So you're standing there in San Francisco, and you just heard about a terrific new pizza emporium in Sausalito, but you can't swim, and you don't have a boat. You need a bridge. Writing a proof can be a lot of work, like building a bridge, but it's worth the effort when there's great pizza, or great math, on the other side. Image number 2 . Now imagine an arch, say, for example one of the arches holding up the Cathedral of Notre Dame in Paris.
Arches are incredible architectural structures.
They direct the weight from the building above them down their sides. With arches channeling the weight of the building, instead of having to have solid walls, you can put in windows, and let in a little light. The stone at the very top of an arch is given a special name. Once I find the keystone, most of the hard work is done, and the rest is the gruntwork of arranging the rest of the stones around it. But make no mistake about this image.