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Difference between revisions of "Chapter 2: An ancient theorem and a modern question"
Chapter 2: An ancient theorem and a modern question (view source)
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$$ 2^a \cdot 2^b = 2^{a+b} $$ | $$ 2^a \cdot 2^b = 2^{a+b} $$ | ||
Now, you may notice that this doesn't help if we are interested in numbers like \( 2^{\frac{1}{2}}\) or \(2^{-1}\). These cases are covered in the | Now, you may notice that this doesn't help if we are interested in numbers like \( 2^{\frac{1}{2}}\) or \(2^{-1}\). These cases are covered in the recommended section if you are interested but are not strictly necessary for understanding this chapter. | ||
=== Pythagorean Theorem \( a^2 + b^2 = c^2 \) === | === Pythagorean Theorem \( a^2 + b^2 = c^2 \) === | ||
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==== Geodesic ==== | ==== Geodesic ==== | ||
A [https://en.wikipedia.org/wiki/Geodesic geodesic] is a curve representing the shortest path between two points in a space. It is a generalization of the notion of a "straight line". In a "flat" space, the straight line is indeed the shortest distance between two points, but in a curved space, this no longer holds true; the shortest distance between two points inherits some of the curvature from the space in which it exists. Geodesics are well explained in the videos pertaining the hyperbolic geometry in the | A [https://en.wikipedia.org/wiki/Geodesic geodesic] is a curve representing the shortest path between two points in a space. It is a generalization of the notion of a "straight line". In a "flat" space, the straight line is indeed the shortest distance between two points, but in a curved space, this no longer holds true; the shortest distance between two points inherits some of the curvature from the space in which it exists. Geodesics are well explained in the videos pertaining the hyperbolic geometry in the essential section. | ||
=== Hyperbolic Geometry === | === Hyperbolic Geometry === | ||