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The Resource Math made visual : creating images for understanding mathematics, Claudi Alsina and Roger B. Nelsen

Math made visual : creating images for understanding mathematics, Claudi Alsina and Roger B. Nelsen

Label
Math made visual : creating images for understanding mathematics
Title
Math made visual
Title remainder
creating images for understanding mathematics
Statement of responsibility
Claudi Alsina and Roger B. Nelsen
Creator
Contributor
Author
Subject
Genre
Language
eng
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
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Alsina, Claudi
Dewey number
510.71
Illustrations
illustrations
Index
index present
LC call number
QA19.C45
LC item number
A47 2006
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Nelsen, Roger B.
Series statement
Classroom resource materials
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematics
  • Digital images
  • MATHEMATICS
  • MATHEMATICS
  • Digital images
  • Mathematics
  • Mathematics
  • Mathematikunterricht
  • Visualisierung
Label
Math made visual : creating images for understanding mathematics, Claudi Alsina and Roger B. Nelsen
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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.
  • Introduction
  • The mediant property
  • 2.3.
  • A Pythagorean inequality
  • 2.4.
  • Trigonometric functions
  • 2.5.
  • Numbers as function values
  • 2.6.
  • Challenges
  • 3.
  • pt. 1.
  • 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.
  • Visualizing mathematics by creating pictures
  • Some inequalities
  • 3.5.
  • Sums of squares
  • 3.6.
  • Sums of cubes
  • 3.7.
  • Challenges
  • 4.
  • Representing numbers by volumes of objects
  • 4.1.
  • 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
  • Representing numbers by graphical elements
  • 1.1.
  • Sums of odd integers
  • 1.2.
  • 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
  • 5.
  • 6.4.
  • The Fermat point of a triangle
  • 6.5.
  • Viviani's theorem
  • 6.6.
  • Challenges
  • 7.
  • Employing similarity
  • 7.1.
  • Ptolemy's theorem
  • Identifying key elements
  • 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
  • 5.1.
  • 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
  • On the angle bisectors of a convex quadrilateral
  • 8.6.
  • Challenges
  • 5.2.
  • Cyclic quadrilaterals with perpendicular diagonals
  • 5.3.
  • A property of the rectangular hyperbola
  • 9.4.
  • The spider and the fly
  • 9.5.
  • Challenges
  • 10.
  • Overlaying tiles
  • 10.1.
  • Pythagorean tilings
  • 10.2.
  • Cartesian tilings
  • 9.
  • 10.3.
  • Quadrilateral tilings
  • 10.4.
  • Triangular tilings
  • 10.5.
  • Tiling with squares and parallelograms
  • 10.6.
  • Challenges
  • 11.
  • Playing with several copies
  • Escaping from the plane
  • 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
  • 9.1.
  • 12.
  • Sequential frames
  • 12.1.
  • The parallelogram law
  • 12.2.
  • An unknown angle
  • 12.3.
  • Determinants
  • 12.4.
  • Challenges
  • Three circles and six tangents
  • 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
  • 9.2.
  • 14.
  • Moving frames
  • 14.1.
  • Functional composition
  • 14.2.
  • The Lipschitz condition
  • 14.3.
  • Uniform continuity
  • 14.4.
  • Challenges
  • FAir division of a cake
  • 9.3.
  • Inscribing the regular heptagon in a circle
  • 15.4.
  • Challenges
  • 16.
  • Introducing colors
  • 16.1.
  • Domino tilings
  • 16.2.
  • L-Tetromino tilings
  • 16.3.
  • Alternating sums of triangular numbers
  • 15.
  • 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
  • Iterative procedures
  • 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
  • 15.1.
  • 18.3.
  • Unfolding polyhedra
  • 18.4.
  • Challenges
  • 19.
  • Using 3D models
  • 19.1.
  • Platonic secrets
  • 19.2.
  • The rhombic dodecahedron
  • Geometric series
  • 19.3.
  • The Fermat point again
  • 19.4.
  • Challenges
  • 20.
  • Combining techniques
  • 20.1.
  • Heron's formula
  • 20.2.
  • The quadrilateral law
  • 15.2.
  • 20.3.
  • Ptolemy's inequality
  • 20.4.
  • Another minimal path
  • 20.5.
  • Slicing cubes
  • 20.6.
  • Vertices, faces, and polyhedra
  • 20.7.
  • challenges
  • Growing a figure iteratively
  • 15.3.
  • A curve without tangents
  • Using soap bubbles
  • Lighting results
  • Mirror images
