I've wasted hours sitting in front of a real life Klein bottle. It's just,
well, incredible. Am I right in thinking that a *true* Klein bottle can't
actually be made in three dimensions? Can it be done in 4
dimensions, or 5 or 6 or 7 or...?
surface area to volume ratios... if you halve somethings size you don't
halve its surface area. The best visual explanation I've seen of this
(for kids) is by cutting an orange in half - it's obvious tha the juicy bit
is extra surface area yet the mass has just halved.
Oh yeah.. the other half of the answer is wind resistance, which is
directly related to surface area..
That's right. Some people who own pet rodents don't seem to understand this, though. They
think, 'well since it's such a small and weak animal compared to me, it can't survive large
drops, so I have to make sure it never drops very far.' While a mouse, say, will not find the
experience of dropping 4 feet particularly pleasant, it's not going to injure the mouse at all
unless it's a REALLY stupid one that doesn't even try to land on its feet. I had a hamster
once that would climb to the top of its cage, start swinging about on the ceiling bars, lose its
footing and fall down again. Scaled up to human size it would have looked very dangerous.
But clearly for my hamster it was so little of a problem that it kept doing it! Mind you, I did
have a rather stupid hamster that would walk off the edge of my hand (with my hand a few
inches above a table maybe) and then land on its nose.