This is my solution to the “Kill the Dragon!” puzzle. Improvements, in both the bounds and formality of the argument, are definitely possible.
Monthly Archives: February 2012
Kill the Dragon!
A hapless lost dragon has accidentally landed in a nearby lake. You, the kingdom’s sworn dragon-slayer, have set out on this foggy night to kill it. You are armed with your trusty trebuchet, which can catapult a fiery projectile to any location on the lake. When the projectile hits the water, it will explode in a lethal circle of Greek fire, killing everything within a radius of metres from the point of impact. Especially dragons.
The fire, however is short-lived, and is extinguished instantaneously. This means the dragon, who swims slowly at a constant speed of metres per minute, can safely doggy-paddle into a previously scorched area. You can launch one missile per minute.
It’s so foggy, that you can’t tell whether you’ve killed the dragon, which is too tired to leave the lake, and you can’t be bothered to fetch a boat to check. If the lake is a circle of radius metres, is it possible to aim your volleys strategically to be sure that you will eventually kill the dragon, no matter how it moves?
For which radius is it possible, and for which is it impossible? What about other shapes of lakes?
[If you're looking for the partial volume equations of a horizontal oil-tank, this article by Dan Jones has a nice write-up. Of course, you could just get someone to make a dipstick for you. My article only gives an overview of the problem, and how to approach it, from the perspective of a pure mathematician.]
This is the second post about real-life enquiries sent to my maths department, this one from a local engineer. Again, here’s the relevant section of the e-mail, partly to illustrate that, what might not at first seem an engaging problem for a pure mathematician, can turn out to be.
I need to calculate the capacity of a cylindrical tank laid horizontally with domed ends, in order to make an accurate dipstick. I would need to do the calculation several times in order to obtain capacities at varying levels.
This post is about how I went about finding a solution to this problem, and checking how good a solution it was. So now, if you happen to need a dipstick that fits these requirements (or just of a simple cylindrical tank), you can have one precision engineered to order. To continue the barge theme from the previous enquiry, you can also get a dipstick made for your barge’s diesel tank.