Bookshelf -- Calculus: An Historical Approach by William McGowen Priestley

When I first made the transition from the humanities to the sciences, I started a long and often discouraging search for books that were well written enough to stand alone rather than simply provide a set of examples and problems for a class.

Priestley's Calculus was one of the best books I came across.

Calculus: An Historical Approach by William McGowen Priestley

Poplollies & Bellibones: A Celebration of Lost Words

I don't have any real math connection, I just felt like posting this.

The Wonderful Paper Trees

From Popular Comics 9

The Shadow Knows

I believe this is by the great cartoonist and puzzler A.W. Nugent (about whom we will be hearing more).

I like this for a few reasons.

First, as a creativity exercise it brings in new and unusual shapes and gives the students open-ended instructions in how to deal with them.

Second, it helps build intuition about geometry (particularly projective geometry).

Third, it looks like fun.

The one change I would make would be to get different shapes from the same crumpled piece of paper by moving the light source.

The greatest board game series ever?

I was never entirely clear on why 3M decided to get into the board game business, but for more than a dozen years they put out 3M's Bookshelf Games (so called because the boxes were designed to look like large hardcover books when placed in their slip covers). The line-up was a mixture of traditional games like chess and go and new games designed by freelancers like the incomparable Sid Sackson (Sackson's classic Acquire was a 3M game). The weakest of the series were still pretty good while the best have become, as mentioned before, classics.

Software developer Dennis Matheson has a detailed and affectionate website devoted to the series, Wikipedia has a good write-up as well, and, if your bookshelf has more space than mine, you can buy most of the games on EBay.

[Originally ran in West Coast Stat Views]

Bookshelf -- The Hinged Square & Other Puzzles by Ivan Moscovich

I haven't seen the rest of the series but based on this book and Moscovitch's reputation, I'd certainly recommend seeking them out. The puzzles are beautifully illustrated and, in some cases, accompanied by a explanation of  the underlying mathematics.

The book also features the extraordinary pencil and paper game racetrack.

Make your own Platonic Solids -- let the conspiracy theories commence

(Via Google, I found these at the Philalethes Society site, so active members of the Anti-Masonic Party might want to skip to the next post)

Here's another chapter in the ongoing playing with paper series. There are any number of interesting lessons you can build around the five Platonic Solids (as usual, Martin Gardner has some clever suggestions), but the best place to start is probably by building intuition by letting the kids make and manipulate them.

Depending on the age and sophistication level of the class, try one or more of the following:

1. Decorate then assemble these patterns;

2. Use these patterns to make dice. Try playing familiar games (chutes and ladders, Parcheesi, etc.) with the new dice;

3. Make mobiles using Platonic solids and paper tubes;

4. Make sculptures with the condition that attached sides have to match (this gives you three types of sculptures -- cube-based, dodecahedron-based and everything else);

5. Measure the surface area of each solid;

5b. Use fine Styrofoam pellets to estimate and compare the volumes of the different solids.

6. Using clear plastic for the outer shell, create dual polyhedron.