Download 3D-XplorMath for Mac - Explore mathematical objects and processes. MacUpdate Mac Mathematics Software Downloads

DESCRIPTION

3D-XplorMath (formerly 3D-Filmstrip) is a highly interactive museum for exploring the visual aspects of the exciting and beautiful universe of mathematical objects and processes. It has been under continual development for over ten years by an international team of renowned mathematical researchers and educators, the 3DXM Consortium. It was originally developed for use in teaching and research, but recently the Consortium has been working hard to make it easy and enjoyable to use by anyone with mathematical curiosity and an appreciation for the visual and logical beauty of mathematics. This museum contains literally hundreds of well-known (and some not so well-known) mathematical objects, arranged logically into numerous "galleries", referred to as Categories. These include: Surfaces, Planar Curves, Space Curves, Polyhedra, Conformal Maps, Dynamical Systems, Waves, and (the latest) Fractals & Chaos. The "3D" in its name refers to the fact that 3D objects can be viewed in strikingly realistic stereo. If you would like to visit a Gallery of just some of the remarkable surfaces that can be created and manipulated with the program, go to: http://rsp.math.brandeis.edu/3D-XplorMath/Surface/gallery.html 3D-XplorMath differs from programs such as Mathematica, Maple, and Matlab that provide visualization back-ends for viewing objects, but require the user to first program the object and its visualization. 3D-XplorMath emphasizes ease of use and does not even require the user to have a pre-existing knowledge of the mathematical definition of an object in order to see it. Every mathematical object in its massive collection is not only pre-programmed, but also has carefully chosen default parameters and associated animations. Merely selecting a gallery object by its name from a menu presents an excellent initial view of the object. The user may then optionally use simple dialogs, controls, and menu choices to customize and animate this default view, perhaps after first learning about its background by choosing About This Object from the Documentation menu. Users can also create and animate new objects on their own by entering simple algebraic formulas into dialogs. All objects including user defined objects can be saved in several graphic formats, and animations can be saved as Quicktime movies. While The 3DXM Consortium is not asking a monetary payment for you to use 3D-XplorMath, we are asking for payment of a different sort: Please send us reports of any difficulties you have with the program and any suggestions you have for new mathematical objects or for improving the user interface and the documentation. Either send email to palais@uci.edu, or if you prefer write your comments as a MacUpdate review.

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WHAT'S NEW

Version 10.5.5:

The Space Curve Category:
A new display of curves, "Show as Pair of Strips", has been added in the Action Menu. It is similar to "Show As Tube", but while the tubes mainly emphasize the curve as 3D object the strips emphasize the curvature properties of the curve.
We have added V.Jones' braid list so that the first 249 prime knots can be viewed in Jones' braid representation. New braid words can be entered in a dialogue. The braids can either be displayed circular and almost planar, or on the surface of a cylinder. A second addition allows to modify the trefoil knot into a sequence of prime knots. The default Lissajous curve is now another prime knot.
The Surface Category:
The conic sections entry "Planes, Cones and Spheres" has been expanded into two views. The first shows the cone intersected by a plane, the default morph changes the inclination of the plane. The second view shows the Dandelin Spheres, the default morph keeps the intersection curve the same and varies the cone angle (down to a cylinder).
All surfaces can now be rendered as point clouds, including the multi-tile surfaces, see "Hopf Fibered Linked Tori".
The contours of all parametrized surfaces can be displayed. To study the contours choose wire frame or point cloud rendering. In patch display the contours are only useful if in "Light Sources" one has chosen "Ambient Only" - for line drawings combined with the painters algorithm to suppress invisible parts of the surface. Pressing Left/Right Arrow during computation changes the line width for the contour.
We have expanded the Dirac Belt demo: 3-frames can be added to the belt to indicate the family of motions and a second morph displays only the first half of the belt thus showing Feynman's Plate Trick.
The Polyhedron Category:
The exhibits have been improved with a very young audience in mind. Dotted hidden edges can be added from the Action Menu. The entry "Show Relation to Cube" now works also for the Rhombic Dodecahedron and the pyramids on the faces of the cube can be flipped into the cube by pressing Left/Right Arrow.
The ODE Category:
The Forced Duffing Oscillator has been added (1D, 2nd order) together with submenu entries that offer playgrounds for experimentation. This includes the Poincare Map. See the ATO.
The Fractals & Chaos Category:
To the list of C-values we added two more with linearly neutral attractors, but large attractor bassins (see Between Attractors). The Action Menu entry for "Julia Sets": 'Show C-value in Mandelbrot Set' also shows a rough images of the Julia sets as the mouse moves.
Other Categories:
No changes.

REQUIREMENTS

Mac OS 9.2, or Mac OS X.