## Sunday, September 26, 2010

### Puzzle: What Is This?

I got a very unusual gift for my birthday. I know what it is, but I'm not sure exactly how to use it yet. I'll have to experiment with it.

Can you guess what it does? (It can move at the joints.)

1. Clearly, by construction, the three points of the arms maintain a constant proportional distance from each other, along the same line. So no matter how far apart (within the physical limits of the device) you spread the outer two points, the middle point will (a) be on the line connecting the out points, and (b) divide the line segment connecting the outer points in a fixed ratio.

Based on others of these I've read about, and an okapi heuristic, I'd guess that the ratio in this case is the Golden Mean, and such a tool is useful for showing all the places where the Golden Mean is famous for showing up (pentagrams, obviously, but also in art, architecture, etc).

2. Is it a Pantograph?

3. I had to go look up some words...

Blaise, I love your description, and you cleared one thing up for me. I was trying to figure our how I'd use it to draw, but it looks like this device can be used more easily to point out the Golden Mean relationship than to create it.

But what do you mean by "okapi heuristic"? ('okapi' wasn't in dictionary.com, was it a typo?)

A pantograph is "an instrument for the mechanical copying of plans, diagrams, etc., on any desired scale." I don't think this could be used for that purpose, but maybe I'm not understanding how it would work. I'd assume a pantograph would have a writing instrument built in.

4. The Okapi formula is part of an information retrieval heuristic - and IDF is the inverse document frequency!

The construction certain looks like a pantograph, but as you say doesn't contain the relevant places for writing implements to be inserted...

As a Scot, I'd have to point out that it is definitely similar to the Parallel motion linkage invented by one of my countrymen...

I'd just use it to scratch the parts of my back that I can't reach for myself! ;-)

Colin