Here's an interesting maths fallacy (and thanks to DH for pointing me to the page with it on).
I also had a nifty scientific idea this morning. I was watching Firefly (TV sci-fi series, they only ever made one series of it) yesterday. One of the odd details is that all the planets and moons are meant to be in the same stellar system, but they all look remarkably like Earth. Odd that.
Anyhow - I was wondering how one might go about getting enough light and heat from the Sun to make them warm enough for habitation, and I figured that putting a lens at the Lagrange Point could well do it. Then I realised that such a lens would need to be pretty huge - nearly planet-sized even, and so would effectively require you to demolish a planet / moon to make it.
Then I thought of an interesting way round - use a Fresnel Lens (like those magnifying sheets you can get). You'd still need a big lens, but it'd be essentially 2D rather than 3D, so would need far far far less material and at least be possible.
It's my birthday! Woo!