proofs they consider charming. Probeer het nog eens. As Professor of Mathematics at the Technical University of Catalonia, Claudi has delivered a wide range of research papers, publications and lectures on mathematics and mathematics education. The authors consider proofs from topics such as geometry, number theory, inequalities, plane tilings, origami and polyhedra.

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Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming, Topics include the integers, selected real numbers, points in the plane, triangles, squares, and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. Theorems and their proofs lie at the heart of mathematics. As in the authors’ previous books with the MAA (Math Made Visual and When Less Is More), secondary school and college and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Ontdek het beste van shopping en entertainment, Gratis en snelle bezorging van miljoenen producten, onbeperkt streamen van exclusieve series, films en meer, Je onlangs bekeken items en aanbevelingen, Selecteer de afdeling waarin je wilt zoeken. Following a short Are elegant mathematical proofs merely an example of the Infinite Monley Theorem. real numbers, points in the plane, triangles, squares and other Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. We gebruiken cookies en vergelijkbare tools om uw winkelervaring te verbeteren, onze services aan te bieden, te begrijpen hoe klanten onze services gebruiken zodat we verbeteringen kunnen aanbrengen, en om advertenties weer te geven. Post some of these and we'll discuss them. There are over 130 such challenges. Probeer het opnieuw. In plaats daarvan houdt ons systeem rekening met zaken als hoe recent een recensie is en of de recensent het item op Amazon heeft gekocht. A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Privacy Policy | © 2020 American Mathematical Society. Published by Oxford University Press. For permissions, please e-mail: [email protected], This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (. very high degree of unexpectedness, combined with inevitability and Many of these people ascribe an almost mystical element to these proofs… Don't already have an Oxford Academic account? The answers are in the back of the book to the challenges, but I would recommend not looking until you finish! This makes the book of special interest to the middle and high school I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. Charming Proofs: A Journey into Elegant Mathematics, https://www.ams.org/exam-desk-review-request?&eisbn=978-1-61444-201-1&epc=DOL/42.E&title=Charming%20Proofs%3A%20A%20Journey%20into%20Elegant%20Mathematics&author=Claudi%20Alsina%3B%20Roger%20B.%20Nelsen&type=R, 1.2 Sums of squares, triangular numbers, and cubes, 2.2 The irrationality of sqrt{k} for non-square k, 3.6 Assigning numbers to points in the plane, 4.2 Drawing an n-gon with given side lengths, 4.5 The stars of the polygonal playground, 4.8 Cycloids, cyclogons, and polygonal cycloids, 5.4 Pappus’ generalization of the Pythagorean theorem, 5.6 The circumcircle and Euler’s triangle inequality, CHAPTER 6 The Enchantment of the Equilateral Triangle, 6.4 A triangular tiling of the plane and Weitzenböck’s inequality, 6.8 The equilateral triangle and the golden ratio, 7.3 Quadrilateral equalities and inequalities, 7.4 Tangential and bicentric quadrilaterals, 7.6 Pythagoras with a parallelogram andequilateral triangles, 9.4 The shoemaker’s knife and the salt cellar, 9.5 The Quetelet and Dandelin approach to conics, CHAPTER 10 Adventures in Tilingand Coloring, 10.2 Tiling with triangles and quadrilaterals, 10.3 Infinitely many proofs of the Pythagorean theorem, 10.7 Dodecahedra and Hamiltonian circuits, 11.1 The Pythagorean theorem in three dimensions, 11.3 Corresponding triangles on three lines, 11.9 Faces and vertices in convex polyhedra, 11.10 Why some types of faces repeat in polyhedra, CHAPTER 12 Additional Theorems, Problems, and Proofs, 12.2 The Cantor-Schro¨ der-Bernstein theorem, 12.4 The arithmetic mean-geometric mean inequality. may wish to use the book as a supplement in an introductory course on In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs “there is a very high degree of unexpectedness, combined with inevitability and economy.” Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. … Theorems and their proofs lie at the heart of mathematics. However, the Pythagorean theorem is in no way central to the book. please many a mathematics fan. MAA Press: An Imprint of the American Mathematical Society. previous books with the MAA (Math Made Visual and When are some challenges that will draw the reader into the process of The book covers In speaking of the purely aesthetic qualities of theorems latter with solutions found at the end of the book. invite readers to enjoy the beauty of mathematics, to share their Some authors supply each of the 12 chapters with challenge problems and the

More than 130 exercises for the reader (with solutions) are also included. challenges, references, and a complete index. Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. © 1996-2020, Amazon.com, Inc. en dochterondernemingen, Klantenservice voor mensen met een handicap, Vertaal alle beoordelingen naar het Nederlands, Ga naar Amazon.com om alle 1 recensies te bekijken, Pakketten traceren of bestellingen bekijken. Topics include the integers, selected Please check your email address / username and password and try again. Charming Proofs presents a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. economy.' This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. challenges. proofs in elementary mathematics that are exceptionally elegant, full I'll keep it short. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. Goedgekeurde derde partijen gebruiken deze tools voor onze weergave van advertenties. all documents, Shipping Information | Less Is More), secondary school, college, and university current document

To purchase short term access, please sign in to your Oxford Academic account above. As with their previous books, the mathematics. It complements my study of pure math and introduces me to many fields of math.