I have three small circles forming a pyramid. I would like to centre that group in a square but have spent a couple of hours trying to calculate the height of the pyramid. I just can't seem to get them vertically centred.
Given a square, a large circle filling the square and then three smaller circles forming a pyramid, what is the height from the bottom of the smallest circle to the top of the smallest circle.
https://googledrive.com/host/0BwFQiTKfux0qY1Y2d1hRdndtSEk/so_question.svg
Calc radius of each circle of n circles in a circle: www.had2know.com/academics/inner-circular-ring-radii-formulas-calculator.html
apothem: www.mathopenref.com/apothem.html
Python code I tried to get working python code
Best Answer
If $r$ is the radius of the blue circles, the the width of the blue figure is $4r$ and the height is $\left(2+\sqrt 3\right)r$. The height of a regular triangle play a role here. By the way, if you rotate the blue pyramid by $30^\circ$, you can grow them a bit bigger.