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Geometry - Inside SOU
Geometry - Inside SOU

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Module 5 Lesson 1: Investigating Angles of Triangles Characteristics

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... Angle Measure Measure Angles If two noncollinear rays have a common endpoint, they form an angle. The rays are the sides of the angle. The common endpoint is the vertex. The angle at the right can be named as ∠A, ∠BAC, ∠CAB, or ∠1. A right angle is an angle whose measure is 90. An acute angle has me ...
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Geometry - 6.5 - Parallel Postulate and Triangle Sum Theorem

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Modern Geometries: Non-Euclidean, Projective, and Discrete

... length. 3. A circle may be described with any center and any radius. 4. All right angles are equal. 5. If a straight line meet two other straight lines so that as to make the interior angles on one side less than two right angles, the other straight lines meet on that side of the first line. ...
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Rational trigonometry

Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales. His ideas are set out in his 2005 book Divine Proportions: Rational Trigonometry to Universal Geometry. According to New Scientist, part of his motivation for an alternative to traditional trigonometry was to avoid some problems that occur when infinite series are used in mathematics. Rational trigonometry avoids direct use of transcendental functions like sine and cosine by substituting their squared equivalents. Wildberger draws inspiration from mathematicians predating Georg Cantor's infinite set-theory, like Gauss and Euclid, who he claims were far more wary of using infinite sets than modern mathematicians. To date, rational trigonometry is largely unmentioned in mainstream mathematical literature.
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