Mathematical Surprises
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| Author | : Mordechai Ben-Ari |
| Publisher | : Springer Nature |
| Total Pages | : 232 |
| Release | : 2022-09-07 |
| Genre | : Mathematics |
| ISBN | : 3031135660 |
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.
| Author | : Nitsa Movshovitz-Hadar |
| Publisher | : Lawrence Erlbaum Associates |
| Total Pages | : 168 |
| Release | : 2013 |
| Genre | : Mathematical recreations |
| ISBN | : 9780873537407 |
"Originally published by Key Curriculum Press"--t.p.
| Author | : Alfred S. Posamentier |
| Publisher | : Prometheus Books |
| Total Pages | : 269 |
| Release | : 2010-03-19 |
| Genre | : Mathematics |
| ISBN | : 1615922946 |
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.
| Author | : John Stillwell |
| Publisher | : CRC Press |
| Total Pages | : 249 |
| Release | : 2006-05-23 |
| Genre | : Mathematics |
| ISBN | : 1439865779 |
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
| Author | : David Acheson |
| Publisher | : Oxford University Press |
| Total Pages | : 240 |
| Release | : 2020-10-22 |
| Genre | : Mathematics |
| ISBN | : 0192585371 |
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.
| Author | : M. Ben-Ari |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : Mathematics |
| ISBN | : 9788303113566 |
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.
| Author | : Barry Cipra |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 108 |
| Release | : |
| Genre | : Science |
| ISBN | : 9780821890431 |
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.
| Author | : Henk Tijms |
| Publisher | : CRC Press |
| Total Pages | : 144 |
| Release | : 2018-08-30 |
| Genre | : Mathematics |
| ISBN | : 0429815492 |
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.
| Author | : Francis Su |
| Publisher | : Yale University Press |
| Total Pages | : 287 |
| Release | : 2020-01-07 |
| Genre | : Mathematics |
| ISBN | : 0300237138 |
"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.
| Author | : Mike Ollerton |
| Publisher | : Bloomsbury Publishing |
| Total Pages | : 269 |
| Release | : 2012-03-08 |
| Genre | : Education |
| ISBN | : 1441180869 |
The third edition of this bestselling book for teachers of secondary mathematics has been brought right up to date and benefits from an extra teacher voice. Together, the authors show how active learning and introducing an element of surprise can bring mathematics alive. With a firm focus on problem solving, independent exploration, thinking skills and applying maths to real-life situations, this book contains new ideas, anecdotes and strategies including brand new chapters on functional mathematics, how to make best use of assessment, and teacher and curriculum development. Brimming with useful tips and inspirational advice on every aspect of teaching, this book is essential reading for maths teachers at any stage of their career.
