the gotic pointed arc

The pointed arc appeared even in romanesque architecture, but it's a main feature in gotic style. In a normal gotic pointed arc the midpoints of the two circular arcs are replaced from the centre of the window unto the corners of it. In the pointed arc you can draw a equilateral triangle. Drag the green point in the applet to the left.

width of the wall

By verticalizing the vault, one could economise on the width of the wall.