulae: Jacobian in 4 dimensions, general in N dimensions. [Wicklin answers]

  3. Simple Questions for All Forum Users (Annie Fetter) 07/01/93
    Request for information from readers. What do you use computers for? [testing theories and making conjectures / writing, playing, talking to people, getting information / word processing, databases, spreadsheets, math lesson preparation for grades 6-9]

  4. Conics as Envelopes of Their Tangents (Martha Smith) 04/22/93
    Does anyone know of sources proving that string figures' resulting curves are the ones claimed? [Veblen & Young, Samuel's _Projective Geometry_ / differential equations / Coxeter & Greitzer's _Geometry Revisited_ / computer environments (Sketchpad) for teaching conics / ways of constructing line conics (paper-folding) / two-circle case as special case of paper folding]

  5. Pythagorean Primitives (Dan Bennett) 03/25/93
    Two formulas that generate Pythagorean triples--where to look to see if they're original? [books on elementary number theory / Stark's book, _An Introduction to Number Theory_ / McDougal/Littell, _Geometry for Enjoyment & Challenge / a geometric interpretation of the formulas]

  6. Geometry and Quilts (Claire Groden) 03/01/93
    Is anyone using computers to investigate the mathematics of patchwork quilts? [using Aldus Freehand / Geometer's Sketchpad / use quilts as examples to discuss what makes something 'geometric' / software: Architecture - Designing Your Own Home / geometry in real life]

  7. Connected Geometry Project (Michelle Manes) 02/26/93
    Brief description of the project: develop high school curriculum materials, tools and support for teachers, give students research experience in math--develop collection of activities. [Curriculum Map Maker / dynamic geometry software / examples of activities / a plug for orienteering / list of papers written about the project]

  8. Geometry Drawing Programs (L.J. Dickey) 02/23/93
    Request for experience reports, for third-year course in geometry. [Cabri-geometre used in independent research on a Mac / fundamental difference between Cabri and Sketchpad / Sketchpad fits best with the Mac / author of Sketchpad comments on Sketchpad and Cabri -- power, interface; 'select, then act' limits complexity; pedagogical ramifications]

  9. Geometry Book (Joe Malkevitch) 01/05/93
    Recommendation: David Well, _The Penguin dictionary of Curious and Interesting Geometry_. [other recommendations: _The Media Magic Catalog_, O'Roarke, _Art Gallery Theorems and Algorithms_]


  1. Proofs - My Thoughts (Michael K. Rogers) 12/14/92
    How does proof enter into the progressive geometry curriculum? [I liked two-column proofs in high school for their organization and sense of power. / effectiveness of teaching proofs / should we rely totally on insight? / 'beauty' of geometry the development of provable theories based on terms (undefined or defined), assumptions (axioms or postulates), previously proven theories (theorems, propositions) / should we eliminate proofs from the high school curriculum? / proofs without words or goal of rigor / use geometry to teach varieties of logic / geometry a microworld of 'shape' / NCTM Standards / Euclidean geometry]

  2. Revitalizing Geometry (Joe Malkevitch) 12/06/92
    How put geometry education on the same exciting footing that events in research in geometry are undergoing? [_Discrete and Computational Geometry_ / current geometry a 'sediment' / Sketchpad a tool for developing spatial intuition / Dirichlet domains / high school teachers teach what they know / college math community responsibility / Wagon's work--results in Mathematica notebook form]

  3. Mazes (J. Shipley Newlin) 12/04/92
    Newton's Apple request for interesting visual sequences that bring out some of the mathematical basis of mazes. [most common mazes are spanning trees for some graph / Euler characteristic vs. number of loops / self-similar maze that fills out a fractal tile of the plane / labyrinths (mazes with no choice of what way to go)]

  4. Geometry Projects (Sue Stetzer) 10/03/92
    Requests for suggestions for independent projects for the first quarter of a course (8th grade academically talented). [ruler and compass constructions / paperfolding / why teach constructions? / reasons for constructing and reproducing geometric figures / Senechal - On the Shoulders of Giants / student projects - interest at Dover Sherborn H.S. / robotics, computer vision, medical imaging problems / graph theory and geometry projects / Geometry Project design outline and evaluation criteria, project proposals and questions, regular evaluation model (Dover Sherborn)]

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The Math Forum
11 June 1997