# Vector Images

I came up with a clever test question last year:

I wanted to tie vectors together with solving triangles for a couple reasons. Primarily, to give purpose to calculating the angle between two vectors. If you go the mathematical route using dot products and all that it's just all so...fake. Second, to connect the idea of vector magnitude to representing something in a geometric shape. In the above problem, the idea is to find the magnitude and angle of side b in order to find the angle between a and b. After all that you can find the area of the triangle or anything else about it.

The issue was I came at this idea at the end of our vector discussion and it generated a lot of confusion. Primarily they weren't making the connection that vectors could actually mean something other than be arbitrary arrows. This year I was going to lead with the idea. In the future, I hope this helps me lay the groundwork for changing Pre-Cal from a random list of topics into a concrete set of applications.

### Computer Machines

I open with a discussion of computer graphics. All the favorite images they love to like and heart are usually rendered as bitmaps, hard coded pixels in a grid. I find a random .jpg from the internet, open it in Photoshop and zoom:

I do the same with a vector image that's been rendered out as a PDF. No grid of dots. What gives? To keep things simple (and because I don't know all the gritty details) we discuss that image files contain information about relatively defined coordinates which the computer uses to dynamically draw whatever lines they see. If you ever zoom in on a PDF and catch it go fuzzy before smoothing out again, this is kinda sorta what's going on, the computer/phone is redrawing everything on the fly. There was a side note that computers are trained to avoid showing you the pixel grid as much as possible through approximation, ie why bitmaps get blurry when blown up.