Hang a chain, flip it upside down, and you have the perfect arch
30seconds
In 1675 Robert Hooke hid a building secret in an anagram. Decoded after his death, it said: as hangs a flexible cable, so, inverted, stand the touching pieces of an arch.
A hanging chain settles into the one shape where every link is in pure tension. Turn that curve upside down and every pull becomes a push, so each stone presses squarely on the next. Gaudí designed a church this way with strings and lead-filled sacks. Drag a chain, hang weights on it, and flip it into an arch.