Be patient while a Java applet and data files load. If things are working correctly, you will see some pictures below. You can interact with each picture. To view a picture from different angles, drag the cursor over a picture while holding down the left mouse button. Being able to view the geometry from various angles is the main purpose of these pictures.
You can also change various features of each picture using control panels. To get the main control panel, press CONTROL-M while the cursor is over a picture. With this control panel active, you can access other features using the menus that appear either in the control panel or added to your usual broswer menus (depending on your browser).
I produced these pictures using JavaView and Mathematica. JavaView (www.javaview.de) is a 3D geometry viewer and mathematical visualization software written in Java that includes the applet used for these pictures. JavaView can render 3D geometries from a wide variety of file formats. Mathematica (www.wolfram.com) is a general purpose mathematical software tool that can be used for symbolic and numeric calculations and to produce graphics. For most, I started with a Mathematica plot and then fine-tuned by using JavaView to add features such as transperancy.
This page is in an early developmental stage. The captions are not carefully written. References are to Integrated Physics and Calculus (IPAC).
I welcome any comments or suggestions for improvements at martinj@ups.edu.
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A parallelepiped and some of the geometry of the
triple scalar product.
cf. IPAC Figure 10.18 |
| A geometric view of the distributive property for the dot
product a·(b+c)
=a·b+a·c. The vector
a is black, the vector b is
blue , the vector c is red, and the vector
b+c is green. The lines indicate projections of
b, c, and b+c in the direction of
a.
The idea for this is taken from Tevian Dray's version. |
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The solid region bounded by the graph of a function, a rectangle in
the xy-plane, and sides perpendicular to the
xy-plane.
cf. IPAC Figure 14.4(a) |
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The same solid region with only the relevant piece of the graph
remaining.
cf. IPAC Figure 14.4(b) | |
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The solid region corresponding to a typical "subrectangle".
cf. IPAC Figure 14.4(d) |
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The electric field due to a positive point charge.
cf. IPAC Figure 17.11(a) |
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The magnetic field due to a current in an infinitely long straight
wire.
cf. IPAC Figure 25.2 |
| The geometry associated with defining surface integral. A surface is broken into pieces. For each piece, a point is chosen and the vector field (in red) is evaluated at that point. The area normal vector (in blue) is also computed. The surface integral is (a limit of) the sum of dot products of vector field and area normal vector. |
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This phase portrait shows solution curves for a 3 by 3 system of linear
differential equations.
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