As an artist who has serious interest but base knowledge of mathematics (other than, say, arithmetic), I devised a formula for determining the vertical nature of cities. This formula isn't the most scientifically constructed out there, but the results I got were fairly consistent with what I've observed about the nature of skylines. Here's how it works:
•It should be noted at first that the final statistic is a function of the three dimensions of a skyline; not only is height considered, but the density of the buildings and their apparent impact on the surrounding city is also taken into consideration.
•The formula is divided into four parts beneath a cubed root radical.
•1) Divide the number of high-rises (hr)—or buildings that are taller than 35 meters—by the area of the city.
•2) Multipy that figure by the division of aggregate height (ag) of all the skyscrapers—or all buildings taller than 100 meters—by the total number of skyscrapers (s).
•3) Next comes the division of the skyscrapers by the high-rises, to distinguish that a city like New York, which has a lot of skyscrapers, is taller than a city that has a lot of high-rises, like Rio de Janeiro.
•4) Multiply those three results by the area of the city.
•5) Throw those four multiplied figures beneath that radical I mentioned earlier, so that you can "compress" the three-dimensional nature of these statistics into one linear figure, and you've got yourself the formula.
Like I said, it's not the most mathematically precise thing out there. If you're a serious mathematician, you've probably pointed out numerous holes in this approach (and if you did, then message me). But this was just a good exercise to have and a solid way of helping me find the answer to a question I've been asking myself for awhile: what cities have the mightiest skylines?