A math question my neighbor asked me this morning

Earlier today David Coffey shared this problem on Twitter:

Coffey’s problem made me what to share a little math problem my neighbor asked me about on our dog walk this morning.

He is writing a little computer program for his work and needed to draw and ellipse around a rectangle as part of a picture he wanted to have on the screen. He was having a little trouble figuring out how big the “big radius” and the “small radius” of the ellipse should be in relation to the length and width rectangle so that the ellipse would just touch the four corners of the rectangle. Oh, and the ellipse and the rectangle are supposed to have the same center. Something like this:


As with David Coffey’s problem above, this is not really that advanced of a problem for a student studying math, but it is kind of a fun little challenge to figure out the right scale factor. In terms of learning math, the same question that Coffey was after is important here: what are the steps you took to solve the problem?

I wrote a quick little computer program on Khan Academy’s site where anyone can play with the problem. Lines 5 and 6 give the x and y coordinates for the upper left hand corner of the rectangle, lines 8 and 9 give the length and width of the rectangle, and line 19 is the scale factor. Feel free to play around with any of the values.

So, my neighbor’s question – what is the scale factor that causes the ellipse to pass through the corners of the rectangle as in the picture above? Does the same scale factor work for all rectangles? Is there more than one scale factor that works?

My Neighbor’s Ellipse Problem