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Math made visual creating images for understanding mathematics

Claudi Alsina Roger B Nelsen

Washington, DC Mathematical Association of America c2006

Comprobar en IME - Inst. Matemática e Estatística    (QA80 A461m )(Obténgalo)

  • Título:
    Math made visual creating images for understanding mathematics
  • Autor: Claudi Alsina
  • Roger B Nelsen
  • Materias: Mathematics -- Study and teaching (Higher); Mathematics -- Charts, diagrams, etc; Digital images; MATEMÁTICA (ESTUDO E ENSINO)
  • Notas: Includes bibliographical references and index
  • Descripción: Introduction -- Visualizing mathematics by creating pictures -- Representing numbers by graphical elements -- Sums of odd integers -- Sums of integers -- Alternating sums of squares -- Challenges -- Representing numbers by lengths of segments -- Inequalities among means -- mediant property -- Pythagorean inequality -- Trigonometric functions -- Numbers as function values -- Challenges -- Representing numbers by areas of plane figures -- Sums of integers revisited -- sum of terms in arithmetic progression -- Fibonacci numbers -- Some inequalities -- Some inequalities -- Sums of squares -- Sums of cubes -- Challenges -- Representing numbers by volumes of objects -- From two dimensions to three -- Sums of squares of integers revisited -- Sums of triangular numbers -- double sum -- Challenges --
    5. Identifying key elements -- On the angle bisectors of a convex quadrilateral -- Cyclic quadrilaterals with perpendicular diagonals -- property of the rectangular hyperbola -- Challenges -- Employing isometry -- Chou Pei Suan Ching proof of the Pythagorean theorem -- theorem of Thales -- Leonardo da Vinci's proof of the Pythagorean theorem -- Fermat point of a triangle -- Viviani's theorem -- Challenges -- Employing similarity -- Ptolemy's theorem -- golden ratio in the regular pentagon - Pythagorean theorem - again -- Area between sides and cevians of a triangle -- Challenges -- Area-preserving transformations -- Pappus and Pythagoras -- Squaring polygons -- Equal areas in a partition of a parallelogram -- Cauchy-Schwarz inequality -- theorem of Gaspard Monge -- Challenges --
    9. Escaping from the plane -- Three circles and six tangents -- FAir division of a cake -- Inscribing the regular heptagon in a circle -- spider and the fly -- Challenges -- Overlaying tiles -- Pythagorean tilings -- Cartesian tilings -- Quadrilateral tilings -- Triangular tilings -- Tiling with squares and parallelograms -- Challenges -- Playing with several copies -- From Pythagoras to trigonometry -- Sums of odd integers revisited -- Sums of squares again -- volume of a square pyramid -- Challenges -- Sequential frames -- parallelogram law -- unknown angle -- Determinants -- Challenges -- Geometric dissections -- Cutting with ingenuity -- "smart Alec" puzzle -- area of a regular dodecagon -- Challenges -- Moving frames -- Functional composition -- Lipschitz condition -- Uniform continuity -- Challenges --
    15. Iterative procedures -- Geometric series -- Growing a figure iteratively -- curve without tangents -- Challenges -- Introducing colors -- Domino tilings -- L-Tetromino tilings -- Alternating sums of triangular numbers -- In space, four colors are not enough -- Challenges -- Visualization by inclusion -- genuine triangle inequality -- mean of the squares exceeds the square of the mean -- arithmetic mean-geometric mean inequality for three numbers -- Challenges -- Ingenuity in 3 D -- From 3D with love -- Folding and cutting paper -- Unfolding polyhedra -- Challenges -- Using 3D models -- Platonic secrets -- rhombic dodecahedron -- Fermat point again -- Challenges -- Combining techniques -- Heron's formula -- quadrilateral law -- Ptolemy's inequality -- Another minimal path -- Slicing cubes -- Vertices, faces, and polyhedra -- 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 -- Hints and solutions to the challenges -- References -- Index -- About the authors
  • Títulos relacionados: Serie:Classroom resource materials
  • Editor: Washington, DC Mathematical Association of America
  • Fecha de creación: c2006
  • Formato: xv, 173 p ill 27 cm.
  • Idioma: Inglés
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