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

 

[blue_raver22]

Hello there,

Thank you for your question. I can provide some insight into the possibility of creating a circular or spiral game board using curved tiles.

Firstly, it is possible to create a circular or spiral game board using curved tiles that are all the same shape and size. However, it would require careful planning and precise measurements to ensure that the tiles fit together seamlessly and create a smooth, continuous surface.

The key to creating a circular or spiral game board using curved tiles is the concept of tessellation. This is the process of fitting identical shapes together without any gaps or overlaps. In your case, the curved tiles would need to tessellate in a circular or spiral pattern.

It is important to note that the size and shape of the curved tiles will determine the overall size and shape of the game board. So, if you want the game board to be a perfect circle or spiral, the curved tiles will need to be a specific size and shape to fit together without any gaps or overlaps.

In terms of production costs, using identical tiles can definitely help cut down on costs. However, it is important to consider the material and manufacturing process of the tiles to ensure they can be produced at a reasonable cost and still maintain the necessary precision for a smooth game board.

In summary, it is possible to create a circular or spiral game board using curved tiles of the same shape and size, but it will require careful planning and precise measurements. I would recommend consulting with a mathematician or engineer to help with the design and production process. I hope this helps and good luck with your game venture!