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3rd Unit
3rd Unit

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Lesson 10.1 Assignment

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... Some shapes are composite shapes, which need to be split up into their basic elements (rectangles/triangles). There is often more than one way to do this. In the example above, we have a rectangle and a triangle. We can either use the triangle area formula directly to find the area of the shaded tri ...
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... defect of each of these triangles is c, so c = c + c, which implies that c = 0. Because it is not possible to have a triangle with a defect of 0 in a hyperbolic geometry, then triangles in a hyperbolic geometry can't all have the same defect. 2. Let MN be the altitude of the Saccheri quadrilateral  ...
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Answer - mrfishersclass

< 1 ... 277 278 279 280 281 282 283 284 285 ... 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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