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Riemannian manifold

math Maturity 7-9

We can measure shapes.

Tangent plane to sphere with vectors.svg
Tangent plane to sphere with vectors.svg
We can find how long a line is. We can see the way a shape bends. This helps us map the world. It even helps us learn about space. Can you find shapes around you?

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🖼️ Images & Media (6)
File:Sphere with tangent plane.svg
Sphere with tangent plane.svg
File:Georg_Friedrich_Bernhard_Riemann.jpeg
Georg_Friedrich_Bernhard_Riemann.jpeg
File:Tangent plane to sphere with vectors.svg
Tangent plane to sphere with vectors.svg
File:Sphere filled blue.svg
Sphere filled blue.svg
File:Punctured plane is not geodesically complete.svg
Punctured plane is not geodesically complete.svg
File:Parallel transport sphere2.svg
Parallel transport sphere2.svg
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Riemannian geometry
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📚 Content adapted from Wikipedia | Readability: FK 13.1 | Vital Level 4