...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

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"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Sunday, September 20, 2015

Two More Books


Just mentioning a couple of volumes today for your consideration (both currently available in paperback, BTW)....

Won't have time to write a full review, but will recommend Alfred Posamentier's (with Bernd Thaller) latest book, Numbers: Their Tales, Types, and Treasures."  It's a typical Posamentier offering... clearly written and organized, without oversimplifying or dumbing-down the wide-ranging material; some interesting and fun things mixed in with historical and classic material.
I enjoyed the second half of the book, and especially the last few chapters, more than the first half with its focus on history (for whatever reason, math history, pre-1800 has never much held my interest). Again it is a great refresher for some adult math enthusiasts and an especially good read for the young person already inclined toward mathematics.
The final chapter of the book focuses on foundations and philosophy of mathematics, although near the end the authors seem to favorably quote Steven Weinberg's portrayal of philosophy as something that does not "provide... any useful guidance" to scientists. They even cite another philosopher as saying that philosophy is a "waste of time... from the point of view of the working mathematician." (Most of the book is definitely more mathematical than philosophical.)

Anyway, if you want to get a greater sense of the volume's overall content, here's a longer review from the Web:
http://tinyurl.com/o97tzvr

    A book I'm currently perusing (haven't finished, but willing to recommend) is "Professor Povey's
Perplexing Problems" by Thomas Povey, who will be familiar to many from his "Perplexing Problems" website:
http://perplexingproblems.com/

The book is a nice compendium of amusing problems with varying difficulty;  a little more challenging mix than often found in standard puzzlebooks. However, only about a quarter of the problems are strictly mathematical. The remainder are more physics-related (though often, of course, still requiring math), so for someone with little interest in physics this may not be a good book choice. Luckily, most math fans probably enjoy physics as well, and young, budding physicists should definitely enjoy.

In the last chapter Povey tells the story of Larry Walters who took flight from his backyard in 1995, in a lawnchair powered by helium balloons, just one of the typically entertaining segments of the book. You can read more about Larry here if you like:
http://www.markbarry.com/lawnchairman.html

You can even view news of Larry's oddball flight on YouTube here:
https://youtu.be/CFFVVo9usFY?t=33s 

And here's a couple of lines that cracked me up for some reason, from chapter 2 of the volume:
"Over dinner once I was told what I believe is a true story about the principal of a Cambridge college taking out a calculator to multiply a number by 100.  In a rare moment of lucidity I quipped, 'was it a difficult number that was being multiplied?' Only the scientists got the joke."
Anyway, you get the idea, in-between the puzzles are some entertaining bits.
To finish out, I'll adapt one of the simpler math problems from the volume for inclusion here (I'm telling it less entertainingly than Povey's rendition):

Captain Fishmonger goes on a treasure-hunting voyage.  He arrives at the deserted island for which he has a treasure map showing just two trees and the instructions, "Walk 50 paces from one tree AND also 50 from the other. There lies the treasure."
But as Fishmonger peruses the island he finds that in the time since the treasure was buried and the map drawn, now 14 more trees have grown up. There are now 16 trees all less than 100 paces from one another.
In the WORST CASE scenario, what is the MAXIMUM number of spots the Captain will need to dig to find his treasure?
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. answer:  240  ...drawing 50-pace circles around any two tree-pairs gives you TWO possible digging (intersecting) points, and combinatorics can be used to calculate the total number of possible tree pairings (120).  2 x 120 = 240 as maximum number of digs required.


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