Read Me File For


Version 10.10 of February 2016

Note:  Version 10.10 of 3D-XplorMath runs native on both Intel-based Macs and PowerPC based Macs and it has been tested on OS X 10.8 (Mountain Lion), 10.9 (Mavericks), 10.10 (Yosemite) and 10.11 (ElCapitain). We are very grateful to Adriaan van Os for porting our older source code to the Free Pascal Compiler to make this possible and also for a large amount of further work towards a version for all platforms... 


3D-XplorMath is a follow-on, OS X version of the well-known Classic Macintosh mathematical visualization tool, 3D-Filmstrip. It has a home page on the web at:

where you will find descriptive material about the program, technical documentation, and a Gallery of visualizations produced by 3D-XplorMath.


The documentation for 3D-XplorMath comes in several parts which can all be reached from inside the program: A Quick Help for using the program (the last item of the Documentation menu). Mathematical Documentations of all the objects in the program (available as About This Object in the Documentation Menu after an object has been selected). A detailed hypertext program documentation (from the Documentation menu or below). Start the program and see About The Documentation (the first item in the Documentation menu) for more details about the documentation, or click here to go to the detailed hypertext documentation.


The standard distribution of 3D-XplorMath comes as a disk image file called 3DXplorMath.dmg that expands to a folder containing this ReadMe file and a subfolder called 3D-XplorMath f containing:

NOTE: It is no longer required to run 3D-XplorMath from within the 3D-XplorMath ƒ folder. This is because the application file is now a bundle that contains the folder 3DFSDocs within it. (Previously, 3DFSDocs was a subfolder of the 3D-XplorMath ƒ folder and the application looked for it there when the user selected "About This Object..." from the documentation menu.) It is still possible to access the 3DFSDocs; just "right click" (i.e., click while holding down Control) the application file and select " Show Package Contents" from the resulting drop-down context-dependent menu.

If you have not previously used 3D-XplorMath, please at least skim the rest of this file, but we highly recommend that you read the most basic part of the documentation called Getting Started. And then, to find out about some of the interesting and fun things that the program is capable of, look at Things to Try.

If you are an old user, then to find out about the new features, read the file What's New in this Version?" also in the 3D-XplorMath f folder.

What is 3D-XplorMath?

3D-XplorMath is a tool that runs native under MacOS X and creates striking, high quality visualizations of mathematical objects and processes. It is a follow-on version of a Classic (Mac OS 9) program called 3D-Filmstrip.

3D-XplorMath has built-in algorithms for displaying mathematical objects of many different types or "Categories" (Plane Curves, Space Curves, Surfaces, Conformal Maps, Polyhedra, various types of ordinary and partial differential equations, Waves, Sound, and Fractals) and also for displaying various animations associated with these categories.

But 3D-XplorMath provides content as well as viewing and animation tools. Each category has a "Gallery" of many pre-programmed objects, and also easy to use methods for entering new User Defined objects from the category. The Gallery items are selected from a menu, while user defined objects are created without any programming by entering algebraic formulas in a dialog.

Most items in the various galleries have associated to them a text file that documents the item. These can be read while the object is being viewed by selecting "About This Object..." from the Documentation menu.

While 3D-XplorMath started out life as a research tool, written by mathematicians for other mathematicians, it has gradually morphed into a program that should be of interest to anyone with an interest in mathematics and who enjoys experimenting with and visually exploring and learning about new mathematical concepts. In fact, a good way to think of 3D-XplorMath is as an Interactive Museum of Mathematical Exploration and Explanation, the various Categories being different galleries of the museum.

The original concept, design, and algorithmic content of 3D-XplorMath was a joint effort of Hermann Karcher and Richard Palais who also carried out most of the actual coding (in Object Pascal), with important contributions from others, especially David Eck and recently Adriaan van Os. In addition, a great many people have contributed their ideas, suggestions, algorithms and documentation.

If you have any bugs to report or suggestions for improvements, please send a message to:

Richard S. Palais
Department of Mathematics
RH 340 UC Irvine
Irvine, CA 92697
Home Page:

The copyright to the program belongs to Richard Palais and Hermann Karcher, but there is a free license to use it for non-commercial purposes in education and research.

News, Old and Recent

  1. The 3DFS Consortium.
    An informal group that goes by the name The 3DFS Consortium has taken
    over joint responsibility for the enhancement of 3D-XplorMath. Currently the
    members of the Consortium are: Luc Benard, David Eck, Martin Guest, Patrick Iglesias, Adriaan vanOs
    Hermann Karcher, Traudel Karcher, Michael Murray, Bob Palais, Richard Palais, Takashi Sakai,
    Markus Schmies, Daniel Steinberg, Chuu-Lian Terng, Nam Trang, Matthias Weber, and Xah Lee.
  2. NSF CCLI Grant Support for Development of 3D-XplorMath.
    The NSF Dept. of Undergraduate Education has funded a CCLI Grant
    (with Richard Palais as the Principal Investigator)
    whose purpose is to further improve 3D-XplorMath as a tool for integrating
    mathematical visualization into the undergraduate mathematics curriculum.
  3. David Eck is leading a project to create a platform neutral Java version of
    3D-XplorMath called 3D-XplorMath-J. It has now reached a fairly advanced
    stage of development, and can be downloaded from: