Discovering Geometry Day 3
... perpendicular lines – lines that intersect to form four 90° angles. skew lines – lines that do not lie in the same plane. On pages 49–50, define the terms in bold. right angle – an angle that measures 90°. acute angle – an angle that measures between 0° and 90°. obtuse angle – an angle that measur ...
... perpendicular lines – lines that intersect to form four 90° angles. skew lines – lines that do not lie in the same plane. On pages 49–50, define the terms in bold. right angle – an angle that measures 90°. acute angle – an angle that measures between 0° and 90°. obtuse angle – an angle that measur ...
Final Exam info
... How much time? 75 minutes long How many points? 150 (16.5% of final grade) Format? 100 Multiple Choice questions worth 1.5 pt each and one page of extra credit Can I use a calculator? Yes! Don’t forget one because the math department will not loan out calculators on the day of the exam, and you may ...
... How much time? 75 minutes long How many points? 150 (16.5% of final grade) Format? 100 Multiple Choice questions worth 1.5 pt each and one page of extra credit Can I use a calculator? Yes! Don’t forget one because the math department will not loan out calculators on the day of the exam, and you may ...
A rigorous deductive approach to elementary Euclidean geometry
... 3. First steps of the introduction of Euclidean geometry 3.1. Fundamental concepts The primitive concepts we are going to use freely are : • real numbers, with their properties already discussed above ; ...
... 3. First steps of the introduction of Euclidean geometry 3.1. Fundamental concepts The primitive concepts we are going to use freely are : • real numbers, with their properties already discussed above ; ...
ABSE 026 Rev May 2014 - Glendale Community College
... level geometry course. In this course students investigate similarity and use similarity in the right triangle to define trigonometric ratios. They investigate circles and prove theorems about them. Connecting to their prior experience with the coordinate plane, they prove geometric theorems using c ...
... level geometry course. In this course students investigate similarity and use similarity in the right triangle to define trigonometric ratios. They investigate circles and prove theorems about them. Connecting to their prior experience with the coordinate plane, they prove geometric theorems using c ...
Geometry 2H Name: Similarity Part I
... functions that take points in the plane as inputs and give other points as outputs. I can compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). ...
... functions that take points in the plane as inputs and give other points as outputs. I can compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). ...
Conditional Statements/ Inductive Reasoning - MrsG-Geometry-CHS
... Lines k1 and k2 intersect at point E. Line m is perpendicular to lines k1 and k2 at point E. Which statement is always true? a. ...
... Lines k1 and k2 intersect at point E. Line m is perpendicular to lines k1 and k2 at point E. Which statement is always true? a. ...
3-6-17 math - Trousdale County Schools
... plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. 4. Develop definitions of rotations, reflections, an ...
... plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. 4. Develop definitions of rotations, reflections, an ...
Lie sphere geometry
Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. It was introduced by Sophus Lie in the nineteenth century. The main idea which leads to Lie sphere geometry is that lines (or planes) should be regarded as circles (or spheres) of infinite radius and that points in the plane (or space) should be regarded as circles (or spheres) of zero radius.The space of circles in the plane (or spheres in space), including points and lines (or planes) turns out to be a manifold known as the Lie quadric (a quadric hypersurface in projective space). Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations which preserve it. This geometry can be difficult to visualize because Lie transformations do not preserve points in general: points can be transformed into circles (or spheres).To handle this, curves in the plane and surfaces in space are studied using their contact lifts, which are determined by their tangent spaces. This provides a natural realisation of the osculating circle to a curve, and the curvature spheres of a surface. It also allows for a natural treatment of Dupin cyclides and a conceptual solution of the problem of Apollonius.Lie sphere geometry can be defined in any dimension, but the case of the plane and 3-dimensional space are the most important. In the latter case, Lie noticed a remarkable similarity between the Lie quadric of spheres in 3-dimensions, and the space of lines in 3-dimensional projective space, which is also a quadric hypersurface in a 5-dimensional projective space, called the Plücker or Klein quadric. This similarity led Lie to his famous ""line-sphere correspondence"" between the space of lines and the space of spheres in 3-dimensional space.