Monday, August 9, 2010

Learned something new from a Dummies book

I flipped over Geometry for Dummies and I am pleasantly suprised that I learned something new today.

A soccer ball is made by starting with a platonic solid, the icosahedron, and chop each corner off! Namely it is a truncated icosahedron.

I have always wonder the shape of a soccer ball... other balls (basketballs, volleyballs, baseballs, etc are made in more straight-forward ways).
Now I know the interesting formation of pentagons and hexagons formation come from that...

In that same Appendix section there was some brief talk on the Golden Ratio. Just about everyone who writes about it are SO fascinated by this number that they just keep praising it is FASCINATING by showing the golden spiral and shell shape.
Most authors simply too excited and never give good details to explain the phenonenom. (This is because φ -1 = 1/φ. You chop 1 off (the square) and you still have the golden ratio, and you can keep doing this)

Dummies book... don't let the title fool you, though it is a bit insulting, but most dummies book actually have some very good information with a splash of humor.

Look at how this author explains logic.
If I study hard, I get good grades
If I get good grades, I become a guy/babe magnet.

Contrast that with this:
Let p, q, r be conditions:
If p => q
and q => r
then, p => r, by transitive property.

Examples! Especially real world examples are nice to have in math texts.

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