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Book Cover
E-book
Author Alsina, Claudi.

Title Math made visual : creating images for understanding mathematics / Claudi Alsina and Roger B. Nelsen
Published Washington, DC : Mathematical Association of America, [2006]
©2006
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Description 1 online resource (xv, 173 pages) : illustrations
Series Classroom resource materials
Classroom resource materials.
Contents 15. Iterative procedures -- 15.1. Geometric series -- 15.2. Growing a figure iteratively -- 15.3. A curve without tangents -- 15.4. Challenges -- 16. Introducing colors -- 16.1. Domino tilings -- 16.2. L-Tetromino tilings -- 16.3. Alternating sums of triangular numbers -- 16.4. In space, four colors are not enough -- 16.5. Challenges -- 17. Visualization by inclusion -- 17.1. The genuine triangle inequality -- 17.2. The mean of the squares exceeds the square of the mean -- 17.3. The arithmetic mean-geometric mean inequality for three numbers -- 17.4. Challenges -- 18. Ingenuity in 3 D -- 18.1. From 3D with love -- 18.2. Folding and cutting paper -- 18.3. Unfolding polyhedra -- 18.4. Challenges -- 19. Using 3D models -- 19.1. Platonic secrets -- 19.2. The rhombic dodecahedron -- 19.3. The Fermat point again -- 19.4. Challenges -- 20. Combining techniques -- 20.1. Heron's formula -- 20.2. The quadrilateral law -- 20.3. Ptolemy's inequality -- 20.4. Another minimal path -- 20.5. Slicing cubes -- 20.6. Vertices, faces, and polyhedra -- 20.7. challenges
5. Identifying key elements -- 5.1. On the angle bisectors of a convex quadrilateral -- 5.2. Cyclic quadrilaterals with perpendicular diagonals -- 5.3. A property of the rectangular hyperbola -- 5.4. Challenges -- 6. Employing isometry -- 6.1. The Chou Pei Suan Ching proof of the Pythagorean theorem -- 6.2. A theorem of Thales -- 6.3. Leonardo da Vinci's proof of the Pythagorean theorem -- 6.4. The Fermat point of a triangle -- 6.5. Viviani's theorem -- 6.6. Challenges -- 7. Employing similarity -- 7.1. Ptolemy's theorem -- 7.2. The golden ratio in the regular pentagon -- 7.3. The Pythagorean theorem -- again -- 7.4. Area between sides and cevians of a triangle -- 7.5. Challenges -- 8. Area-preserving transformations -- 8.1. Pappus and Pythagoras -- 8.2. Squaring polygons -- 8.3. Equal areas in a partition of a parallelogram -- 8.4. The Cauchy-Schwarz inequality -- 8.5. A theorem of Gaspard Monge -- 8.6. Challenges
9. Escaping from the plane -- 9.1. Three circles and six tangents -- 9.2. FAir division of a cake -- 9.3. Inscribing the regular heptagon in a circle -- 9.4. The spider and the fly -- 9.5. Challenges -- 10. Overlaying tiles -- 10.1. Pythagorean tilings -- 10.2. Cartesian tilings -- 10.3. Quadrilateral tilings -- 10.4. Triangular tilings -- 10.5. Tiling with squares and parallelograms -- 10.6. Challenges -- 11. Playing with several copies -- 11.1. From Pythagoras to trigonometry -- 11.2. Sums of odd integers revisited -- 11.3 Sums of squares again -- 11.4. The volume of a square pyramid -- 11.5. Challenges -- 12. Sequential frames -- 12.1. The parallelogram law -- 12.2. An unknown angle -- 12.3. Determinants -- 12.4. Challenges -- 13. Geometric dissections -- 13.1. Cutting with ingenuity -- 13.2. The "smart Alec" puzzle -- 13.3. The area of a regular dodecagon -- 13.4. Challenges -- 14. Moving frames -- 14.1. Functional composition -- 14.2. The Lipschitz condition -- 14.3. Uniform continuity -- 14.4. Challenges
pt. 2. Visualization in the classroom -- Mathematical drawings : a short historical perspective -- On visual thinking -- Visualization in the classroom -- On the role of hands-on materials -- Everyday life objects as resources -- Making models of polyhedra -- Using soap bubbles -- Lighting results -- Mirror images -- Towards creativity -- pt. 3. Hints and solutions to the challenges -- References -- Index -- About the authors
Introduction -- pt. 1. Visualizing mathematics by creating pictures -- 1. Representing numbers by graphical elements -- 1.1. Sums of odd integers -- 1.2. Sums of integers -- 1.3. Alternating sums of squares -- 1.4. Challenges -- 2. Representing numbers by lengths of segments -- 2.1. Inequalities among means -- 2.2. The mediant property -- 2.3. A Pythagorean inequality -- 2.4. Trigonometric functions -- 2.5. Numbers as function values -- 2.6. Challenges -- 3. Representing numbers by areas of plane figures -- 3.1. Sums of integers revisited -- 3.2. The sum of terms in arithmetic progression -- 3.3. Fibonacci numbers -- 3.4. Some inequalities -- 3.4. Some inequalities -- 3.5. Sums of squares -- 3.6. Sums of cubes -- 3.7. Challenges -- 4. Representing numbers by volumes of objects -- 4.1. From two dimensions to three -- 4.2. Sums of squares of integers revisited -- 4.3. Sums of triangular numbers -- 4.4. A double sum -- 4.5. Challenges
Summary The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication, and teaching of mathematics
Bibliography Includes bibliographical references and index
Notes Description based on print version record
Subject Digital images.
Mathematics -- Charts, diagrams, etc.
Mathematics -- Study and teaching (Higher)
Genre/Form Graphs.
Form Electronic book
Author Nelsen, Roger B.
ISBN 1614441006 electronic bk
9781614441007 electronic bk