- #1

Roger Thomas

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Recently, the following math problem was posed to me:

http://www.notobaccoads.com/Images/Math_FindTheArea.jpg

What that chicken scratch above shows is a problem I have not yet been able to solve. By what formula can one determine the area of the space in between three circles of the exact same size touching each other in the arrangement shown above?

The area in the middle isn't a straight edged triangle, it's a three sided space with each side having a curve that somehow relates to the diameter of each circle, I think.

If anyone has any thoughts on how to create a formula to solve for the middle area given any diameter for the three circles or if anyone could point me in the right direction I would appreciate it.

http://www.notobaccoads.com/Images/Math_FindTheArea.jpg

What that chicken scratch above shows is a problem I have not yet been able to solve. By what formula can one determine the area of the space in between three circles of the exact same size touching each other in the arrangement shown above?

The area in the middle isn't a straight edged triangle, it's a three sided space with each side having a curve that somehow relates to the diameter of each circle, I think.

If anyone has any thoughts on how to create a formula to solve for the middle area given any diameter for the three circles or if anyone could point me in the right direction I would appreciate it.

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