Proof
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Lesson Summary:
In this video on proof, Björn Hartgerman explains the importance of proving mathematical theorems and how to do it. Using the example of proving the stereographic projection of circles, he shows that a mathematical proof must use reasoning to be convincing, and has to explain why it is indeed true. He covers important concepts like Euclid's axioms, Pythagoras' theorem, and Thales' theorem, and shows how they can be used to prove theorems. Ultimately, he demonstrates how the stereographic projection carries circles onto circles, proving the importance of proof in mathematics.
Lesson Description:
Learn what it means to prove theorems in mathematics and why it is important.
Questions answered by this video:
- Who is Bernhard Riemann?
- What is proof?
- What does it mean to prove something in math?
- What is an axiom?
- How can you prove that the stereographic projection projects circles onto circles?
- How can you prove that when a plane cuts a sphere, the intersection is a circle?
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Staff Review
This lesson uses ideas from several of the previous lectures in the Dimensions video lecture series. Stereographic projections on a sphere are used for proof in this lesson. The images are not only interesting and useful, they are very beautiful. The math can be rather intimidating at times, but the visuals help.
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