[math-fun] Penguin Dictionary of Curious and Interesting Geometry
Do people know this book, "The Penguin Dictionary of Curious and Interesting Geometry" by David Wells (1992)? I just chanced on it on my shelf of Long Lost Books, and find that it bears many repeated browsings. It has a number of old chestnuts, but also a huge number of geometric tidbits (and a few topological ones) that I hadn't seen before or knew very little about. It's written engagingly and pretty clearly, and has excellent B&W graphics to accompany each little squib. For example, the 6 circles theorem: Given a triangle in the plane, draw a circle tangent to just a pair of its sides. Now pick a different pair of sides, and draw the unique circle tangent to those sides and the first circle. Now there will always be a unique new circle if you keep choosing the pair of sides not used for the last 2 circles and repeat this operation. Theorem: After six circles are drawn this way, the seventh is the first, the eighth is the second, etc. (David Wells also wrote the "Penguin Dictionary of Curious and Interesting Numbers", which I've heard is also good.) Dan
At 05:15 PM 3/7/2005, Daniel Asimov wrote:
Do people know this book, "The Penguin Dictionary of Curious and Interesting Geometry" by David Wells (1992)?
(David Wells also wrote the "Penguin Dictionary of Curious and Interesting Numbers", which I've heard is also good.)
I have heard of the geometry one but not seen it. I have two editions of the second one, and it is a lot of fun.
There are many interesting facts in this book which I didn't know, and I try to keep up with elementary geometry. One is an asymmetrical figure containing a point such that every line through it divides the figure's perimeter in half (page 30). Another is the answer to the question "Given a square made of equal rods hinged at their ends, what is the minimum number of additional rods, of the same length and hinged at their ends, are needed to make the square rigid (in that plane)? The answer is 19, more than I would have guessed. There is also at least one theorem I needed as a reference in a paper which I couldn't find anywhere else. (Of course it's hard to search for a geometry theorem because you never know how to describe it.) In fact right now I can't remember what it is, or (needless to say) find it in this book! I recommend it, but there are very few references to the professional literature. I'd be reluctant to cite this book in a paper, because it's a dead end, and the reader would not know where to find more information. Steve Gray
Do people know this book, "The Penguin Dictionary of Curious and Interesting Geometry" by David Wells (1992)?
(David Wells also wrote the "Penguin Dictionary of Curious and Interesting Numbers", which I've heard is also good.)
I have heard of the geometry one but not seen it. I have two editions of the second one, and it is a lot of fun.
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(David Wells also wrote the "Penguin Dictionary of Curious and Interesting Numbers", which I've heard is also good.)
In my edition, the least uninteresting whole number is 43. Here's a coincidence: 43 is also the least whole number absent from the Holy Bible. (Chapter and Verse numbers don't count.) And, it's the first atomic number missing from nature (Technetium). In one other circle, 43 is very interesting; whenever Sloane's A000043 is extended, it's news. -- Don Reble djr@nk.ca
Also, 43 is the largest non-McNugget number, the largest number of Chicken McNuggets that you could not order in the original standard boxes of 6, 9 and 20 McNuggets. ----- Original Message ----- From: "Don Reble" <djr@nk.ca> To: <ham>; "math-fun" <math-fun@mailman.xmission.com> Sent: Tuesday, March 08, 2005 1:08 AM Subject: Re: [math-fun] Penguin Dictionary of Curious and Interesting Geometry
(David Wells also wrote the "Penguin Dictionary of Curious and Interesting Numbers", which I've heard is also good.)
In my edition, the least uninteresting whole number is 43. Here's a coincidence: 43 is also the least whole number absent from the Holy Bible. (Chapter and Verse numbers don't count.) And, it's the first atomic number missing from nature (Technetium).
In one other circle, 43 is very interesting; whenever Sloane's A000043 is extended, it's news.
-- Don Reble djr@nk.ca
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participants (5)
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Daniel Asimov -
David Wilson -
Don Reble -
Jud McCranie -
Steve Gray