I’ve actually got enough comics for yet another Reading The Comics post. But rather than overload my Recent Posts display with those I’ll share some pointers to other stuff I think worth looking at.
So remember how the other day I said polynomials were everything? And I tried to give some examples of things you might not expect had polynomials tied to them? Here’s one I forgot. Howard Phillips, of the HowardAt58 blog, wrote recently about discrete signal processing, the struggle to separate real patterns from random noise. It’s a hard problem. If you do very little filtering, then meaningless flutterings can look like growing trends. If you do a lot of filtering, then you miss rare yet significant events and you take a long time to detect changes. Either can be mistakes. The study of a filter’s characteristics … well, you’ll see polynomials. A lot.
For something else to read, and one that doesn’t get into polynomials, here’s a post from Stephen Cavadino of the CavMaths blog, abut the areas of lunes. Lunes are … well, they’re kind of moon-shaped figures. Cavadino particularly writes about the Theorem of Not That Hippocrates. Start with a half circle. Draw a symmetric right triangle inside the circle. Draw half-circles off the two equal legs of that right triangle. The area between the original half-circle and the newly-drawn half circles is … how much? The answer may surprise you.
Cavadino doesn’t get into this, but: it’s possible to make a square that has the same area as these strange crescent shapes using only straightedge and compass. Not That Hippocrates knew this. It’s impossible to make a square with the exact same area as a circle using only straightedge and compass. But these figures, with edges that are defined by circles of just the right relative shapes, they’re fine. Isn’t that wondrous?
And this isn’t mathematics but what the heck. Have you been worried about the Chandler Wobble? Apparently there’s been a bit of a breakthrough in understanding it. Turns out water melting can change the Earth’s rotation enough to be noticed. And to have been noticed since the 1890s.
nebusresearch 