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24 July 2000 Vol. 5, No. 30
THE MATH FORUM INTERNET NEWS
Zero Saga & Confusions with Numbers - Arsham DPGraph - Parker | Fly & Trains - Dr. Math FAQ
THE ZERO SAGA & CONFUSIONS WITH NUMBERS Prof. Hossein Arsham; University of Baltimore
A critical panoramic view of basic mathematical fallacies surrounding zero, such as:
- dividing by zero - taking the limit - IEEE special floating point - the notion of zero throughout history - when zero is "not there" - the origin of infinity and its symbol - taking the square root of both sides of an equality - manipulation on divergent series - taking conventions for proofs - taking the derivative with respect to a discrete variable - misplacement of the sign (square root) - confusion between a number and an operation, and - "errant views"
Notes, further readings, and references are included.
Written in assembly language, DPGraph runs under Windows and Windows emulators. The software allows you to:
- display multiple simultaneous dynamic photorealistic 3D implicit equalities and inequalities, and intersections of their volumes; - spin, slice, and view time-dependent (moving) photorealistic surfaces in real time; and - construct 2D, 3D, 4D, 5D, 6D, and 7D graphs (as an example of a 7D graph, DPGraph can do 3D arrays of time-dependent 3D vectors, i.e., dynamic vector fields).
Information on site licensing and costs, software reviews, technical support and FAQs, upgrades, and a library of graphs, movies, and links are available onsite.
The June issue of Visual Mathematics featured a gallery devoted to DPGraph, with graphs created by mathematicians and scientists from around the world, including three high school students and one junior high school student. The credits for the graphs are at the end of the gallery.
Two trains 150 miles apart travel toward each other along the same track, the first train at 60 miles per hour, the second at 90 miles per hour. A fly buzzes back and forth between the two trains until they collide. If the fly's speed is 120 miles per hour, how far will it travel?