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Relativistic velocity, core circles and Paul Miller's protractor (I) | Rational Geometry MF142

4,336 views · Published 31 May 2015 · 33:01 · Indexed 1 October 2026

Channel: Insights into Mathematics · 2015 · Education

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We introduce an important variant to the unit circle---what we call the core circle, which has diameter the unit interval [0,1]. For understanding the projective line, this core circle is a very useful object, and forms a bridge from projective geometry to Euclidean planar geometry.

Here we establish some basic facts and formulas for this object, and show how quadrances between points on the core circle exactly agree with projective quadrances between the corresponding projective 1-points. We also find a pleasant formula for the quadrea of a triangle on the core circle.

Video Content:
4:32 Relativistic velocity addition
7:27 A. Einstein's special theory of relativity
12:57 Distinction between velocities
16:26 Relativistic addition
18:48 Invariance of the Interval
23:34 Relativistic rotation
27:41 One-dimensional projective geometry

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