The Non-Euclidean, Hyperbolic Plane: Its Structure and Consistency (Universitext)

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9780387905525: The Non-Euclidean, Hyperbolic Plane: Its Structure and Consistency (Universitext)

The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in­ fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces­ sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de­ signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli­ dean geometry with some mastery.

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P. Kelly, G. Matthews
Editore: Springer-Verlag New York Inc., United States (1981)
ISBN 10: 0387905529 ISBN 13: 9780387905525
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Descrizione libro Springer-Verlag New York Inc., United States, 1981. Paperback. Condizione libro: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid s, had a profound in- fluence on man s understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces- sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de- signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli- dean geometry with some mastery. Softcover reprint of the original 1st ed. 1981. Codice libro della libreria LIE9780387905525

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P. Kelly, G. Matthews
Editore: Springer-Verlag New York Inc., United States (1981)
ISBN 10: 0387905529 ISBN 13: 9780387905525
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Descrizione libro Springer-Verlag New York Inc., United States, 1981. Paperback. Condizione libro: New. Language: English . Brand New Book ***** Print on Demand *****.The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid s, had a profound in- fluence on man s understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces- sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de- signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli- dean geometry with some mastery. Softcover reprint of the original 1st ed. 1981. Codice libro della libreria AAV9780387905525

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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387905525_lsuk

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Descrizione libro Springer, 1981. Paperback. Condizione libro: NEW. 9780387905525 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0411115

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Descrizione libro Springer, 2013. Condizione libro: New. This item is printed on demand for shipment within 3 working days. Codice libro della libreria LP9780387905525

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Descrizione libro Springer-Verlag New York Inc., 1981. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387905525

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P. Kelly, G. Matthews
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Descrizione libro Springer-Verlag New York Inc., United States, 1981. Paperback. Condizione libro: New. Language: English . Brand New Book ***** Print on Demand *****. The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid s, had a profound in- fluence on man s understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces- sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de- signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli- dean geometry with some mastery. Softcover reprint of the original 1st ed. 1981. Codice libro della libreria AAV9780387905525

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Descrizione libro Springer-Verlag New York Inc., 1981. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780387905525

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Kelly, P.; Matthews, G.
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Descrizione libro Springer, 1981. Paperback. Condizione libro: New. This item is printed on demand. Codice libro della libreria INGM9780387905525

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Descrizione libro Springer. PAPERBACK. Condizione libro: New. 0387905529 New Condition. Codice libro della libreria NEW6.3071831

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