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Hello,

Just discovered this forum as I'm so intensely curious about this question I sought out just such a place!

I'm currently designing a circular patio using 6-in square blocks in concentric circles. While using a combination of Excel and Adobe Illustrator, I uncovered something unexpected. Each new circle required a consistent number of additional blocks, when rounded up to the value of a whole block. 7 to be exact. It is my goal to understand how and why this works, and hopefully to learn a formula that will let me repeat it and change things like block size.

I began with a 36-inch circle which would be a firepit. I determined I would need 18.85 6-inch blocks. I'm not planning to cut them, so I rounded up to 19 blocks and backed into the circumference that would accommodate it (114 inches). I went to the next ring and more or less repeated the same process: approximated circumference, determined a fractional number of blocks, rounded up to nearest whole block, backed into precise circumference. Rinse, repeat.

After about six rings, I wanted to know how many rings I'd need to get to a 16-foot diameter, so I figured I'd average the diameter increase between each consecutive ring, hoping to extrapolate an estimate. I was surprised to find each circle was the exact same increase from its adjacent circle (1.114085 ft). And that's when I noticed the consistency in the blocks.

If I was aiming to have circumferences that accommodated only whole blocks, I learned that each new circle required exactly 7 additional blocks.

How is this so precise and predictable? I'm assuming it has something to do with effectively turning the circle into a polygon by using blocks, since they are flat. So the first "circle" is really a 19-sided polygon, the next a 26-sided polygon, etc. But I don't know the first thing about complex polygons.

Furthermore, I'd love learn HOW this works. If I had a formula of some kind, I could change the size of the blocks at will and speed up my estimates.

Thanks for any help! Attached an image for reference

Just discovered this forum as I'm so intensely curious about this question I sought out just such a place!

I'm currently designing a circular patio using 6-in square blocks in concentric circles. While using a combination of Excel and Adobe Illustrator, I uncovered something unexpected. Each new circle required a consistent number of additional blocks, when rounded up to the value of a whole block. 7 to be exact. It is my goal to understand how and why this works, and hopefully to learn a formula that will let me repeat it and change things like block size.

I began with a 36-inch circle which would be a firepit. I determined I would need 18.85 6-inch blocks. I'm not planning to cut them, so I rounded up to 19 blocks and backed into the circumference that would accommodate it (114 inches). I went to the next ring and more or less repeated the same process: approximated circumference, determined a fractional number of blocks, rounded up to nearest whole block, backed into precise circumference. Rinse, repeat.

After about six rings, I wanted to know how many rings I'd need to get to a 16-foot diameter, so I figured I'd average the diameter increase between each consecutive ring, hoping to extrapolate an estimate. I was surprised to find each circle was the exact same increase from its adjacent circle (1.114085 ft). And that's when I noticed the consistency in the blocks.

If I was aiming to have circumferences that accommodated only whole blocks, I learned that each new circle required exactly 7 additional blocks.

How is this so precise and predictable? I'm assuming it has something to do with effectively turning the circle into a polygon by using blocks, since they are flat. So the first "circle" is really a 19-sided polygon, the next a 26-sided polygon, etc. But I don't know the first thing about complex polygons.

Furthermore, I'd love learn HOW this works. If I had a formula of some kind, I could change the size of the blocks at will and speed up my estimates.

Thanks for any help! Attached an image for reference