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Here’s a quick sketch of the idea that’ll make me a millionaire…

The Ladybug and I have been listening to Here Come the 123s, a CD that combines two of my favorite things: They Might Be Giants and mathematics.  Here is another song off the album called “Figure Eight,” which besides being really catchy makes an number of interesting geometric observations, including a parametric description of a Figure Eight (the chorus), a comment on the rotational transformation between the infinity symbol and the Figure Eight, and a homotopy construction of the Figure Eight from the circle.  And you can watch the video on YouTube, too.

Figure Eight

Round.
Can you go around?
And if you can turn around without falling down
You can skate in a Figure Eight.
If you can turn, if you can go straight.

Turn left! (Eight!)
Go straight! (Eight!)
Turn right! (Eight!)
Straight again! (Eight!)
And then do it over (Eight!)
Repeat forever (Eight!)
That all you need to know (Eight!)
That’s the way you skate in a Figure Eight.

If you can grab a circle in your hands and twist it, that’s an Eight.

If it weren’t for the Zamboni
You would never leave the ice.
And I think I know the reason why you never take a break:
The sign that means “forever” is a sideways number “eight.”

Turn left! (Eight!)
Go straight! (Eight!)
Turn right! (Eight!)
Straight again! (Eight!)
And then do it over (Eight!)
Repeat forever (Eight!)
That all you need to know (Eight!)
That’s the way you skate in a Figure Eight.

And if you twist the number Zero you will get the number Eight.

Turn left! (Eight!)
Go straight! (Eight!)
Turn right! (Eight!)
Straight again! (Eight!)
And then do it over (Eight!)
Repeat forever (Eight!)
That all you need to know (Eight!)
That’s the way you skate in a Figure Eight.

If you can grab a circle in you hands and twist it, that’s a Eight.
Grab a circle in your hands and twist it, that’s an Eight.
Twist the number Zero, you will get the number Eight.

The Ladybug and I have been listening to Here Come the 123s, a CD that combines two of my favorite things: They Might Be Giants and mathematics.  Here’s one of my favorite songs off the album, whose video is fortuitously on YouTube.

Nonagon

Everybody at the party is many-sided polygon.
When a guest arrives they will count how many sides it has on.
Standing by the window over there
There is a shape with four sides, so it’s a Square,
And the one who has nine is lookin’ fine
And its name is Nonagon.

Everybody turns just in time to see the Pentagon arrive.
Counting up the sides, it is clear the Pentagon has five.
Chatting in the kitchen we see
There is a Triangle, who sides number three,
And it’s talking to the shape that has nine who is known as Nonagon.

Nonagon!

Nonagon lets in a guest who has shown up late.
Its name is Octogon and its sides add up to eight.
Turning the music on is a six-sided Hexagon,
And they all get in a line and do a dance called the Nonagon.

The Nonagon!

The Nonagon!

Spied on a CS major’s tee-shirt:

A mathematician named Klein
Thought the Moebius band was divine
Said he: “If you glue
The edges of two
You’ll get a weird bottle like mine.”

Then Bennet, in a great huff,
Declared “One just ain’t enough!
I’ll start off with three
And embed them, you see…
Voila! Some fine, artsy stuff.”

Thanks to Jake O, for showing me this cool triple Klein bottle at sciencemuseum.