A Rose is a Rose is a Butterfly Varieties of Roses shows off the spectacular diversity of design that can be generated with iterated 2D function plots.
The section on Fermat’s Last Theorem may be your best hope of understanding 300 years at attempts at a proof and the dramatic proof finally announced by Andrew Wiles in 1995. Besides background on Diophantine equations like Fermat’s, the program includes a biography of Dr.Wiles and a for-mere-mortals notebook outlining his proof that finally resolved centuries of speculation.
There are notebooks with conventional-sounding titles (Calculus, Formulas for Pi) that nonetheless contain novel information on some old problems; notebooks for classic math topics (Four-Color Problem, Prime Numbers, Riemann Hypothesis); and notebooks whose titles are guaranteed to intrigue (Square Wheels, Varieties of Roses, Turtle Fractalization). The material on cryptography is especially enlightening (Secret Codes, Importance of Check Digits) because you can watch Mathematica carry out all the front labor of the encoding process – you’ll get to understand the working theory of public-key cryptography and the imperfect security of encoded Internet messages. A special section of biographies of mathematician from the Greeks to the present round out the collection.
Old Mathematica hands will start using Explorer right away but newcomers will need some time to familiarize themselves with the Help Browser and some fussy notebook conventions. Another mild complaint is that the interface style is exactly the same for all topics – although the content is entertaining on it own the CD would benefit from a better design.
Explorer uses a full Mathematica kernel (it lacks Mathematica’s subject libraries) so you can develop notebooks that expand on any of the Explorer topics and format them for exchange or viewing on the Web.
Macworld’s Buying Advice
Anyone who’s bought and enjoyed a copy of Scientific American is likely to spend hours fascinated by Mathematical Explorer. After spending a modest amount of time learning the interface, you’ll have equal access to numerical party tricks and the latest research developments.