For a arch to be prefect, it must be shaped such that it is in uniform compression.   Basically the inverse of a hanging chain.   So we can build what Robert Hooke describes in 1675 "as hangs the flexible line, so but inverted will stand the rigid arch".  So, we can hang strings from a sheet of plywood, trace and cut... As the thin shell innovator Heinz Isler would say "One does not actually create the form; one lets it become, as it has to according to its own law".  Also, this is an exceedingly complex mathematical shape called the hyperbolic cosine or catenary.

So we cut ...

Remove...

And build...