My first aim in this story of ellipses, cones, and spacetime geometry is to stimulate cross-disciplinary thinking. I make connections between Euclidean and hyperbolic geometry, the latter providing the idiom of special relativity. The facts of hyperbolic geometry and linear algebra that I need are fairly elementary, but the physical intuition required to apply them depends strongly on your experience and background. The section titled Light Rays, Clocks, and Rulers: A Visual Primer (in special relativity) is my modest attempt to reinforce and develop that style of thinking.
My second purpose is to recruit 3-dimensional graphics as a heuristic method that can illustrate the hyperbolic geometry of and support visual intuition of some elementary facts of special relativity. For that, my pages (from page 5 on) have two components:
Static Hypertext Component: You may view the full text in any browser by continuing on with the numbered pages. Each page (after the Introduction on page 3) also contains a link to the same page in Portable Document Format (PDF), which you can download, read, and/or print at your leisure.
A Mathwright Microworld
, in which you can ask your own questions and experiment as you read along in your browser.
If you are on a Windows platform (Windows 98/ME/NT/2000/XP) with an ActiveX-enabled browser, such as Internet Explorer 5.0 or later, I strongly recommend that you interact with the dynamic component. You will find a link on each page (from page 5 on) to the Microworld, which will open in a new browser window. Each Microworld has instructions for the interactions within it -- click the Information button. You will need to switch back and forth between the static and dynamic windows.
If you have already downloaded the MathwrightWeb Player
, you need no further preparation. If not, please click to get the Player
, and then continue on page 3.
James E. White, "Special Relativity and Conic Sections - Our Story and Ways to View/Read It," Convergence (October 2004)
Journal of Online Mathematics and its Applications