The Math Found In Cities.

 

Think about the term, urban geometry.  The geometry of urban areas.  Picture if you will, standing almost at the center of Madison Square Park in New York City.  The Math museum is behind you while the Flatiron building is in front of you.  The Flatiron building got its name because it's shape reminded people of a clothes iron but the block it inhabits is actually shaped like a right triangle.  The souvenirs sold are in shaped like an isosceles triangle because people prefer symmetry.

The cross street near the end of the building is 23rd and it intersects at almost a 23 degree angle which happens to be the tilt of the planet.  In addition, twice a year, near the summer solstice, the sun shines down the numbered streets. 

Furthermore, the "east-west" streets of Midtown Manhattan actually run northwest - southeast and when they run into the Hudson and East Rivers, they intersect at almost a 90 degree angle.  But in Chicago, the street grids are almost oriented to the North.  On the other hand, in older cities like London, there are no right angled grids.

All of these observations have lead to the new field of Quantitative Urbanism which is so new, it doesn't have a journal yet.  This field is trying to take observations like the above and translate them into mathematical formulas.  In other words, use math to explain cities.  

Studying cities dates back to the time of the Greek, Herodotus. By the time, we arrived in the 20th century,  scientists were studying things such as zoning theory, public health, sanitation, transit and traffic engineering, all apart of urban development.  This continued and in 2003, the new field emerged when a group of people met to discuss how one would mathematically "model" human society.  Out of the meeting came a paper on factors which might effect the size of a city. 

One observation is that as cities grow, many things increase at an exponential rate of between one and two which is referred to as "superlinear scaling".  For instance, private employment has an exponent of 1.34 while new patients is 1.27, serious crime is at 1.26 and gross national product ends up between 1.13 to 1.26.  As cities grow, a person's productivity increases by 15% because there are more people to collaborate with and innovation also increases.  It makes sense because as cities grow, the opportunity for interaction increases and other things increase. 

On the other hand, certain things end up at less than one because they are usually lagging as cities increase.  For instance, gas stations tend to run at 0.77, total surface area of roads is at 0.88, and total length of wiring in the electrical grid is at 0.87.  This makes a lot of sense.  I have a cousin who live in an area of Virginia which is within easy commuting of Washington D.C, so people began moving to the area. They needed places to live, streets to drive on, and the road system was way behind with tons of people driving on two lane roads which hadn't been redone to handle the increased traffic.

This is just a short introduction to the topic.  It is quite fascinating.  Let me know what you think, I'd love to hear.  Have a great day.