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

I am slightly puzzled the following method doesn't appear. Maybe I'm just being confused and it's not a real method.

1) Draw a regular pentagon.
2) Join each vertex with the second next one (say, counting them clockwise).

Of course the difficulty was swept underneath the carpet. Here's the easy way to carry out item 1. You only need a compass, which needs to stay open with the same radius R throughough the construction process:

1a) Draw a circle.
1b) Point your compass anywhere on the circle, thus marking "Point 1".
1c) Mark the only point on the circle which is at distance R located clockwise from "Point 1": name it "Point 2".
1d) By the same process, construct "Point 3", "Point 4", "Point 5".
1e) The five points define a regular pentagon (or, joining them in the order 1-3-5-2-4-1, a pentagram). You can check that carrying on step 1d, the "Point 6" would actually fall onto "Point 1" again.



An amusing method for a pentagon is as follows: Take a ribbon of paper and knot it (with the simple "usual" knot). Flatten carefully the result: you get a pentagon-shaped flat knot

Oh, it appear to be the "improve your guess" method

So: No need for fuzzy guesswork, just keep the same compass opening.

You must live in a different space-time than the rest of us - in a "flat" space-time the circumference of a circle is 2*pi*R, so unless you change the setting of your compass after drawing the circle, your marks will never join up (as pi is irrational).

Your method gives a hexagon, not a pentagon. The paper-knot method's a good one, though.

I probably live in a different space-time anyway

Yet I'm quite sure of my fact. If you draw a straight line of length R between two points of a circle of radius R, the piece of circle between these points will have length a bit more than R.

Believe me, it works.

Hexagon! Of course. Mea culpa. Eeer, leave me some time to find an excuse now

The triangle bounded by a chord of the same length as the radius of a circle and two radii is equilateral. In a flat Euclidean space, all internal angles of an equilateral triangle are 60 degrees. Six such triangles meeting at a point will subtend 360 degrees.