or Kusumapura in 476 CE. There is no clear evidence of the place of birth (Indian Streams Research General‚ September 2012). Aryabhata studied in Kusumapura and stayed there for some time. The evidences from Hindu‚ Buddhist tradition‚ and Bhaskara I (629 CE) recognize Kusumapura as Pataliputra‚ currently known as Patna. Aryabhata was the head of an institution at Kusumapura. The University of Nalanda was in Pataliputra at the time. This university had an astronomical observatory that forces
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Greeks. The ancient Greek mathematician Euclid influenced mathematics in a large way after developing the Pythagorean theorem. His theorem (written around 300 B.C.) stated that “If two straight lines cut one another‚ the vertical‚ or opposite‚ angles shall be the same” (Doc. 5). Euclid wrote this theorem to set a base rule to help find the sum of the angles of a triangle. The Pythagorean theorem is still used today in mathematics thanks to Euclid’s contribution to society. Perhaps the most famous
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Following completion of your readings‚ complete exercise 4 in the “Projects” section on page 620 of Mathematics in Our World. Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this. After building your triples‚ verify each of them in the Pythagorean Theorem equation. The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs. Your introduction should
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all the mathematicians of his time‚ his work was the most discussed and argued about. Ptolemy gave the name to the Ptolemy’s Planetary theory. The book is mostly devoted to astronomy and astronomy. Ptolemy’s theorem was a powerful result. With its help we established the Pythagorean Theorem. Combined with the
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Treasure Hunt: Finding the Values of Right Angle Triangles This final weeks course asks us to find a treasure with two pieces of a map. Now this may not be a common use of the Pythagorean Theorem to solve the distances for a right angled triangle but it is a fun exercise to find the values of the right angle triangle. Buried treasure: Ahmed has half of a treasure map‚which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map
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* Deductive Reasoning – * making a specific conclusion based on a collection of generally accepted assumptions. * There are no counterexamples * Premises – undefined terms‚ definitions and postulates (or previously proven theorems) * Fallacy: A conclusion that does not necessarily follow from the premises. * Proof by Negation – Indirect Proofs – * Start with the Givens * Assume the negation of the Conclusion/Proof * The conclusion of the
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Rock. When she get there to walk x paces to the north‚ and then walk 2x + 4 paces to the east. I wonder what X could equal to‚ if Ahmed and Vanessa come together in finding the treasure they would save a lot of time of digging. In this Pythagorean equation we will see how far Ahmed would walk 2x+6 paces and Vanessa would have to walk 2x+4‚ x in desert to find the Castle Rock. Ahmed and Vanessa would need equipment for their journey they will use rope‚ compasses and sticks with colored flags
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the Euclidean Summary of Proclus. This contains an outline of the development of Greek geometry from early times until Euclid (Allen‚ 1997). Thales is often considered to be one of the first Greek mathematicians. The proposition known as the “Theorem of Thales” states‚ “The diameter of a circle always subtends a right angle to any point on the circle” (Thomas‚ 1991‚ p. 119). There are few primary sources that are able to describe early Greek Mathematics‚ hence the reliance on Proclus‚ but it is
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Where will I ever need algebra? Where do you need square roots? When will I ever use the Pythagorean Theorem? Will algebra even be ’relevant ’ in the future? These are a few of the many questions that one asks when they have to take an algebra course. This is a required subject in most colleges to further ones education. The first year of algebra is a prerequisite for all higher-level math: geometry‚ algebra II‚ trigonometry‚ and calculus. It is quite true‚ while many people get by without an education
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Geometry is typically the second math course taken by high school students. Major topics discussed include introductory logic; coordinate geometry; congruence‚ similarity and proof; right triangle trigonometry; transformations; locus; constructions; circles; and three-dimensional objects. Students will garner reasoning skills and learn how to form logical and coherent arguments. This course is aligned with the Common Core Learning Standards and integrates the eight Standards for Mathematical Practice
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