h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I'm going to describe to you a very odd mathematical coincidence. You might find it somewhat disturbing. I certainly did.

I'll present it in the form of a puzzle. I suggest you have a go at this yourself. It's not difficult.


You'll need a sheet of squared paper and a pen or pencil. If you need to print off some squared paper, you'll find some here:

http://www.freewebs.com/ccbaker/apps/photos/photo?photoid=27068643


Now, here are the instructions. I want you to start at a point in the middle and trace the following path:

Move forward two, then turn right;
Move forward three, then turn right;
Move forward one, then turn right;
Move forward two, then turn left;
Move forward one, then turn left.

Repeat these five steps from the beginning until you get back to where you started.


Done it yet?

OK, now I want you to do it again, but instead of turning 90 degrees left or right, I want you to turn a sharper angle, 120 degrees.

This time you need to plot it on a triangular grid - here's one you can print off and use:

http://mathforum.org/varnelle/trianglegrid.html

So, follow exactly the same instructions as before: what do you get?

I'll post the answer and an explanation tomorrow.

[Amy P]

Deb

I actually tried to do this, you buzzard. Then I saw the rest of it...no way...I got lost at 'turn left' and 'turn right'...

I was reckoning without your sense of spatial awareness, Dmitri

You sunk my battleship!

<BB<

I got it. I had to restart the triangle one as I did a 60 degree left turn instead of 120, but once I corrected that it made sense.


BTW... if you swap left turns with right, the first design becomes much more .

a butter churn....

I got it too, even though my left and right got mixed up half way through both drawings when I had to start again from the step 1s

I got lost completely on the triangle one. Tried it three times, I kept getting confused with my left and right.

Don't have the space/tools to do this.

You'll need a piece of paper at least 2 inches by 2 inches.

Yeah, I roughed in my triangle grid by tracing the three axes on my monitor and then just running lines parallel to those roughly hitting the intersections the previous lines create.

It worked well enough to see the pattern.

Well I never.