Скачать или смотреть Relativistic velocity, core circles, and Paul Miller's protractor (II) | Rational Geometry MF143

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:
2:58 Review of the unit circle
9:35 The core circle
13:36 Advantage of the core circle
17:53 Parametrization of the core circle
20:38 Expression of parametrization of the core circle
23:58 Three points on the core circle
29:57 Proving the Core circle theorem
34:03 Core circle quadrance theorem

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