Crimson Sunbird

I am just about the complete opposite of you – I learn more on my own than by talking to other people. Talking to other people tends to be rather distracting for me whereas my concentration is better when I’m doing and focusing on my own research.

Your solution looks fine to me.

It has to do with the fact that water has a much higher specific heat capacity than land. Water (compared with land) takes a long time to heat up, and once heated up takes a long time to cool down.

Exactly! It’s wrong. Apparently the hind legs of locusts weren’t counted as legs. http://www.tektonics.org/af/buglegs.html Likewise some people think crabs have only eight legs because they don’t count the animals’ claws as legs – but that’s also wrong! Crabs have ten legs, not eight.

Don’t forget that short-term memory and long-term memory are very different types of memory. Information in long-term memory is less easy to forget than in short-term memory.

Maybe the science of taxonomy was not as well developed then as it is today? That might explain why the ancient Hebrews didn’t have different words for avian ouphs and mammalian ouphs. And as for why they thought locusts had four rather than six legs, I suppose it’s the same as why some people think decapod crabs have eight rather than ten legs.

[latex]B[/latex] is a quantity called the bulk modulus of the material through which the sound is travelling; it is a measure of the material’s resistance to uniform compression and is defined by [latex]B=-V\frac{\mathrm dp}{\mathrm dV}[/latex] where [latex]V[/latex] is volume and [latex]p[/latex] is pressure. Think of it as the (infinitesimal) ratio of the increase in the external pressure applied to the relative decrease in volume produced.

I’ve just read about something called ankle jerk. Apparently, if I stretch the Achilles tendon of my foot tight by flexing it at the ankle and then tap my Achilles tendon, I should experience a reflex contraction of my calf muscles. I just tried it on my foot – but didn’t experience any involuntary muscle twitching! Is this abnormal? Or am I doing the ankle-jerk experiment correctly?

What do you mean by [latex]\frac{-2}{0}=-\infty[/latex]?

I think there’s an old discussion of this here: http://www.scienceforums.net/topic/15843-iron-iii-chloride-to-dissolve-copper/

[latex]\begin{pmatrix}1 & 2 & 0 & -2 & 0 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}\begin{pmatrix}a \\ b \\ c \\ d \\ e\end{pmatrix}=\begin{pmatrix}a+2b-2d \\ c+2d \\ e\end{pmatrix}=\begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix}[/latex] So, letting [latex]b=t,d=u[/latex], the general solution is [latex]\mathbf{x}\,=\,\begin{pmatrix}-2t+2u \\ t \\ -2u \\ u \\ 0\end{pmatrix}[/latex]

[latex]\sin x+\sin y = 2\sin\frac{x+y}2\cos\frac{x-y}2=\pm2\sin\frac{x+y}2\sqrt{1-\sin^2\frac{x-y}2}[/latex] NB: [latex]\cos\frac{x-y}2=\color{red}\pm\color{black}\sqrt{1-\sin^2\frac{x-y}2}[/latex] as [latex]\cos\frac{x-y}2[/latex] can be negative (e.g. when [latex]x=270^{\circ},y=30^{\circ}[/latex]).

How about … [latex]\pi\,=\,(-\pi)e^{i\pi}[/latex]

The largest currently known prime is [latex]2^{57885161}-1[/latex] – a staggering 17-million-digit Mersenne prime, discovered earlier this month by GIMPS (Great Internet Mersenne Prime Search). http://www.newscientist.com/article/dn23138-new-17milliondigit-monster-is-largest-known-prime.html