## Wednesday, August 26, 2009

### A square root

It started innocently when Alton Brown, my favorite TV cook, did a show on mushrooms. Alton said the mushroom is the spore-bearing fruit of an underground fungus. He went on to say the underground part could easily extend over an acre in size.

My house sits on a lot that is 1/3 acre. I asked my wife,

If that mushroom was growing here, how much area would it take up?

Sounds like a question for the blog, she replied. With a yawn.

Now how can I figure this out with the least amount of work? I started by dredging up a drawing of our property. I don't know the scale, but it looks like this:

Since it's not strictly rectangular or square, calculating the area can be a bit difficult. But I really don't want to know the dimensions, I just want to see what a mushroom might look like compared to my yard.

So here's my next step. Make a rectangle with the same area as my yard, without having to do any measuring or calculating.

I drew a rectangle (green) and overlaid it on my yard diagram (red). I compared the size visually and made the rectangle as close as possible. Then I created some triangles to make sure I was right on.

Triangles 1 and 3 represent the area where my rectangle is outside (larger than) the original lot boundaries.

Triangles 2 and 4 represent the area of the original lot that my rectangle does not cover.

Those triangle pairs (1 & 2) and (3 & 4) roughly offset one another, so my green rectangle does represent the area of my lot.

I know the lot is 1/3 acre, so all I have to do now is draw a square or circle 3 times the size of the rectangle. How do I do this in the easiest way?

It's a simple job to calculate the area of the rectangle. I could have used a ruler to measure the rectangle, but I had this drawing in Adobe Illustrator. The software told me the numbers are 506 x 128 pixels.

That means its area is about 65,000 square pixels. Notice that I don't need to convert to feet; I just need my one-acre shape to be 3 times the size of the rectangle. I need about 200,000 square pixels.

Using trial and error, I mentally I think 5 x 5 is 25; that's too big. 4 x 4 is 16; that's too small. I need a square about halfway in-between. 450 x 450 in size. I quickly make a square and here it is!

Wow! That's one big square root.

This much land area (in Uganda where it rains a lot) can produce 4,560kg or 10,000 lbs of mushrooms a year!

PS - yes, I could also have said to Illustrator, Scale this up 3 times. But where's the fun in that?