Monday, August 31, 2015

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

Events 

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.

Book 

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. 


Misc.

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?

Monday, August 17, 2015

8/17/15 Pythagorize Seattle Photos

Today MoMath celebrated the Pythagorean Triple comprised of  the date: 8^2 + 15^2 = 17^2 with a math happening at South Lake Union. In case its not obvious: 225 folks in blue shirts lined up on one square and 64 in green on the other. We then all moved to the hypotenuse and confirmed the triple. I'm hoping someone took an aerial view that I can add later.

It included a very silly song they wrote to the tune of "Shut up and Dance with me": http://momath.org/about/pythagorize-seattle-song/

Here's my photos from the event. The last one's the triangle pub down by my office which apparently is really 8x15x17 meters.

















Tuesday, August 11, 2015

A quiet week

Updates

I'm really starting to miss interacting with the kids and there are still nearly 8 weeks to go before we start up. In reality, there's not much that needs to be done in the summer.  Already I've been assigned a room number and fixed the enrollment cost for next quarter. I think we're the cheapest activity since I just try to cover my parking costs, entry fees and supplies.  I've also signed up to man a table on Back To School night and need to fine tune my club blurb for next year. Finally, I've been working on singing up to administer the AMC8 in the fall. Exposing the kids to the AMC8 is one of my new goals for the year.

Blurb

Here's what I had last year mostly based on the previous volunteers wording:


"Math Club is a great place for 4th and 5th graders who enjoy math, are interested in more challenging problems and/or math competitions."



This is okay but I'm hoping to really improve it. Here's my current draft:


"Are you hungry for more math? Math club is looking for fourth and fifth graders who enjoy puzzles, challenge problems and spending an hour after school with others who share their passion. We will be exploring a variety topics from geometry to a little number number theory to combinatorics. There will also be a chances to compete in contests like the MOEMS Math Olympiad."

Teasers


Last year since we started late and did not have a classroom until the end of October I ended up sending out some teaser problems for those who were excited to start (besides myself).  

I've saved them here:


I'm going to reuse them again this year but instead point those who are interested to try them out before signing up.  I will definitely update the encoded message so its topical. I figure this will let the kids and parents see what I'm aiming at and hopefully attract those kids who are.

Link for a problem with an interesting meld of graph theory and number theory:
http://blog.ifem.co.uk/fmsp-favourite-problems-number-3/
The blog above already did an excellent write up.

Corny Joke:

Why did the Chicken cross the mobius strip? To get to the other ... er ... oh never mind.


Wednesday, August 5, 2015

Squaring the Rectangle

This  Tiling Problem published in wordplay by Matt Enlow looks like a great first day activity.
The question it asks is given an n x m rectangle what is the smallest number of squares it can be divided into. You can make it harder by requiring each of the squares be a different size.



Its more in the noticing and wondering category but  hopefully allows the kids in the math club to find some interesting algorithms and patterns.

Some history on the problem class:
http://www.squaring.net/history_theory/brooks_smith_stone_tutte_II.html

This has a cool relationship to the Euclidean algorithm. If you do a greediest algorithm the final square size is the GCD.

The greedy algorithm basically find the quotient via the largest square with the remainder being what's left which is why its the same thing as the standard Euclidean algorithm to find the GCD.  Note: getting the kids to see this as division will probably take some experimenting i.e. ask the question "Is there a pattern to what the left over area is after you take away the biggest squares?"

See:  an animation half way down in the following link:
https://en.wikipedia.org/wiki/Greatest_common_divisor

Which is something I've liked to develop but haven't found a good entree yet.  This may be it.

My main worry is whether there is enough time to fit this in if I also do the intro discussion. This feels like an almost full slot worth of activity. I could have everyone work on the conceptualizing of division and then split off with one set of kids looking for patterns on what's left over and a second looking for the smallest set of squares that tile the rectangle and patterns for finding them.

Semi-Related variant or math homonym:

How to take a rectangle and find a square with the same length. This requires the Pythagorean
theorem to prove.

http://mathworld.wolfram.com/RectangleSquaring.html