Pythagorean Triangles
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Pythagorean Triangles
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Author : Waclaw Sierpinski
language : en
Publisher: Courier Corporation
Release Date : 2013-04-10
Pythagorean Triangles written by Waclaw Sierpinski and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-10 with Mathematics categories.
This classic text, written by a distinguished mathematician and teacher, focuses on a fundamental theory of geometry. Topics include all types of Pythagorean triangles.
A Pythagorean Introduction To Number Theory
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Author : Ramin Takloo-Bighash
language : en
Publisher: Springer
Release Date : 2018-11-26
A Pythagorean Introduction To Number Theory written by Ramin Takloo-Bighash and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-26 with Mathematics categories.
Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.
The Pythagorean Theorem
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Author : Merle A. Barlow
language : en
Publisher: WestBow Press
Release Date : 2016-02-05
The Pythagorean Theorem written by Merle A. Barlow and has been published by WestBow Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-05 with Mathematics categories.
Pythagoras, a famous Greek scholar, sathematician, and philosopher, formulated a proof for a theorem that is named for him—the Pythagorean theorem. This theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagorean theorem for right-angled triangles likely was known long before the time of Pythagoras. It was probably used by the ancient Egyptians to construct the pyramids. The theorem is quite believable without rigorous proof to anyone willing to expend a modest effort in some experimentation. One method is to draw a number of right-angled triangles in as wide a variety as practicable and measure all of the sides. It will be determined that, for each triangle drawn, the square of the length of the side opposite the right angle is about equal to the sum of the lengths of the squares of the other two sides. Another method requires the availability of a balance. For this more interesting experiment, construct a right-angled triangle and a square on each side using a piece of sheet metal or cardboard. Then cut out the three squares and weigh them on the balance. The square on the hypotenuse should balance the other two. Contained within this book are some rigorous proofs and some interesting perspectives regarding right angles and right-angled triangles. Doubtless, this theorem is one of the most useful concepts in mathematics.
The Pythagorean Triangle Or The Science Of Numbers
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Author : George Oliver
language : en
Publisher:
Release Date : 1875
The Pythagorean Triangle Or The Science Of Numbers written by George Oliver and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1875 with Freemasonry categories.
The Metaphysics Of The Pythagorean Theorem
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Author : Robert Hahn
language : en
Publisher: State University of New York Press
Release Date : 2017-05-01
The Metaphysics Of The Pythagorean Theorem written by Robert Hahn and has been published by State University of New York Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-01 with Philosophy categories.
Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike.
Beginning Math Problems Using Pythagaorean Triples
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Author : Colin Gardner
language : en
Publisher:
Release Date : 2003-05
Beginning Math Problems Using Pythagaorean Triples written by Colin Gardner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05 with categories.
This small book is a powerful tool to teach math students of all ages, young and old to calculate the sides of All-Integer Pythagorean triangles for any integer greater than 2, without the use of a square-root operation. Two methods are provided (1) using algebraic equations and (2) parabola equations, which allow the hypotenuse to be obtained by addition from its two legs. Illustrations of equation usages with more problems are provided. Learn to build quadratic equations on Pythagorean triangle sides two different ways. Learn to determine (recover) prime integer sides on Pythagorean triangles, given only angle data. Learn different equations that find missing (integer) triangle sides without the use of a square-root operation. Learn to add and subtract two angles, (including overlapping triangles) using Pythagorean triples, without knowledge of trigonometry equations. Learn to develop 5 kinds of equations (like quadratic equations, parabola parameters, sines and cosines, etc) on the sides of All-Integer Pythagorean triangles, with conversions from one type to another. Learn trigonometric equations that represent a combination of sides of All-Integer Pythagorean triangles, plus several GENERAL EQUATIONS that compute more. Learn the benefits and uses of four additional parameters for the quadratic equation, like SQR(b*b -4ac) = an integer, and their relationships to All-Integer Pythagorean triangles.
The Pythagorean Triangle
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Author : Rev George Oliver
language : en
Publisher: Literary Licensing, LLC
Release Date : 2014-03
The Pythagorean Triangle written by Rev George Oliver and has been published by Literary Licensing, LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03 with categories.
This Is A New Release Of The Original 1922 Edition.
The Pythagorean Triangle Or The Science Of Numbers
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Author : George Oliver
language : en
Publisher: Theclassics.Us
Release Date : 2013-09
The Pythagorean Triangle Or The Science Of Numbers written by George Oliver and has been published by Theclassics.Us this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1875 edition. Excerpt: ... PROGRESSIVE GENERATION OF THE TETRAD OR SOLID, REPRESENTING FIRE. THE SOLID, TETRAD, QUATERNARY, OR THE NUMBER FOUR. CHAPTER IV. THE SOLID. TETRAD, QUATERNARY, OR THE NUMBER FOUR. "By that pure, holy, Four-Letter Name on high, Nature's eternal fountain and supply, The parent of all souls that living be, By Him, with faithful oath, I swear to thee." Oath Of Pythagoras. "The Grand and Sacred Name ought to be saluted four times in four peculiar positions, for the following reasons."--Old Lectdbes. HE tetrad, though not essentially masonic, for the only instances in which it I is exemplified, viz., in the Sacred Name and the Cherubim, are attached to the third degree only, was esteemed the most perfect number, and referred to the Author of nature, or T.G.A.O. T.U.; and his name was therefore composed of four letters, nW, and was called Tetragrammaton by the Jews, and Tetractys by the Gentiles; of the latter of whom Hierocles, in his exposition of the Golden Verses of Pythagoras, says, "He is the Demiurgus, the architect and maker of all tilings." These are his words: "The author of these verses shows that the tetrad, which is the fountain of the perpetual orderly distribution of things, is the same with God who is the Demiurgus; an intelligible god, the source of the celestial and sensible good." The tetrad, as Mr Taylor thinks, is, however, the animal itself of Plato, who, as Syrianus justly observes, was the best of the Pythagoreans; subsists at the extremity of the intelligible triad, as is most satisfactorily shown by Proclus in the third book of his treatise on the theology of Plato. And between these two triads, the one intelligible, and the other intellectual, another order of gods exists, which partakes of both extremes. This number...
Pythagorean Triangle
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Author : George Oliver
language : en
Publisher:
Release Date : 2019
Pythagorean Triangle written by George Oliver and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
The Pythagorean Triangle Or The Science Of Numbers Or The Science Of Numbers
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Author : George Oliver
language : en
Publisher: Wentworth Press
Release Date : 2019-02-27
The Pythagorean Triangle Or The Science Of Numbers Or The Science Of Numbers written by George Oliver and has been published by Wentworth Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
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