Examples of non euclidean geometry
[DOC File]Depth of Knowledge Levels (DOK) Mathematics
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We discussed parallel lines, perpendicular lines, and ways to make 3-D objects look real in a 2-D computer screen. This is when I realized that most students do not encounter non-Euclidean geometry in particular perspective geometry in the typical mathematics curriculum.
[DOC File]Module 1 - UH
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Examples include Non-Euclidean Geometric systems, projective geometry, and analytic geometry as evident in the Calculus. Here is what an equilateral triangle looks like in Hyperbolic Geometry. And the same triangle after manipulating a point of one of the circles.
[DOC File]According to the NCTM (2000) “Instructional programs from ...
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Construct a non-Euclidean geometry. Table 1: Applying Webb’s Depth of Knowledge Levels for Mathematics (Adapted from Karin Hess, Center for Assessment/NCIEA. by the Kentucky Department of Education, 2005) Webb’s DOK Levels Recall and Reproduction (DOK 1) Skills and Concepts/ Basic Reasoning (DOK 2) Strategic Thinking/ Complex Reasoning
[DOC File]Non-Euclidean Geometries
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Spherical Geometry – the first non-Euclidean geometry. Answering the first question: Spherical geometry can be said to be the first non-Euclidean geometry. It developed early in the Navigation/Stargazing Strand. The connections of spherical geometry with other strands will be covered in the following sections.
[DOC File]Geometry Scavenger Hunt
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For example, he uses the development of "strange" algebras or "strange" geometries as examples of this. Non-Euclidean geometry doesn't invalidate Euclidean geometry, as Morris seems to suggest, nor does imply the loss of certainty of Euclidean geometry. It only means that Euclidean geometry is one of infinite possible mathematical spaces.
What Are Euclidean and Non-Euclidean Geometry?
Why is this a Non-Euclidean Geometry? The axioms are totally different from Euclidean Geometry. Note that this geometry has several distinctly different models – and Euclidean Geometry has essentially only one model. (This is a new fact for you!) Incidence Geometry Exercise: Find at least one way that this geometry is like Euclidean Geometry.
[DOC File]What Euclid Did : a section of The Unreasonable Influence ...
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.The measure of an exterior angle of a triangle is greater than either non-adjacent interior angle.
[DOC File]Non-Euclidean Geometries
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This is a categorical finite non-Euclidean geometry. [In fact, all finite geometries are non-Euclidean.] The Three Point Geometry: Undefined Terms: point, line, on. Axioms: A1 There are exactly 3 distinct points. A2 Two distinct points are on exactly one line. A3 Not all the points are on the same line. A4.
[DOC File]Mathematics: The Loss of Certainty (Galaxy Books) (Paperback)
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Euclidean geometry was history's first example of a system of knowledge. Egyptian and Babylonian geometry texts are little more than lists of facts and formulas. But Euclid had not just put together a set of facts, he had assembled those facts into a structure.
[DOC File]THE GEOMETRY OF PERSPECTIVE AND PROJECTIVE GEOMETRY
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5. The name and brief description of two non-Euclidean geometries. (15) 6. A square nut (10), hexagonal nut (15), and/or pentagonal nut (25) 7. An advertisement for a specific item showing vertical angles (15) 8. An advertisement that uses a conditional statement. (10) 9.
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