Mathematical Surprises

Mathematical Surprises

Author: Mordechai Ben-Ari

Publisher: Springer Nature

Published: 2022-09-07

Total Pages: 232

ISBN-13: 3031135660

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This is open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction. Among the most surprising theorems are the Mohr-Mascheroni theorem that a compass alone can perform all the classical constructions with straightedge and compass, and Steiner's theorem that a straightedge alone is sufficient provided that a single circle is given. The highlight of the book is a detailed presentation of Gauss's purely algebraic proof that a regular heptadecagon (a regular polygon with seventeen sides) can be constructed with straightedge and compass. Although the mathematics used in the book is elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and other interested readers will relish the opportunity to confront the challenge of understanding these surprising theorems.


Book Synopsis Mathematical Surprises by : Mordechai Ben-Ari

Download or read book Mathematical Surprises written by Mordechai Ben-Ari and published by Springer Nature. This book was released on 2022-09-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction. Among the most surprising theorems are the Mohr-Mascheroni theorem that a compass alone can perform all the classical constructions with straightedge and compass, and Steiner's theorem that a straightedge alone is sufficient provided that a single circle is given. The highlight of the book is a detailed presentation of Gauss's purely algebraic proof that a regular heptadecagon (a regular polygon with seventeen sides) can be constructed with straightedge and compass. Although the mathematics used in the book is elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and other interested readers will relish the opportunity to confront the challenge of understanding these surprising theorems.

One Equals Zero, and Other Mathematical Surprises

One Equals Zero, and Other Mathematical Surprises

Author: Nitsa Movshovitz-Hadar

Publisher: Lawrence Erlbaum Associates

Published: 2013

Total Pages: 168

ISBN-13: 9780873537407

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"Originally published by Key Curriculum Press"--t.p.


Book Synopsis One Equals Zero, and Other Mathematical Surprises by : Nitsa Movshovitz-Hadar

Download or read book One Equals Zero, and Other Mathematical Surprises written by Nitsa Movshovitz-Hadar and published by Lawrence Erlbaum Associates. This book was released on 2013 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Originally published by Key Curriculum Press"--t.p.

Mathematical Amazements and Surprises

Mathematical Amazements and Surprises

Author: Alfred S. Posamentier

Publisher: Prometheus Books

Published: 2010-03-19

Total Pages: 269

ISBN-13: 1615922946

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With many entertaining examples of mathematical curiosities, educators Posamentier and Lehmann have created the perfect introduction to the wonders of mathematics for the general reader, requiring only a high school background in the subject.


Book Synopsis Mathematical Amazements and Surprises by : Alfred S. Posamentier

Download or read book Mathematical Amazements and Surprises written by Alfred S. Posamentier and published by Prometheus Books. This book was released on 2010-03-19 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many entertaining examples of mathematical curiosities, educators Posamentier and Lehmann have created the perfect introduction to the wonders of mathematics for the general reader, requiring only a high school background in the subject.

The Wonder Book of Geometry

The Wonder Book of Geometry

Author: David Acheson

Publisher: Oxford University Press

Published: 2020-10-22

Total Pages: 240

ISBN-13: 0192585371

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How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.


Book Synopsis The Wonder Book of Geometry by : David Acheson

Download or read book The Wonder Book of Geometry written by David Acheson and published by Oxford University Press. This book was released on 2020-10-22 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.

Mathematical Surprises

Mathematical Surprises

Author: M. Ben-Ari

Publisher:

Published: 2022

Total Pages: 0

ISBN-13: 9788303113566

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This open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction. Among the most surprising theorems are the Mohr-Mascheroni theorem that a compass alone can perform all the classical constructions with straightedge and compass, and Steiner's theorem that a straightedge alone is sufficient provided that a single circle is given. The highlight of the book is a detailed presentation of Gauss's purely algebraic proof that a regular heptadecagon (a regular polygon with seventeen sides) can be constructed with straightedge and compass. Although the mathematics used in the book is elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and other interested readers will relish the opportunity to confront the challenge of understanding these surprising theorems.


Book Synopsis Mathematical Surprises by : M. Ben-Ari

Download or read book Mathematical Surprises written by M. Ben-Ari and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction. Among the most surprising theorems are the Mohr-Mascheroni theorem that a compass alone can perform all the classical constructions with straightedge and compass, and Steiner's theorem that a straightedge alone is sufficient provided that a single circle is given. The highlight of the book is a detailed presentation of Gauss's purely algebraic proof that a regular heptadecagon (a regular polygon with seventeen sides) can be constructed with straightedge and compass. Although the mathematics used in the book is elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and other interested readers will relish the opportunity to confront the challenge of understanding these surprising theorems.

