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[DOC File]Front cover - ResearchGate
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The Fermat-Torricelli point of a triangle minimizes the sum of distances from the vertices of the triangle on the given surface. ... Investigations of the problem in non-Euclidean geometries ...
examples of non euclidean geometry

[DOC File]Depth of Knowledge Levels (DOK) Mathematics
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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
euclidean geometry definition

Message from the President - KCTM
Sketch a taxi-equilateral triangle. Explain a method you can employ to sketch taxi-equilateral triangles. Hint: The figure below may help. Sketch a taxi-equilateral triangle that is also an isosceles triangle in Euclidean geometry. Justify your work. Sketch a taxi-equilateral triangle that is also a scalene triangle in Euclidean geometry.
what is non euclidean geometry

[DOC File]Chapter 3
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non-euclidean geometries In the previous chapter we began by adding Euclid’s Fifth Postulate to his five common notions and first four postulates. This produced the familiar geometry of the ‘Euclidean’ plane in which there exists precisely one line through a given point parallel to a given line not containing that point.
non euclidean geometry for dummies

[DOC File]According to the NCTM (2000) “Instructional programs from ...
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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.
euclidean and non euclidean geometry

[DOC File]Chapter 2, Section 5 - UH
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This completes the example of a non-Euclidean metric that has the triangle inequality property. Moment for Discovery page 85. Here’s some information about another way to measure distance…what is the formula being used? This is important to work out because we’ll be using this formula in . Chapter 3. The distance from (0, 8) to (10, 0) is 18.
euclidean vs non euclidean geometry

[DOC File]Taxicab Geometry - UH
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Is this triangle congruent to the TCG equilateral triangle of side length 4 that is to the right on the x axis? Why or why not? Can you say the triangles have the quality SAS? Is SAS an axiom in this geometry? Do you see why this geometry is non-euclidean?
euclidean vs non euclidean

[DOC File]Chapter 1
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A close look at the proof above shows that it is independent of Euclid’s Fifth postulate and hence every triangle, whether Euclidean or non-Euclidean, has an incenter and an inscribed circle. It may come as an even greater surprise is that triangles have many more properties than the ones taught in high school.
applications of non euclidean geometry

[DOC File]Non-Euclidean Geometry - Advanced Pre-Calculus
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The model for Euclidean geometry is the flat plane. The model for hyperbolic geometry is the outside bell of a trumpet. The model for spherical geometry is the sphere. I. We have proved that the sum of the angles of a triangle is 180(. On a globe, is it possible to have a triangle with more than one right angle? _____ Is this a Euclidean triangle?
examples of non euclidean geometry

Property/Postulate/Theorem “Cheat Sheet”
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. Hypotenuse-Leg (HL) Congruence (right triangle) If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent.
euclidean geometry definition

Non euclidean triangle