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so this is lecture 17 we're starting the second half of this series of lectures and today is kind of finite differences day first lecture about steady-state equations Laplace being the outstanding example we're in 2d of course we're doing partial differential equations and it's that step-up in dimension that makes these serious numerical problems so if I just look here so I'll describe the standard replacement the Laplace finite difference equation the five-point scheme has the basic accuracy we could upgrade it to a nine-point scheme with higher accuracy the issues are the solution of that system how much would it cost by direct elimination methods and those are by no means ruled out first cuz they're so simple and you know we're a lot of sub practice with Gaussian elimination but then the we can often save an order of magnitude in the computing time by some iterative method well-chosen so I'll speak about some of these I've just at th...

PROFESSOR: All right. Lecture 17 was about folding polygons into polyhedra, and today we will do it with real pieces of paper. But before we get there, I want to talk about some things we could make. In lecture, I demonstrated this perimeter having technique where you take any convex polygon and you pick any point on the perimeter. Then you measure out the perimeter halfway on each side. You get the antipodal point, y. And then just glue-- locally, you glue everything around x and around y. So I mean, you just start. We call this zipping where you don't glue any extra material in here, you just start zipping these guys together. I guess these circles or when you happen to hit this vertex, well, then you just keep going-- zip, zip, zip, zip, zip. So that's one thing we could make with convex polygons. Slightly more general is called a pita form. This is defined in the textbook. And the idea is instead of a convex polygon, you could take any convex body. It could ha...