Yearning for the Impossible

Yearning for the Impossible

Author: John Stillwell

Publisher: CRC Press

Published: 2006-05-23

Total Pages: 249

ISBN-13: 1439865779

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This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress: - Irrational and Imaginary Numbers - The Fourth Dimension - Curved Space - Infinity and others The author puts t


Book Synopsis Yearning for the Impossible by : John Stillwell

Download or read book Yearning for the Impossible written by John Stillwell and published by CRC Press. This book was released on 2006-05-23 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress: - Irrational and Imaginary Numbers - The Fourth Dimension - Curved Space - Infinity and others The author puts t

What's Happening in the Mathematical Sciences

What's Happening in the Mathematical Sciences

Author: Barry Cipra

Publisher: American Mathematical Soc.

Published:

Total Pages: 108

ISBN-13: 9780821890431

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Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.


Book Synopsis What's Happening in the Mathematical Sciences by : Barry Cipra

Download or read book What's Happening in the Mathematical Sciences written by Barry Cipra and published by American Mathematical Soc.. This book was released on with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.

1089 and All that

1089 and All that

Author: D. J. Acheson

Publisher: Oxford University Press, USA

Published: 2002

Total Pages: 200

ISBN-13: 9780198516231

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This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famouscartoonists. This unusual book is one of the most readable explanations of mathematics available.


Book Synopsis 1089 and All that by : D. J. Acheson

Download or read book 1089 and All that written by D. J. Acheson and published by Oxford University Press, USA. This book was released on 2002 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famouscartoonists. This unusual book is one of the most readable explanations of mathematics available.

Surprises in Probability

Surprises in Probability

Author: Henk Tijms

Publisher: CRC Press

Published: 2018-08-30

Total Pages: 144

ISBN-13: 0429815492

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This book brings together a variety of probability applications through entertaining stories that will appeal to a broad readership. What are the best stopping rules for the dating problem? What can Bayes’ formula tell us about the chances of a Champions League draw for soccer teams being rigged? How could syndicates win millions of lottery dollars by buying a multitude of tickets at the right time? What’s the best way to manage your betting bankroll in a game in which you have an edge? How to use probability to debunk quacks and psychic mediums? How can the Monte Carlo simulation be used to solve a wide variety of probability problems? Are seven riffle shuffles of a standard deck of 52 playing cards enough for randomness? Provides seventeen engaging stories that illustrate ideas in probability. Written so as to be suitable for those with minimal mathematical background. Stories can be read independently. Can be used as examples and exercises for teaching introductory probability. These questions and many more are addressed in seventeen short chapters that can be read independently. The engaging stories are instructive and demonstrate valuable probabilistic ideas. They offer students material that they most likely don’t learn in class, and offer teachers a new way of teaching their subject.


Book Synopsis Surprises in Probability by : Henk Tijms

Download or read book Surprises in Probability written by Henk Tijms and published by CRC Press. This book was released on 2018-08-30 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a variety of probability applications through entertaining stories that will appeal to a broad readership. What are the best stopping rules for the dating problem? What can Bayes’ formula tell us about the chances of a Champions League draw for soccer teams being rigged? How could syndicates win millions of lottery dollars by buying a multitude of tickets at the right time? What’s the best way to manage your betting bankroll in a game in which you have an edge? How to use probability to debunk quacks and psychic mediums? How can the Monte Carlo simulation be used to solve a wide variety of probability problems? Are seven riffle shuffles of a standard deck of 52 playing cards enough for randomness? Provides seventeen engaging stories that illustrate ideas in probability. Written so as to be suitable for those with minimal mathematical background. Stories can be read independently. Can be used as examples and exercises for teaching introductory probability. These questions and many more are addressed in seventeen short chapters that can be read independently. The engaging stories are instructive and demonstrate valuable probabilistic ideas. They offer students material that they most likely don’t learn in class, and offer teachers a new way of teaching their subject.

Mathematics for Human Flourishing

Mathematics for Human Flourishing

Author: Francis Su

Publisher: Yale University Press

Published: 2020-01-07

Total Pages: 287

ISBN-13: 0300237138

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"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.


Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.