Circular/Spiral Game Board Question

[Zii]

I'm completely new to these fourms, have a rudimentary understanding of geometry, and wasn't sure where to post this question, so appologies if this is the wrong forum, I'd be appreciative if you could direct me to the right place.

My question is whether it is possible to create a circular or spiral game board out of curved tiles that could all be the same shape and size. This is for a game venture my friend and I are working at, and the idea is that the game board is composed of interchangeable tiles so that it is customizable. We would like to have the pieces all be the same size in order to cut down on production costs, but if it's impossible to do we can work around pieces needing to be larger or smaller.

 

[HallsofIvy]

"Circular", yes. Make each tile the section of a circle between two fixed radii, r_2 and r_2 with r_1< r_2 and fixed center angle \theta.

You cannot have a spiral having all tiles of the same size and shape.

 

[Zii]

Thank you! I'll give it a try.

 

[Ben Niehoff]

You cannot have a spiral having all tiles of the same size and shape.

Sure you can! The shape will be an Archimedean spiral. Here's a page with some example spiral tessellations:

http://www.squamificio.net/books/spira/spira.htm