1) compare and contrast euclidean geometry and spherical geometry be sure to include these points: a) describe the role of the parallel postulate in spherical geometry. Brief explanation of some of the differences between euclidean geometry and spherical geometry. Objective: compare and contrast eclidean, spherical and hyperbolic geometry fill in the following table with as much detail as you can comparing and contrasting the 3 geometries. When it comes to euclidean geometry, spherical geometry and hyperbolic geometry there are many similarities and differences among them for example, what may be true for euclidean geometry may not be true for spherical or hyperbolic geometry.
Euclidean geometry is what describes the shortest path between and 2 points on a sphere is a along a circle lines are a process in euclidean geometry however in spherical geometry they are not in euclidean geometry the sum of any triangles angle measures must equal a 180 degrees. Reasoning is the statement spherical geometry is a subset of euclidean geometry true or false explain your reasomng writing in math do similar or congruent triangles exist in spherical geometry. Teachers compare and contrast euclidean trigonometry with spherical trigonometry, and are assessed on their knowledge and understanding via homework, exams, projects, and presentations mathematical concepts, procedures, and the connections among them for teaching upper level functions, algebra, and concepts of calculus including. Comparing planar and spherical geometry complete the table below to compare and contrast lines in the system of plane euclidean geometry and lines (great circles) in spherical geometry on the plane on the sphere 1 is the length of a line finite or infinite.
Find euclidean geometry lesson plans and teaching resources from euclidean geometry proofs worksheets to non-euclidean geometry videos, quickly find teacher-reviewed educational resources they complete internet geometry activities and write essays comparing and contrasting hyperbolic geometry to euclidean geometry in this spherical. In contrast, on a sphere (think of the earth's surface) the shortest distance between two points is a great circle in a plane, the circumference of any circle is 2pir but suppose we imagine traveling r miles along the earth's surface from the north pole, then drawing a circle (a parallel of latitude, really) around the pole from that point. 3-9 comparing spherical and euclidean geometry teks focus teks (4)(d) compare geometric relationships between euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.
Euclidean, hyperbolic and elliptic geometry posted by john baez there are two famous kinds of non-euclidean geometry: hyperbolic geometry and elliptic geometry (which almost deserves to be called ‘spherical’ geometry, but not quite because we identify antipodal points on the sphere. Comparing and contrasting euclidean, spherical, and hyperbolic geometries - when it comes to euclidean geometry, spherical geometry and hyperbolic geometry there are many similarities and differences among them. Spherical geometry is an example of a geometry which is not euclidean it is the study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in euclidean geometry. Euclidean, spherical and hyperbolic geometry are different on small scales the sum of the angles in a triangle is different, for example however, for really small triangles in spherical and hyperbolic geometry, the triangles begin to look a lot like their euclidean cousins. Join now to read essay comparing and contrasting euclidean, spherical, and hyperbolic geometries when it comes to euclidean geometry, spherical geometry and hyperbolic geometry there are many similarities and differences among them.
Find out what you understand about euclidean vs non-euclidean geometry with this worksheet/quiz combo two branches of geometry and the study of spherical surfaces - compare and contrast. The essential difference between euclidean geometry and these two non-euclidean geometries is the nature of parallel lines: in euclidean geometry, given a point and a line, there is exactly one line through the point that is in the same plane as the given line and never intersects it. Pearson texas geometry: topic 3 parallel and perpendicular lines goodrich isd, tx study guide by rhonda_brodie includes 30 questions covering vocabulary, terms and more quizlet flashcards, activities and games help you improve your grades. Comparing planar and spherical geometry complete the table below to compare and contrast lines in the system of plane euclidean geometry and lines (great circles) in spherical geometry.
Spherical geometry is the geometry of the two-dimensional surface of a sphere contrast this with euclidean geometry, in which a line has one parallel through a given point, and hyperbolic geometry, in which a line has two parallels and an infinite number of ultraparallels through a given point. Comparative geometry with geogebra, spherical easel and other didactic tools phd anna rybak university of bialystok, poland continuously comparing and contrasting one with the other we i lénárt - non-euclidean adventures on the lénárt sphere, key curriculum press, usa, 1996. Non - euclidean hyperbolic geometry spherical geometry in hyperbolic geometry there are at least two distinct lines that pass through the point and are parallel to (in the same plane as and do not intersect) the given line. Integration of hyperbolic and spherical geometry with the euclidean geometry—non-euclidean geometries are not divided into separate chaptersevery geometric notion is explored in relation to the euclidean plane, on spheres and on hyperbolic planes.
Inherited from euclidean geometry theorem 2: each point is on at least two lines each point is on an infinite number of lines theorem 3: there is a triple of lines that do not share a common point fe, gc, and ad for example now for the usual: cw chapter 2 #5 compare and contrast the klein disc to spherical geometry visit in groups and then we’ll turn in #5 29. Non-euclidean geometry, literally any geometry that is not the same as euclidean geometryalthough the term is frequently used to refer only to hyperbolic geometry, common usage includes those few geometries (hyperbolic and spherical) that differ from but are very close to euclidean geometry (see table. Project for geometry, comparing euclidean and spherical geometry may 2009.