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

It's time to put you all out of your misery regarding yesterday's puzzle. Well, not all of you - it's clear that many of you found the solution, so well done!

OK, if you correctly followed the instructions, you will find that on a square grid it traces a swastika, and on a triangular grid it traces the Star of David. Clearly this is disturbing as these symbols represent Nazi atrocities during World War II. It's just a weird mathematical coincidence that both symbols can be drawn using the same instructions.

* * *

If you didn't see the symbols, then these two resources may help:

1. Here's a Youtube video showing the exercise:

http://www.youtube.com/watch?v=20UFsVPfKOo


2. This is an online computer program which can plot these patterns:

http://math.fau.edu/MLogan/Pattern_Exploration/Spirolaterals/SL.html

Now, the program isn't particularly user-friendly, so apply these settings:

Enter Name: 69363 (I scaled up our program by 3 to make the pattern bigger)
Iterate By: text
Pattern: RRRLL (click on R 3 times, then L twice)
Degrees: 90 or 120 (move the slider)
Grid = checked
Line Width = thick

When you've set it, press the Iterate button repeatedly to draw your figure.

* * *

The figures drawn by programs such as the one in this puzzle are known to mathematicians as 'spirolaterals'. They were first discovered in 1962 by a chemistry student at the University of Aberdeen. The discoverer, Frank Odds, would doodle them on graph paper during boring lectures. Ten years later he corresponded with the mathematician Martin Gardner, who then described them in his mathematical column in the magazine Scientific American. They have been widely used in teaching computer programming, among other things.

If you'd like to learn more, here's a web resource on the art of spirolaterals:

http://www.mi.sanu.ac.rs/vismath/krawczyk/spdesc00.htm

* * *

Frank Odds went on to become an world-renowned expert on fungal infections, but in an email in 2003 he said that he was more proud of those figures than of any of his other possible achievements.

Deb

I drew it out on a tiny scrap of paper, then wrote a short Logo program to do the same thing and check I was right.

You'll also find it in David Wells' book "Curious And Interesting Geometry", under 'Spirolaterals'.

I rather suspected that solution when I *could* do the square papered version.

*goes to play with spirolaterals*

[Amy P]

[[[ asteroidlil ]]]

verrrry interesting...