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Tuesday, March 1

Hairy Ball Theorem...

If f is a continuous function that assigns a vector in R3 to every point p on a sphere, and for all p the vector f(p) is a tangent direction to the sphere at p, then there is at least one p such that f(p) = 0. In other words, it is not possible to comb the hair on a ball smooth, not without a bald spot.
Nuts, ain't it?
As AC/DC used to say,

some balls are held for charity and some for fancy dress, but when they're held for pleasure, they're the balls that I like best...

Note that donuts CAN be combed smooth in a fascinating variety of ways, thru the hole, or along the edge, or in a spiral.
Might take some work, tho...
Hours of endless fun with nary but a hairy donut (link not safe for male readers prone to fainting spells or penis envy) and a comb, proving that the male fascination with holes is as powerful and inevitable as, say, nuclear fusion.

7 Insights :

Blogger Takhara intuited...

Sometimes I wonder about you, Mathieu. ;)

3/01/2005 11:04:00 AM  
Blogger Mathieu intuited...

Who, moi?

*blink blink*

I'm just a nerd with a passion for maths and physics :)

3/01/2005 11:09:00 AM  
Blogger Alekx intuited...

My dear we really need to get you a hobby.

3/01/2005 10:00:00 PM  
Blogger Ria intuited...

Just having a bad hair day, I guess. Need to walk the earth until you find that point where the air is perfectly still.

Hold on. You've found a bald spot, haven't you? That so-called hairy doughnut is the top of your head.

Mathieu, don't be ashamed. Bald means balls. Now the whole subtext of the post falls into place!

3/01/2005 10:29:00 PM  
Blogger Mathieu intuited...

Ria, I'll have you know that we early-white-hair gents don't go bald, and that I have very thick, dense hair that the barber has to thin everytime I go there.

So there :P

3/01/2005 11:17:00 PM  
Blogger Kate intuited...

And I particularly like the *geek* stuff. :D

BTW The lady in your photo blog with the brown hair and camera-shy looks ... is that the princess? She's GORGEOUS!!

3/02/2005 12:51:00 PM  
Blogger Mathieu intuited...

That would be my daughter Chloe, Kate :D

I used to keep a rock-salt loaded blunderbuss handy when she was growing up, but now that she's eighteen and a student in another city, I've bowed to the inevitable and merely grind my teeth. ;P

3/02/2005 08:58:00 PM  

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