What's the shape of a rainbow?

I just used Geometer's Sketchpad and an image that I pulled down from Google to investigate the shape of a rainbow.

Now I understand why conics is called conics!!!

This is really heady stuff. (I feel like a 14-year old, wanting to emphasize every sentence with italics, bold and exclamation marks.)

Yesterday after class, I was talking to Robin about telling stories with numbers, and one word in our conversation just stuck with me. Rainbows.

It took about 10 to 15 minutes of web searches to figure out how to set an image as a background in GSP. Unfortunately, GSP is not that intuitive. (And this functionality has been there since at least 2003.)

It took another 5-10 minutes to get GSP to do this reliably. Actually this was the most frustrating part of the process.

5 more minutes to find an image I liked from Bing / Google. (I liked Google's selection better).

Under 2 minutes to superimpose a circle and a parabola on the image. This was super easy.

Okay, my image is not a circle or a parabola.

You'd think it should be related to a circle in some way, should it not?

5 more minutes of searching on the web to verify what the shape of a rainbow should be.

Now we are in some really serious terrain. I am going to have to figure out how to do projections in GSP. And I have to figure out a mental model of how exactly a rainbow works.

All this in under 45 minutes, or one class period.


The really scary thing is that 2 minutes ago, if you asked me, I would have told you that I know how rainbows are formed. But did I really know?


Tune in next week to find out. [My evaluation version of GSP won't let me export or cut-and-paste images, so I can't show you until I'm back on campus.]

I wonder if I can use this for my class final project...?

[Update, Sunday 10/18: I can now visualize why it is an ellipse. Looks like I will need to use both Fathom and GSP. Fathom can't import images. GSP does not have sliders. Plotting things like conics seems easier in Fathom. Having to move data back-and-forth between applications is always frustrating. I really dislike having to do that. ]