# Explaining the algebra behind a problem in computer geography

For work, I tend to have to explain quantitative ideas to people with only some informal computer science training.

Yesterday, my friend wanted to draw a map on his computer and was concerned we could locate specific latitude and longitude on his computer screen. This image is 256 pixels across and 256 pixels wide.

Here a really close-up view of San Juan, Puerto Rico. According to Openstreetmap the scale is

Level    Degree  Area             m / pixel  ~Scale
13       0.044   village or town  19.093     1:70,000
14       0.022                     9.547     1:35,000*
15       0.011   street            4.773     1:15,000


Since all maps are stored as squares tiles of various sizes, he has to identify the tiles he will need and place them together himself.

Then if he wants to identify specific landmarks - he needs to compute the proportion between the pixels and the lat-long using information he can find in this page on the various zoom levels or other resource.

Even though it is easy to point things out on a map, this is because computers do the quantitative reasoning for us. This is about as simple as I can make the work-flow for my friend -- and I didn't do nearly as good a job yesterday.

These concepts are not obvious and it took me a while to learn about map projections and re-learn them when using them on a computer.

The "math" involved was hardly traditional... I think we do one or two multiplcation problems in the entire process. Instead we deal with issues like scale and proportion maybe angle.

Worst of all, I didn't get to explain to him that in Mercator Projection, column 4 - meters per pixel - actually changes with the latitude on the map

What level would this be considered? More importantly, this computation is a sequence of steps I will have to explain over and over - how could I explain this better?

• "The "math" involved was hardly traditional... I think we do one or two multiplcation problems in the entire process. Worst of all, I didn't get to explain to him" ..... Looks like you got cut off ... What is the question here? – Brendan W. Sullivan Jun 5 '14 at 22:13
• @brendansullivan07 he needs to know where a specific latitude and longitude (e.g. that of this house) appears in the figure. – john mangual Jun 6 '14 at 6:20
• There is no question mark in the post -- what is the question here? – user173 Jun 6 '14 at 12:32
• @MattF. this site was giving me an error and it seems to have posted an incomplete version. I will fix it when i get the chance – john mangual Jun 6 '14 at 12:38
• Your map illustration is incorrect. Using a mercator projection only the horizontal scale gets modified. However at scales that span cities the viewable distortion of different projections is small, assuming that the images are in a coordinate system that is at least approximately tangent to the earth at the area of interest. – Sherwood Botsford Sep 17 '14 at 4:22