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.
