Arches are part of the design feature set of our house — so is a mansard roof, but I am not as keen to replicate it — and as I add or replace various features on the house, I would like to add the same kind of flattened arch that features on facade of the house and in some of the cabinetry. For that, I need math. In particular, given the width of a given opening and how high I would like the arch to be, I need to be able to calculate the length of material of the resulting arch.
For those who missed this particular part of geometry, here are the parts involved:
For the math, we need the following:
(x – x)^2 + (y – y)^2 = r^2
x = c/2
y = (s – x^2/s) / 2
r^2 = x^2 + y^2
Y = y + sqrt(r^2 – (x – x)^2)