I'm so glad you asked. The short answer is no. You can only infringe a patent if you make, use, sell, offer to sell, or import the patented device without authorization.
Displaying images of an invention or explaining how an invention works doesn't infringe the patent, although there are two related concerns. It's unclear whether patent drawings -- the drawings included with the application (see above -- Patent No. 6,293,874) -- are protected by copyright. (Although there is no clear ruling, caselaw and federal regulations seem to indicate they are protected.) So, you're best served by having someone re-create the drawings unless you want to make a case for fair use.
Second, you can use the trademarked name of a patented invention without permission if it's for informational or editorial purposes -- that is, you're not using the trademark to sell something, or to confuse consumers. The same is true for trademark logos and designs (although, you should avoid any alterations to those visual images).
In any case, the patent division of the Dear Rich staff is excited about your software and its benefits --- after all, in the case of dangerous inventions like matches, the user can see how the invention operates without the potential hazards. (Let's not even think about all those inventors killed by their own inventions?)
