What is Morley’s Miracle?
نویسنده
چکیده
Overview Let ∆ABC be a triangle, and let the radian measure of these angles bem(]CAB) = 3α, m(]ABC) = 3β, and m(]BCA) = 3γ, so that α+ β + γ = π/3.1 We trisect each (interior) angle of the triangle, and take the intersections of the proximal or adjacent trisectors; for example, to choose the intersection between a trisector of the angle at A and the angle at B, we choose the trisector from A closer to B, and the trisector from B closer to A. This gives us three points: one between a trisector from B and a trisector from C (labeled P ), one between a trisector from C and a trisector from A (labeled Q) and one between a trisector from A and a trisector from B (labeled R). See Figure 1. For the duration of this article, all angle measure will be in radians.
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