3D-XplorMath 10.4.1 review
Download3D-XplorMath is a mathematical visualization program for Macintosh computers running version 9 or later of MacOS.
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3D-XplorMath is a mathematical visualization program for Macintosh computers running version 9 or later of MacOS.
It presents itself as a gallery of interesting mathematical objects, ranging from planar and space curves to polyhedra and surfaces to ordinary and partial differential equations, and fractals.
Morever, the carefully chosen default parameters and viewing options may be changed by the user so that the gallery is turned into a experimental lab.
Every exhibit has its own online documentation with suggestions for how to explore it further.
We hope that in this way the program will be useful to the interested layperson, the teacher, and the research scientist.
Here are some key features of "DXplorMath":
A 3D object (e.g., a surface or a polyhedron) can be rotated to any desired orientation by simply dragging it with the mouse. If you release the mouse button while you are still dragging the object, it will continue to spin about the same axis.
Most 3D-XplorMath objects depend on parameters, and the user can easily watch the object morph as the parameters vary along a user selected line in the parameter space.
3D-Objects can be viewed in stereo.
There are extensive facilities for investigating fractals, and in particular the interesting relation between the Mandelbrot set and Julia sets.
What's New:
The Plane Curve Category: Now most planar curves come with a "decoration" that explains how the curve is defined. The latest addition is a mechanical construction of the Lemniscate. We have also made the various decorations perform in a more uniform fashion---for example, now all decorations remain visible if one stops their animation with a mouse click.
The Space Curve Category: We have added Curves of Constant Curvature to the exhibits (with many closed ones in the default morph) and curves of constant torsion (again closed ones in the default morph). We had not seen closed space curves of constant curvature treated before and found them interesting to look at. Although computed from their Frenet differential equation, all of the entries for explicitly parametrized curves in the Action Menu remainavailable for this new exhibit, and the same holds for Curves of Constant Torsion. See the ATOs for further interesting details.
The Surface Category: In the minimal surface subcategory there is a new Action Menu item: Show Associated Grids. It shows on the left the grid on which we perform the numerical integration, in other words, this grid defines which parameter lines appear on the surface. On the right we either show the Gauss image of the integration grid (left), or, for surfacesof genus > 0, we show the image grid under the complex third coordinate function.
The Fractals & Chaos Category: Instead of showing only still pictures of the Henon attractor and of the Feigenbaum tree we have added some dynamics so that one can now see how the final pictures evolve from early approximations. The use of colors shows clearly where a mixing behaviour occurs. Also, in the Henon Attractor, if you hold down Command, you can drag out a "zoom rectangle" on the screen (i.e., the window will zoom to a magnified view of the part of the attractor included in that rectangle). Important improvements have been made to the Julia Set animations.
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