this is for holding javascript data
João Paulo Pesce edited 3.tex
about 10 years ago
Commit id: f3da14cc89ec9a836f234813e8a9e07a5555ed95
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That looks good. At about 2km, scores start to get quite low (25) and by $\sim$4km the user will get almost no points. That's pretty reasonable for a city the size of Belo Horizonte, but if you take a really small city, getting 25 points for a 2km distance might be just too much. So let's adjust the score based on the size of the city.
Suppose $A_{\mbox{bh}}$ is Belo Horizonte's area, we can create a coefficient $\alpha=A_{\mbox{city}}/A_{\mbox{bh}}$. As the value of $\alpha$ decreases, less points should be awarded to the user and more points should be awarded if otherwise. So, the same way we did for easiness $e$, we also divide $d$ by this coefficient, but since it represents an area (which follows the \href{https://en.wikipedia.org/wiki/Square-cube_law}{square cube law}), we take it's square root first. Which leads us to:
\begin{equation}
S = \frac{100}{1 + \left(\frac{d}{e\sqrt{\alpha}}\right)^4}
\end{equation}
For a city the size of Barcelona, for example, with $\alpha \approx 0.5$ we get: