Flat Earth

Converting a two dimentional ideal into the real thing isn't as simple as you'd think. …

In an earlier post I was looking at the various curves on the surface of the earth with a cut out disc of some 60 degrees. To get the dimension I merely set the point of a compass on zero at the equator and the pencil point at 30 degrees.

Simple, eh?

Too right.
I must need my bumps read.

And I never noticed until I tried to make one at 90 degrees. So I set the compass at 45 degrees as for the 30 above. And the disk covers 100 degrees of the globe.

What really gets me is that I pointed out in the earlier post that "for obvious reason" you can't translate a 2D image to a 3D one.

It's the little things like that that keep me humble. There must be some way to set the compass to the right radius so that I can draw a disc the right size. Blowed if I know though.

It's got to be one of those xy problems.
(x+y)(x-y) where at 30 degrees the disk is 62.5 degrees and at 45 is fractionally under 110 degrees. A something something equation if I could only remember back most of half a century. I suppose I might be able to draw a graph with just two points to form on?

Edit:
No, you need three points minimum to draw a graph. Damn, I need togo back to school.

Or get a trammel, someething like a giant compass or marking gauge. So it's back to the drawing board.