Comments on: Comments on 21286

Post number 21286

Morphic — Fri, 01 Nov 2002 08:50:56 -0800

Recreational mathematics and fractal graphics continue to stimulate the mind and foster student interest in mathematics. Some favorite authors & books in this area include: Martin Gardner's books (like The Colossal Book of Mathematics and The Night is Large), Cliff Pickover's books (like The Mathematics of Oz and The Zen of Magic Squares), Calvin Clawson's Mathematical Mysteries, Ian Stewart's books and puzzles, and Ivars Peterson's writings (like Islands of Truth). What are your favorite books and web sites in this area for stretching the mind and eye?

By: blogRot

blogRot — Fri, 01 Nov 2002 09:13:21 -0800

((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0 Best. Poem. Ever.

By: Pretty_Generic

Pretty_Generic — Fri, 01 Nov 2002 09:44:45 -0800

Arcadia, the Tom Stoppard play I'm going to be in (Bloomsbury Theatre, London, 14-16 November!) is largely about fractals and iterative algorithms. It's also incredibly funny.

By: qDot

qDot — Fri, 01 Nov 2002 10:06:42 -0800

One of my favs has always been Burlekamp's Dots and Boxes: Sophisticated Childs Play. It's a mathematical breakdown of the dots and boxes game I'm sure everyone has played at least once in their life. I'm a big fan of all of Burlekamp and Conway's stuff though (If you want some good Conway stuff, pick up On Numbers And Games or Winning Ways For Your Mathematical Plays Just as a side note, the field of Recreational Mathematics was started by Roger Penrose, who you may know from "The Emporer's New Mind" fame. He created the Penrose tesselation which once again, you've probably seen but I can't find a link to that the moment. Many of his tesselations are now available as puzzles, which are sold at Pentaplex.

By: andrew cooke

andrew cooke — Fri, 01 Nov 2002 10:23:41 -0800

if anyone is interested in gödel, formal languages, and modern set theory (who knows - maybe someone is!) i think i've found the perfect book - discovering modern set theory (part 1 - the basics) by just and weese. you need a basic maths background (eg i have a degree in physics), but it is very nicely written (it's based on lectures, with many comments and jokes addressed to the reader) and (so far - i've only had it a day or two) pretty clear. (i know this isn't exactly recreatoinal maths, but it's fascinating, and deeply important, stuff)

By: modge

modge — Fri, 01 Nov 2002 10:29:46 -0800

Metamagical Themas : Questing for the Essence of Mind and Pattern by Douglas R. Hofstadter is good.

By: entrustNoOne

entrustNoOne — Fri, 01 Nov 2002 10:46:32 -0800

Another of my favorites is Gödel, Escher, Bach: An Eternal Golden Braid, also by Hofstadter. Linking the 3 was pure genius. I've read it twice and would read it a third time, if I could find my frayed copy.

By: andrew cooke

andrew cooke — Fri, 01 Nov 2002 10:49:11 -0800

[self link] - i wrote a little python package for creating parquet deformations like those described in metamagical themas. it's not very good - i would do it differently now - but anyone who read the book might be interested.

By: swordfishtrombones

swordfishtrombones — Fri, 01 Nov 2002 11:24:22 -0800

I recently read Ian Stewart's book about zebra stripes and the shape of snowflakes. The knowledge you need to explain these shapes is immense: fractals, symmetry breaking, turbulence, etc. Great book. I also loved his book with Pratchett and Cohen (the Science of Discworld), which I consider one of the best (and funniest) accounts of 'holistic science'. The sequel was not quite as good.

By: swordfishtrombones

swordfishtrombones — Fri, 01 Nov 2002 11:28:16 -0800

and don't forget Simon Singh's "Fermat's Enigma"...

By: notsnot

notsnot — Fri, 01 Nov 2002 11:32:22 -0800

I'll second/third the recommendations for Hofstedter's works (GEB and MT). I've tried to describe GEB to those that have never heard of it, and failed miserably. Anyone here have a good, concise way of describing the wonder, breadth and scope of that work?

By: andrew cooke

andrew cooke — Fri, 01 Nov 2002 11:38:17 -0800

any description should include the word "whimsical" (if only because, if you don't like whimsy, it's a rather trying read).

By: trharlan

trharlan — Fri, 01 Nov 2002 12:00:54 -0800

I find the math stuff pretty interesting, but have yet to find that seminal work that unlocks it for lay people. Is there anyone who has done for math theory what Hawking has done for cosmology or Briggs and Peat have done for chaos theory?

