*Viewpoints: Mathematical Perspective and Fractal Geometry in Art*

*https://en.wikipedia.org/wiki/Viewpoints:_Mathematical_Perspective_and_Fractal_Geometry_in_Art*

* Viewpoints: Mathematical Perspective and Fractal Geometry in Art* is a textbook on
mathematics and art. It was written by mathematicians Marc Frantz and
Annalisa Crannell, and published in 2011 by the
Princeton University Press (
ISBN
9780691125923). The Basic Library List Committee of the
Mathematical Association of America has recommended it for inclusion in undergraduate mathematics libraries.

^{ [1]}

## Topics

The first seven chapters of the book concern
perspectivity, while its final two concern
fractals and their
geometry.^{
[1]}^{
[2]} Topics covered within the chapters on perspectivity include
coordinate systems for the plane and for
Euclidean space,
similarity,
angles, and
orthocenters,
one-point and multi-point perspective, and
anamorphic art.^{
[1]}^{
[3]} In the fractal chapters, the topics include
self-similarity,
exponentiation, and
logarithms, and
fractal dimension. Beyond this mathematical material, the book also describes methods for artists to depict scenes in perspective, and for viewers of art to understand the perspectives in the artworks they see,^{
[1]} for instance by finding the optimal point from which to view an artwork.^{
[2]} The chapters are ordered by difficulty, and begin with experiments that the students can perform on their own to motivate the material in each chapter.^{
[3]}

The book is heavily illustrated by artworks and photography (such as the landscapes of
Ansel Adams) and includes a series of essays or interviews by contemporary artists on the mathematical content of their artworks.^{
[1]}^{
[3]}
An appendix contains suggestions aimed at teachers of this material.^{
[3]}

## Audience and reception

*Viewpoints* is intended as a textbook for mathematics classes aimed at undergraduate
liberal arts students,^{
[1]}^{
[2]}^{
[4]} as a way to show these students how
geometry can be used in their everyday life.^{
[2]} However, it could even be used for high school art students,^{
[2]}^{
[3]}
and reviewer Paul Kelley writes that "it will be of value to anyone interested in an elementary introduction to the mathematics and practice of perspective drawing".^{
[2]} It differs from many other liberal arts mathematics textbooks in its relatively narrow focus on geometry and perspective, and its avoidance of more well-covered ground in mathematics and the arts such as
symmetry and the geometry of
polyhedra.^{
[2]}

Although reviewer Blake Mellor complains that the connection between the material on perspective and on fractal geometry "feels forced", he concludes that "this is an excellent text".^{
[4]} Reviewer Paul Kelley writes that the book's "step-by-step progression" through its topics makes it "readable [and] easy-to-follow", and that "Students can learn a great deal from this book."^{
[2]} Reviewer
Alexander Bogomolny calls it "an elegant fusion of mathematical ideas and practical aspects of fine art".^{
[1]}

## References

- ^
^{a}^{b}^{c}^{d}^{e}^{f}^{g}Bogomolny, Alexander (September 2011), "Review of*Viewpoints*",*MAA Reviews*, Mathematical Association of America - ^
^{a}^{b}^{c}^{d}^{e}^{f}^{g}^{h}Kelley, Paul (December 2012 – January 2013), "Review of*Viewpoints*",*The Mathematics Teacher*,**106**(5): 399, doi: 10.5951/mathteacher.106.5.0398, JSTOR 10.5951/mathteacher.106.5.0398 - ^
^{a}^{b}^{c}^{d}^{e}Marchetti, Elena (February 2015), "Review of*Viewpoints*",*Nexus Network Journal*,**17**(2): 685–687, doi: 10.1007/s00004-015-0237-9 - ^
^{a}^{b}Mellor, Blake (December 2011), "Review of*Viewpoints*",*Journal of Mathematics and the Arts*,**5**(4): 221–222, doi: 10.1080/17513472.2011.624443