To start the last week of March Mathness, because it’s a Monday, I’m going to go easy on y’all with some light, easy topics. (Maybe I can lull you into paying attention for the major topic of the month: matrix rotation.)
It has occurred to me that, if I’m talking about math in March, I absolutely must mention one of my all-time favorite mathematical objects, the Mandelbrot. I’ll try to get to that today, but the main topic is a simple something that I ran into while working on my 3D model of the big island of Hawaii.
The question was: How many miles are there per degree of latitude?
The maps you find in some buildings and malls have a little marker flag that says, “You are here!” The marker connects the physical reality of where you are standing at that moment with a specific point on a little flat map.
Your GPS device provides your current location in terms of longitude and latitude. Those numbers link your physical location with a specific point on any globe or map of the Earth.
But to fully represent our location, longitude and latitude are not quite enough. (We might be high overhead in a hot air balloon!) To fully represent our position, we need a little more ‘tude, but in this case that’s altitude, not attitude.
We need three (and only three) coordinates to completely represent our location in space. This post is about why.