PPT-Non-Euclidean Geometry

By Victoria Leffelman Any geometry that is different from Euclidean geometry Consistent system of definitions assumptions and proofs that describe points lines and planes Most common types of nonEuclidean geometries are spherical and hyperbolic geometry . By the early 1 th century however a nascent interest in higher dimensions led to the realization that an ordinary sphere which is the 2D surface of a 3D ball has a higherdimensional counterpart called the hyper sphere which is the 3D surface of a D Euclidean Spanners: Short, Thin, andLanky Sunil Ary a  Gautam Das y David M. Moun tz Jerey S.Salo ex Mic hiel Euclidean spanners areimp ortan datastructures algorithm design, b ecausethey pro- vide TWSSP Thursday. Welcome. Please sit in your same groups from yesterday. Please take a moment to randomly distribute the role cards at your table and read through your group role.. Thursday Agenda. Agenda. . Anthony Lasenby. Astrophysics Group. Cavendish Laboratory. Cambridge, UK. a.n.lasenby@mrao.cam.ac.uk. www.mrao.cam.ac.uk/~clifford. Overview. Want to share two recent exciting developments. Recent progress in cosmology. Maryam Amini. Main Objectives. . : . Understand the basic idea of Euclidean Geometry. Understand the basic idea of non-Euclidean Geometry. . Conclusion. What is Euclidean Geometry? . is a mathematical . - Euclidean Geometry – Fall 2007 Dr. Hamblin Axiomatic Systems An axiomatic system is a list of undefined terms together with a list of statements (called “axioms”) that are p Anthony Barcellos. American River College. CMC. 3. December 2012. Three Interviews. Three Guys talk about Math. Anthony Barcellos. American River College. CMC. 3. December 2012. My Near-Great Life. Anthony Barcellos. TWSSP Wednesday. Welcome. OK, OK, I give in! You can sit wherever you want, . if …. You form groups of 3 or 4. You promise to assign group roles and really pay attention to them today. AND you promise to stay on task, minimize your side conversations, and participate actively in our whole group discussions. . Binary. . Image. . Selection. From. . Inaccurate. . User. Input. Kartic Subr, Sylvain Paris, Cyril Soler, Jan Kautz. University College London, Adobe Research, INRIA-Grenoble. Selection is a common operation in images. Using Taxicab Geometry to Model Urban Environments. Forrest Hinton. [Mathematical power] denotes an individual’s abilities to . explore. , conjecture, and reason logically, as well as the ability to use a variety of mathematical methods effectively to solve . ARM Research. 9. . Unification. Euclidean geometry. L9 . S. 2. Represent the Euclidean point . x. by null vectors. Distance is given by the inner product. Read off the Euclidean vector. D. epends on the concept of the origin. Geometry in Nature is Everywhere. Proportions of the human body. In the shape of a shell. .. .. . .. . The bees make their hives into regular hexagons. Honeycomb. The following slides are some more examples of geometry in nature. Does space exist?. What is the relation between a theory and reality?. Views of Reality: a spectrum. The common person. There are definite events independent of observation. Our senses record these events. Theories can represent genuine causal patterns inherent in the events. Generally, the features we use to describe things, e.g. size, time…, are inherent in the events themselves. The world consists of collections of 'things'.. Main Objectives. . : . Understand the basic idea of Euclidean Geometry. Understand the basic idea of non-Euclidean Geometry. . Conclusion. What is Euclidean Geometry? . is a mathematical . system. assuming .