  • Towards creativity
  • pt. 3.
  • Hints and solutions to the challenges
  • References
  • Index
  • About the authors
  • 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
Control code
794855553
Dimensions
unknown
Extent
1 online resource (xv, 173 pages)
File format
unknown
Form of item
online
Isbn
9781614441007
Lccn
2005937269
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctt59h1f0
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)794855553
Label
Math made visual : creating images for understanding mathematics, Claudi Alsina and Roger B. Nelsen
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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.
  • Introduction
  • The mediant property
  • 2.3.
  • A Pythagorean inequality
  • 2.4.
  • Trigonometric functions
  • 2.5.
  • Numbers as function values
  • 2.6.
  • Challenges
  • 3.
  • pt. 1.
  • 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.
  • Visualizing mathematics by creating pictures
  • Some inequalities
  • 3.5.
  • Sums of squares
  • 3.6.
  • Sums of cubes
  • 3.7.
  • Challenges
  • 4.
  • Representing numbers by volumes of objects
  • 4.1.
  • 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
  • Representing numbers by graphical elements
  • 1.1.
  • Sums of odd integers
  • 1.2.
  • 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
  • 5.
  • 6.4.
  • The Fermat point of a triangle
  • 6.5.
  • Viviani's theorem
  • 6.6.
  • Challenges
  • 7.
  • Employing similarity
  • 7.1.
  • Ptolemy's theorem
  • Identifying key elements
  • 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
  • 5.1.
  • 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
  • On the angle bisectors of a convex quadrilateral
  • 8.6.
  • Challenges
  • 5.2.
  • Cyclic quadrilaterals with perpendicular diagonals
  • 5.3.
  • A property of the rectangular hyperbola
  • 9.4.
  • The spider and the fly
  • 9.5.
  • Challenges
  • 10.
  • Overlaying tiles
  • 10.1.
  • Pythagorean tilings
  • 10.2.
  • Cartesian tilings
  • 9.
  • 10.3.
  • Quadrilateral tilings
  • 10.4.
  • Triangular tilings
  • 10.5.
  • Tiling with squares and parallelograms
  • 10.6.
  • Challenges
  • 11.
  • Playing with several copies
  • Escaping from the plane
  • 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
  • 9.1.
  • 12.
  • Sequential frames
  • 12.1.
  • The parallelogram law
  • 12.2.
  • An unknown angle
  • 12.3.
  • Determinants
  • 12.4.
  • Challenges
  • Three circles and six tangents
  • 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
  • 9.2.
  • 14.
  • Moving frames
  • 14.1.
  • Functional composition
  • 14.2.
  • The Lipschitz condition
  • 14.3.
  • Uniform continuity
  • 14.4.
  • Challenges
  • FAir division of a cake
  • 9.3.
  • Inscribing the regular heptagon in a circle
  • 15.4.
  • Challenges
  • 16.
  • Introducing colors
  • 16.1.
  • Domino tilings
  • 16.2.
  • L-Tetromino tilings
  • 16.3.
  • Alternating sums of triangular numbers
  • 15.
  • 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
  • Iterative procedures
  • 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
  • 15.1.
  • 18.3.
  • Unfolding polyhedra
  • 18.4.
  • Challenges
  • 19.
  • Using 3D models
  • 19.1.
  • Platonic secrets
  • 19.2.
  • The rhombic dodecahedron
  • Geometric series
  • 19.3.
  • The Fermat point again
  • 19.4.
  • Challenges
  • 20.
  • Combining techniques
  • 20.1.
  • Heron's formula
  • 20.2.
  • The quadrilateral law
  • 15.2.
  • 20.3.
  • Ptolemy's inequality
  • 20.4.
  • Another minimal path
  • 20.5.
  • Slicing cubes
  • 20.6.
  • Vertices, faces, and polyhedra
  • 20.7.
  • challenges
  • Growing a figure iteratively
  • 15.3.
  • A curve without tangents
  • Using soap bubbles
  • Lighting results
  • Mirror images
  • Towards creativity
  • pt. 3.
  • Hints and solutions to the challenges
  • References
  • Index
  • About the authors
  • 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
Control code
794855553
Dimensions
unknown
Extent
1 online resource (xv, 173 pages)
File format
unknown
Form of item
online
Isbn
9781614441007
Lccn
2005937269
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctt59h1f0
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)794855553

Library Locations

    • Curtis Laws Wilson LibraryBorrow it
      400 West 14th Street, Rolla, MO, 65409, US
      37.955220 -91.772210
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