By: TedW

TedW — Fri, 01 Nov 2002 12:03:38 -0800

One of the best and most comprehensive math books out there is Mathematics: From the Birth of Numbers by Jan Gullberg, a Swedish surgeon. It has everything from the history of numbers and counting to detailed explanations of fractals and topolgy. Well worth a look, although at 1200 pages, it is hardly something to breeze though at the beach. On preview: this may be the book you are looking for, trharlan. I enjoy mathematical ideas, but never excelled in it in school and am definitely a layperson when it comes to math, but I have enjoyed the book both as entertainment and as a reference.

By: gleuschk

gleuschk — Fri, 01 Nov 2002 12:06:31 -0800

Erm, trharlan, both of those examples are subsets of mathematics. The theories that Hawkings and others describe are essentially mathematical, and chaos theory is a field of specialization within mathematics. Your question is similar to, "I understand football and baseball, why can't someone explain sports?"

By: Joey Michaels

Joey Michaels — Fri, 01 Nov 2002 12:21:55 -0800

Best. Friday Fun. Ever.

By: antimony

antimony — Fri, 01 Nov 2002 12:22:52 -0800

blogRot: That's one of my favorites too! Along with: I used to think math was no fun 'cause I couldn't see how it was done Now Euler's my hero For I now see that 0 =e^(i*pi) + 1

By: ptermit

ptermit — Fri, 01 Nov 2002 12:40:48 -0800

There's a few really good ones out there. Simon Singh's Fermat's Enigma has been mentioned already. George Ifrah's The Universal History of Numbers is a relatively easy-to-read survey (and a good reference). Charles Siefe's Zero was a surprisingly fun book to read. Tobias Dantzig wrote a really good one about numbers, but I think it's out of print, unfortunately.

By: Loudmax

Loudmax — Fri, 01 Nov 2002 12:56:35 -0800

I'll add another voice in encouragement for Goedel Escher, Bach. It was one of the most thought-provoking books I've ever read. It's also a lot of fun. Chaos is another good book on match.

By: Loudmax

Loudmax — Fri, 01 Nov 2002 12:57:54 -0800

..errr, "book on math." Sorry. :P

By: crunchland

crunchland — Fri, 01 Nov 2002 13:00:04 -0800

something is very, very wrong here.

By: Schismatic

Schismatic — Fri, 01 Nov 2002 13:26:34 -0800

Another book that is on mathematics, but without covering any specific area, is G.H. Hardy's A Mathematician's Apology. It would perhaps be better to call it a book about the philosophy of pure mathematicians than actual math, but it's nevertheless an interesting insight into the field as a whole.

By: namespan

namespan — Fri, 01 Nov 2002 13:26:49 -0800

An old but fun book The Eight by Katherine Neville. Not very mathematical, but interesting how math is woven into the plot.

By: Flat Feet Pete

Flat Feet Pete — Fri, 01 Nov 2002 13:28:54 -0800

[self link] I've written an app to wrap six arbitrary images onto a hexaflexagon (as mentioned in the Colossal Book Of Mathematics). A fun way to carry around pictures. http://hexaflexagon.sourceforge.net/

By: Schismatic

Schismatic — Fri, 01 Nov 2002 13:55:17 -0800

People here don't seem to be mentioning websites and there are a vast number of great ones. Here are some that I keep handy. The de facto standard is MathWorld, although it is more of a mathematical dictionary than a place to explore new concepts. Knot a Braid of Links can send you to many sites that don't assume technical knowledge, but are on interesting subjects like the mathematics used in 17th century war or, my favorite, topological lego structures. If set theory (or quantum logic) is more your style, Metamath should be sufficient to keep you for a while, although it can get hard to follow due to lack of prose. (Gotta love the proof that x=x) Finally, for a mix of random topics explained in good detail (including relations to physics) and understandable to anyone with a slight background in calculus, try MathPages.

By: dhartung

dhartung — Fri, 01 Nov 2002 19:00:04 -0800

A good book for the armchair mathematician is Innumeracy by John Allen Paulos, who's also written a few other engaging works in the same vein. This one discusses how people are very poor at handling basic mathematical concepts, which inhibits their ability to understand budgets, manage projects, and compare practical risks. How much is a trillion? What happens if you double the width and length of a farmfield (answer: you quadruple your expenses)? Which is more dangerous, an airplane ride, or jaywalking to drop off a letter? I don't know a better way to explain GEB than "an accessible yet challenging overview of the intimate relationships between mathematical theory, artistic perception, and human creativity" -- or "the perfect gift for the geek in the family".