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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

Resource Information

The item Math made visual : creating images for understanding mathematics, Claudi Alsina and Roger B. Nelsen represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.
This item is available to borrow from 1 library branch.

Creator

Alsina, Claudi

Author

Contributor

Nelsen, Roger B.

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

Language: eng

Work

Publication

Washington, DC, Mathematical Association of America, ©2006

Extent: 1 online resource (xv, 173 pages)

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

Isbn: 9781614441007

Instance

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

Alsina, Claudi

Contributor

Nelsen, Roger B.

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

Math made visual : creating images for understanding mathematics

Publication

Washington, DC, Mathematical Association of America, ©2006

Antecedent source: unknown

Bibliography note: Includes bibliographical references and index

Carrier category: online resource

Carrier category code

Carrier MARC source: rdacarrier

Color: multicolored

Content category: text

Content type code

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

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

Carrier MARC source: rdacarrier

Color: multicolored

Content category: text

Content type code

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

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

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