The Pointed Arch
The flying buttress and the rib vault were two important things that gave us the gothic style. But the gothic style would not be complete without the pointed arch.
Churches before the gothic style used round arches and barrel vaults to make their ceilings. This was a problem not just because of the great weight of these arches, but because round arches over a church bay meant the bay had to be square in shape. If two sides of the bay measured one width and the other two sides measured another width, then the tops of the arches across those widths would not be at the same height. If the vaults going east and west in a church were higher than the vaults going north and south, this made the vault bay hard to construct. Things didn't line up.
But the pointed arch solved this problem. If your arches within the rib vaults were pointed, you could place the uppermost points of those arches at any height you wanted. The width of the vault did not matter. Because of this, churches using pointed arches could make their vaulted bays any width or length they needed. Construction would not be affected.
Gothic churches made great use of the pointed arch to build the longest, tallest, most inspiring churches in the world.