SUJET : that goes through it with the most curvature an

that goes through it with the most curvature and the moment the least and then multiply those together So in this case, this is the segment with the most curvature curse outward just a little so it's got that positive curvature Then this segment the one perpendicular to it has the least curvature In fact, this didn't curve at all just went straight down the side. So it has zero curvature That means we have positive times zero curvature which gives us zero Gaussian curvature at that point But the same thing could be said about any point on the lateral surface of the cylinder So yes, the cylinder is curved but it's Gaussian curvature is zero So now we're ready for a theorem I found really interesting and that's the theorem agree geom which was discovered by Gauss and what this theorem says Pretty much is that if you smoothly deform a surface its gaussian curvature at any point is not going to change so because





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