Non-Euclidean Geometries
... The Most Controversial The Parallel Postulate: In layman’s terms * Given a line and a point not on that line, there is exactly one line through the point that is parallel to the line. ...
... The Most Controversial The Parallel Postulate: In layman’s terms * Given a line and a point not on that line, there is exactly one line through the point that is parallel to the line. ...
Fundamentals of College Math
... F-TF.2-Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. F-TF.3-(+) Use special triangles to determine geometrically the values of sine, ...
... F-TF.2-Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. F-TF.3-(+) Use special triangles to determine geometrically the values of sine, ...
GEOMETRY
... School systems may offer Geometry and Geometry A and Geometry B. Content standards 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 26, 30, 31, 32, 33, and 34 must be taught in the Geometry A course. Content standards 2, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 35, 36, 37, 38, 39, 40, ...
... School systems may offer Geometry and Geometry A and Geometry B. Content standards 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 26, 30, 31, 32, 33, and 34 must be taught in the Geometry A course. Content standards 2, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 35, 36, 37, 38, 39, 40, ...
Analytic geometry
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. The numerical output, however, might also be a vector or a shape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.