Specifying planes in three dimensions | Introduction to Euclidean geometry | Geometry | Khan Academy
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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/intro_euclid/e/points_lines_and_planes?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson: https://www.khanacademy.org/math/geometry/intro_euclid/v/geometric-precision-practice?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geometry/intro_euclid/v/drawing-lines-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Geometry channel: https://www.youtube.com/channel/UCD3OtKxPRUFw8kzYlhJXa1Q?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Comments
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2:44 DAB!
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No, because D is not on the plane, it is part of another line.
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can we call Plane S as Plane JBD? why or why not? thanks!
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In geometric terms, since a plane, line, or ray extend forever, is geometry based on astronomy?
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Oh right, well I just heard the terminology here for the first time so thanks for clearing that up!
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n non-collinear points for an n-dimensional space (rather than shape). The plane only appears to have a shape because we bound it for purposes of illustration. If I remember correctly, you need n+1 barycentrically independent points for an n-dimensional affine space, and n-dimensional spaces through the origin (vector spaces) require n linearly independent vectors. Here the notions of barycentric and linear independence are closely related to collinearity.
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So basically, you need n non-colinear points for n-dimensional shape?
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Hoping to see new plane equation videos soon! Thanks Khan.
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Three points means three 3D vectors, which in turn means a total of 9 real numbers. But what if i only specify a line using two points and take the plane perpendicular to that line and intersecting it in the first point? This way i only need 6 real numbers to specify a unique plane (and maybe one additional bit to specify which one is the "first" point).
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You fellas, this makes CAD easy, learn it!
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CAN I HELP U
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Fantastic .
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