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GEOMETRY GRADES 9-12 THE EWING PUBLIC SCHOOLS 1331
GEOMETRY GRADES 9-12 THE EWING PUBLIC SCHOOLS 1331

... mathematics of geometry has developed into one of the most practical and useful areas of mathematics over the last 2300 years. Simply put, geometry is the study of the size, shape and position of two-dimensional shapes and three-dimensional figures. However, geometry is used daily by almost everyone ...
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ALL TRIANGLES ARE RAMSEY {A * B: A G A, B 6 B}, where for A

... Let Rn denote n-dimensional Euclidean space. A finite pointset A = {Ai,.. .,Aa} is said to be Ramsey if for every integer r there exists an no = 7io(A, r), so that if the points of Rn are partitioned into r classes one can always find a congruent copy of A inside one class. In [1] it is proved that ...
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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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