The book was written by a famous author.

The book was penned by a renowned author. ’s another model I think I’m going to have to look at

I like rugby, but I’m not a good player. There are some interesting consequences of the rules I want to explore, which is actually a famous piece of Applied Maths about a real world sporting problem. To explain some of the rules for clarity: you can score points by putting the ball down over a line, which is called a try (similar to an American Football touchdown). After scoring a try in rugby, you then get a chance to get bonus points with what they call a conversion, where you kick over the posts. In American Football, you can take the kick from in front of the posts, but in rugby you have to take the conversion kick somewhere in line with where you put the ball down.

If you have the choice (which you do every time you score a try), how far back should you take the kick? If you’re really close, then you can imagine the post being at a weird angle, but if you go really far back, you can technically go to the other end of the pitch, but it wouldn’t be wise for range reasons.

If you put the try down under the posts, you have to take the kick in line with that, and there isn’t really a problem. If you put a try down to the side of the posts, it can be difficult to take the kick from far away, as the range starts to become an issue. However, the further back you go, the narrower the angle looks because you’re further away.

There is a five meter line on the rugby pitch, and it’s generally accepted that the angle most people kick at is about 30 degrees. As long as you’re a distance the other side of that line, you’re likely to be able to clear the crossbar. If you’re closer than that, you’ll have to do a proper chip. Using Pythagoras’ Theorem, it can be determined that the distance, $y$, of a right angle triangle is a function of $x$ and $d$, where $d$ is 2.8 meters.

$$y = \sqrt{x^2 - \frac{d^2}{2}}$$ were saying is actually a pretty good way to get close to the best spot.

The rule of thumb for calculating the best spot to kick the ball after scoring a try in rugby is to walk 45 degrees from the center of the goal posts. This is a much quicker way to get very close to the answer than using the formula, which is tough to do in your head. The only place where the 45 degree line doesn’t overlap with the actual best spot is close to the goal, which is too close to kick from anyway.