MATH-M 311 Lecture Notes - Lecture 7: G2 Phase, Maxima And Minima, Paraboloid
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Section 12. 6 notes- cylinders and quadric surfaces in. How do we comprehend 2-dimensional surfaces living in : cross sections (traces) intersect figure with vertical or horizontal planes. Cylinder- surface consisting of all lines (called rulings) parallel to a given line and pass through a given plane curve: ex. Equation of does not involve ; any vertical plane with equation intersects as vertical trace in shape of parabola. Rulings parallel to -axis: if one variable missing from equation of surface, surface is cylinder, ex. missing from ; represents circle with radius 1 in plane , surface is circular cylinder whose axis is. Omitting (equation ) makes rulings in direction. When you intersect some surface given by some equation with plane , intersection has equation: can do with or, to find cross sections parallel to or planes, substitute in constant for or, ex. Intersecting with plane: line of intersection/linear cross section.