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Chap 1 homework packet

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... Because the two triangles share a common vertex at Point A, angle A is congruent to angle A in both triangles by the reflexive property. Since segment DE is parallel to segment BC, angle D is congruent to angle B and angle E is congruent to angle C because they are corresponding angles. Note: The re ...
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... Remark: This is a striking result! It says that “elliptic parallelism” is inconsistent with the Hilbert axioms. There are two natural candidates for elliptic geometry: the sphere (with the great circles as the lines) and the projective plane (the sphere with antipodal points identified). Since two g ...
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... Remark: This is a striking result! It says that “elliptic parallelism” is inconsistent with the Hilbert axioms. There are two natural candidates for elliptic geometry: the sphere (with the great circles as the lines) and the projective plane (the sphere with antipodal points identified). Since two g ...
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< 1 ... 481 482 483 484 485 486 487 488 489 ... 612 >

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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