I was thinking, while I defined division as a fundamental operation in Units of Reality, I wondered if the division of circumference and radius should fall under that model.

Then I thought, no. Because in order to divide something by something, you need to have the entity be made of the same principles as the entity with which you are dividing it by.

If you were to divide a length by a length, you would get a rational number. If you were to divide a number by another number, you would get a rational number. But ideas like square root and pi fall under different operations.

To give a proper description, a circle has the property of curvature. Now for any being who is living in a curved universe, they may just happen to perceive lines in their own universe as straight. So here, were are dealing with relative curvature. [NOTE: I may be wrong about that, I don't know if curvature can be estimated universally].

So what's my idea?

I was thinking about what makes a line different from a curve. I haven't studied curvature myself, so I'll

[deviation of a line from a parallel line of equal length, as it curves into a circle, while maintaining the projected length]

OOOOOOOOOOOO                OOOOOOOOOOOOOOOOOO
                    VS                        
OOOOOOOOOOOO                     OOOOOOOO     
                               OOOOOOOOOOOO   
                             OOOO        OOOO 
                            OOO            OOO

Left-click: follow link, Right-click: select node, Scroll: zoom