3D-XplorMath

10.11

Explore mathematical objects and processes.

**3D-XplorMath** is a freely available Mathematical Visualization program. To download your personal copy of the latest version, click on the Download tab above. The older Pascal version runs only on Macintosh computers, but there is also a cross-platform Java version, called **3D-XplorMath-J**, and while it has fewer features and Exhibits, we hope eventually to give it all the functionality of its older Pascal brother.

The program presents itself as series of galleries of different categories of interesting mathematical objects, ranging from planar and space curves to polyhedra and surfaces to ordinary and partial differential equations, and fractals.

Moreover, the carefully chosen default parameters and viewing options may be changed by the user so that each gallery is turned into a experimental lab.

Each exhibit has its own online documentation with suggestions for how to explore it further. We hope in this way to make the program useful to the interested layperson, the teacher, and the research scientist

We have created a series of short tutorial movies explaining various features of the program and also some interesting ways in which it can be used. In particular, you can click here to see a basic introduction to **3D-XplorMath** and some of its Exhibits.

Another interesting sequence of movies can be found here. These show the time-development of what are called Ward Solitons.

Most Exhibits of the Pascal version of **3D-XplorMath** have associated to them a so-called "About This Object" PDF file that explains the mathematics behind the pictures. We have collected these files in a hypertext Collected_ATOs for reading and/or downloading as a single inter-linked pdf file.

Version 10.11 (get info version 10.10.1):
##### The Space Curve Category:

##### The Surface Category:

**Note:** Now requires OS X 10.6 or later

- Work by Adriaan van Os on the conversion to Linux and Windows is still in progress. In spite of extensive code changes the response to users stayed the same, except that earlier settings files do not work any more. The code compiles now under Linux, some exhibits already run, but further GTK work still needs to be done.
- About half the additions to 10.11 result from the update of the Virtual Math Museum, since the earlier program version could not quite produce what we wanted.
- Missing ATOs were added (always: to the program and to the ATO hypertext collection).
- The Menu entries of active objects have checkmarks.
- Discovered bugs were fixed.

- More constant curvature space curves were added, the new ones lie on cylinders. A plane with a circle can be rolled into cylinders while deforming the circle to keep its space curvature constant. Spherical lemniscates were added together with their mechanical construction, analogous to the planar case.
- Finding and moving of closed geodesics on implicit surfaces was improved.

- Scaling parameters were added to the definitions of several minimal surfaces so that they can be made small enough to allow views from far away.
- For many minimal surfaces with translation symmetries the number of shown tiles can be controlled from the Action Menu.
- Scherk defined his singly periodic surface as an implicit surface, this historic version was added.
- The Inverted Boy minimal surface is too complicated for one picture, we show three different parts.
- Parameters hh, ii were added to the Clifford torus to allow torus knots as parameter lines. The inside-out conformal morph changes p-q-knots to q-p-knots.
- An ODE-based computation of selfintersection curves was added to Klein, Whitney Umbrella, Right Conoid, both Boy surfaces and Snail Shell. These curves are visible when 'Draw with Contours' is selected.
- Untangling an SO(3)-loop was added (rotations are visualized by moving spherical polygons on concentric spheres).
- A new exhibit, 'Projected Sphere', is added with Action Menu entries specific to spheres: The sphere can be shown with four different coordinate grids; stereographic projection or Archimedes' projection can be added in suitable cases; spherical curves with their mechanical constructions can be added.

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App requirements:

- Intel 64
- Intel 32
- PPC 32
- Mac OS X 10.6.0 or later

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