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Increasing numbers of lone pairs on a central atom cause bond

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... millennium before Pythagoras, circa 1900 1600 BCE , the Babylonians (Babylon located in modern day Iraq) identify what are now called Pythagorean triples (a set of positive integers a, b, c such that a2 + b2 = c2 ...
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Activity_2_3_2a_052115 - Connecticut Core Standards

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acuu ,
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Geometer`s Sketchpad and the New Geometry Strands

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... b.) Prove that there exist three distinct lines that do not contain a common point. (Assume the Euclidean Parallel Postulate.) Prove: The opposite sides of a parallelogram are congruent (definition of parallelogram - quadrilateral with both pairs of opposite sides parallel). Prove that vertical angl ...
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History of geometry



Geometry (from the Ancient Greek: γεωμετρία; geo- ""earth"", -metron ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)
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