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Extractions: Home Education Social Science Education ... The History of Pascal's Triangle Views: Post a Comment Flag View Transcript I Did This Part of the video series: Geometry Tips The history of Pascal's triangle begins with the Indians and the Persians who first started working on this pattern of numbers, and it developed through China in the 13th century hundreds of years before Pascal was even born. Learn about the evolution of Pascal's triangle with instructions from a college-level math teacher in this free video on geometry. By Jimmy Chang eHow Contributor Jimmy Chang has a Master's Degree in math and has been a math teacher at St. Pete College for more than eight years. His specialties include Calculus, Algebra, Liberal Arts and... read more URL: Embed: Word Verification* Post a Comment More and en-US
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Extractions: Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need. Project-based learning is a terrific way to link your curriculum with real world events and applications of concepts that your students are learning. These resources will: One of the greatest benefits of project-based learning is gains in students' critical-thinking skills. However, as Bryan Goodwin (2010) found in reviewing the literature, a major shortcoming in many student projects is that educators tend to assign projects just for the sake of doing them. "Educators can avoid this phenomenon and realize the potential of projects to promote students' critical-thinking by framing projects around a driving question Is the project devoted only to mathematics (or a single subject area), or is there a link to other curricular areas?
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Extractions: Research Papers and Essays for All Search words.comment_error_title="A comment heading is required."; words.comment_error_text="A comment is required."; words.enter_query="No query entered!"; We have many premium term papers and essays on Hyperbolic Geometry And Omega Triangles. We also have a wide variety of research papers and book reports available to you for free. You can browse our collection of term papers or use our search engine HYPERBOLIC GEOMETRY AND OMEGA TRIANGLES Hyperbolic geometry was first discovered and explored by Omar Khayyam in the 9th century and Giovanni Gerolamo Saccheri in the 15th century. Both were attempting to prove Euclid’s parallel postulate by proving the concept of hyperbolic geometry to be inconsistent, and ironically they discovered it to be a new type of geometry. It wasn’t until the 19th century that it became fully developed with help from Karl Friedrich Gauss, Janos Bolyai, and Nikolai Ivanovich Labachevsky. Later on, Eugenio Beltrami developed models of it and used these to prove that hyperbolic geometry is consistent if Euclidean geometry is. Hyperbolic geometry is a form of non-Euclidean geometry. It upholds all of Euclid’s principles except the parallel postulate that says that if given a line [pic]and a point[pic] not on [pic], there is exactly one line through[pic] that doesn’t intersect [pic]. Hyperbolic geometry instead has the following modified postulate: “given any line [pic], and point[pic]not on [pic], there are exactly two lines through[pic]which are hyperparallel to [pic], and an infinite number of lines through[pic]ultraparallel to [pic]” (Wikipedia). Hyperbolic geometry has become well-understood in two dimensions; however, not much is known about it in three dimensions except that it can make dodecahedra.
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