Simple City

Two things (one interesting, one very silly) that I have recently learnt about the sine function:

1. The sine rule, as most school-students know, says that in any triangle, is constant, whichever side A and opposite angle a you pick.

Less well-known is that this quantity actually has a geometric meaning: it gives the diameter of the triangle’s circumscribing circle. The Math Less Travelled has pictures.

2.

This may seem an innocuous enough fact. But prepare to be amazed! If you convert into degrees, you get 666^o, which is of course the the Number of the Beast. And you might spot the ubiquitous Golden Ratio lurking on the other side of the equation. So now our formula becomes:

The standard numerological-satanic interpretation of this fact, I am reliably informed, is that the Devil is the opposite of God (hence the minus sign), and only half as powerful. Where exactly the trigonometry fits in, I’m not sure…