Monday, August 31, 2015

Book Review: A beginner's guide to constructing the universe + some updates


After returning from our last road trip of the summer I received news that the back to school night was cancelled due to a teacher contract vote. Fortunately, I hadn't started actively working on a banner for the table. On the other hand, I now need to throw together a quick flier that parent and kids can pick up on  the first day of school. I've drafted one based on the blurb and some teaser problems that I may throw up here once its done. Hopefully, this won't affect the recruiting process. More seriously, I hope the district and union reach an agreement without deteriorating into a strike.


On a lighter note, my copy of A beginner's guide to constructing the universe by Michael Schneider arrived at the library. I found a reference to this book in a blog elsewhere that suggested it might have interesting ideas for activities within it. After reading a few chapters, I'll cut to the chase. You'd be much better off looking at Paul Lockhart's Measurement for an exploratory approach to geometry and numbers. 

The author's central tenet is that rote computation has divorced mathematics from its connection to the natural and spiritual world. He then organizes chapters around the numbers 1 to 10. Each one starts with the geometric construction of a corresponding n-gon (1 uses a circle and 2 a line).  From there he branches off to various natural, classical or psychological references. For example, the chapter on three starts with a reference to Sir Percival and then a reference to how the root of three is found in the words through and threshold.  Some of this historical material is interesting but it often has a strong new age flavor. I'll give a quick sample: "The discovery and appreciation of the circle is our earliers glimpse into the wholeness, unity and divine order of the universe. Some psychologists say that the discovery of the circle arrives as the child discovers the self and distinguishes himself from another." 

While there are occasional mathematical discussions. They are not explained just presented as a mystery. If you're interested in a new-age / mathematical text this might work well for you. For even learning construction I think there are better resources organized around more interesting frameworks.  I'd rather skim Numberphile videos or directly  read about Plato and Euclid rather than see them melded as done here. 

One riff I thought about while looking at the chapter was how the author would handle the non- constructible polygons like the case for 7 or 9 . Sadly he chose to present non-regular versions that can be scribed and left off the really interesting part as far as I'm concerned: what governs this property. I think a dive into Gauss's theory is not really manageable at the math club level but it does make me wonder how interesting it would be to talk about pencil and compass construction practicing some basic techniques and then having the kids try to discover which n-gons they could make. 


This problem from Math For Love is interesting.  I've only stared for a moment and come up with sqrt(5) so far on the theory equalize the distance on each face.

An ant wants to crawl from one corner of a cube to the opposite corner. What is the quickest path it can take along the surface of the cube, and how long is this path?

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