Reference Bibliography

 

List of References used in these "A Mathematician Paints" posts

7/23/23: Tavis Leaf Glover has a post on 4 books he recommends for learning Dynamic Symmetry with pro's and con's of each: https://ipoxstudios.com/dynamic-symmetry-grids-for-photographers-and-painters/#gridtopbooks

11/14/2022: Continuously updated as new references become available or are used in these posts. 

Major Books on Mathematics within Art:

Amazon links.  Most have Kindle options. Also google them for possibly free pdf downloads. 

Painters-Secret-Geometry-Study-Composition by Charles Bouleau. A study of composition in art.

The Elements of Dynamic Symmetry by Jay Hambridge

The Geometry of Art and Life by Matila Ghyka

The Art of Composition. A simple Application of Dynamic Symmetry by Michel Jacobs

Mathematical Thought from Ancient to Modern Times by Morris Kline,  1972.

Creative Illustration by Andrew Loomis. Informal Subdivision, pg 36-39.

Geometry of Design by Kimberly Elam. Beautiful little book.  The transparent over leaves are a real plus. A good one to read if this is the only one you read. It does promote the golden mean as a design principle.

Classical-Painting-Atelier-Contemporary-Traditional by Juliette Aristides. Harmonic Armature.


Websites with extensive material on Armatures:

http://www.the-art-of-composition.com/ Harmonic Armature 
https://ipoxstudios.com/#home Dynamic Symmetry and Root Grids

Link(s) by Current Artists

https://www.oilpaintersofamerica.com/2022/03/dynamic-symmetry-and-how-i-incorporate-it-into-my-plein-air-and-studio-and-practice/ Michele Byrne

Link to article about an Architect teaching connections between math and art

 https://cooperalumni.org/2017/04/in-memoriam-arthur-corwin-a54/. about Arthur Corwin.

Golden Mean:

Extensive list with the first few to be considered first.

https://www.goldennumber.net/art-composition-design/. Meisner. Major website on the golden number. Examples of artwork designed with the golden rectangle.

https://en.wikipedia.org/wiki/Golden_rectangle  (construction; brief history)

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number. Mario Livio. Critical of the attention paid to the golden ratio.

https://www.goldennumber.net/golden-ratio-misconceptions-by-george-markowsky-reviewed/  Meisner - debunking the debunkers. 

https://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/13/golden-ratio-beautiful-new-curve-harriss-spiral. (even the Guardian chimes in with a new curve inspired by the golden spiral.)

https://www.britannica.com/science/golden-ratio (nice explanation; brief history)

More extensive Golden Mean list in chronological order:

1509: https://en.wikipedia.org/wiki/Luca_Pacioli.  Luca Pacioli, a Franciscan friar, author of the De Divina Proportione, used by many artists in the Renaissance and referenced throughout these articles and posts. 

19th Century: https://en.wikipedia.org/wiki/Gustav_Fechner: study on the preference of the golden rectangle over other rectangles. Referenced throughout the following articles and posts.

1992: Mathematician George Markowsky, author of a 1992 paper called Misconceptions about the Golden Ratio,  published in the College Mathematics' Journal of 1992 and online in 2018. The paper was based on a talk Markowsky developed for a group at Harvard.

2002:  The Golden Ratio: The Story of PHI, the World's Most Astonishing Number. Mario Livio. Critical of the attention paid to the golden ratio.

May 2007: https://www.maa.org/external_archive/devlin/devlin_05_07.html Keith Devlin. Short article on reasons debunking the use of the golden rectangle. 

May 4, 2014: https://www.goldennumber.net/art-composition-design/. Meisner. Examples of artwork designed with the golden rectangle.

June 16, 2014: https://www.goldennumber.net/golden-ratio-myth/  Meisner. Comprehensive article and list of references about the golden-ratio. Critical of mathematicians, Markowsky and Devlin, who debunked or downplayed the importance of the golden-ratio. 

April 14, 2015: https://www.fastcompany.com/3044877/the-golden-ratio-designs-biggest-myth by Brownlee.  Examples from history.  Quite an incendiary article with loaded terms used throughout debunking the use of the golden ratio by designers.

Apr 21, 2015: https://medium.com/@quick_brown_fox/why-the-golden-ratio-matters-583f6737c10c by Designer, Darren Crescenzi, as a critical response to Brownlee's Fast Company Apr 14 article.

Nov 9, 2015: https://www.goldennumber.net/golden-ratio-design-beauty-face-evidence-facts/ Meisner. Detailed discussion and critique of a 2015 Science Interview with Devlin. (Actually more about facial beauty). Mentions the April Fast Company reference and the critique by Crescenzi listed above with this commendt by Crescenzi: described the article as “dangerous” and “under-informed nonsense,” motivating him to write the six page counterpoint referenced above. 

Feb 1, 2016: https://www.goldennumber.net/golden-ratio-misconceptions-by-george-markowsky-reviewed/  Meisner - debunking the debunkers. 

2020: https://www.goldennumber.net/parthenon-golden-ratio-design/ by Meisner. Golden Ratios of the Parthenon.  Oct 11, 2020. New article to follow up on others, using high resolution calculations for the Parthenon.

2020: https://quantumgravityresearch.org/lay-person-overview/ (scroll down for the video): referenced by Meisner: 

"What if the belief that the golden ratio is a foundational building block of the universe turned out to be true? Long thought to be the fodder of mystics and cranks, it now appears that once was thought to be myth may in fact be at the center of the math that defines reality as we know it.

https://anthonywaichulis.com/fools-gold-a-primer-on-pictorial-composition-part-v/: worth reading.


https://www.goldennumber.net/art-composition-design/. Meisner. "Without mathematics there is no art,”  said Luca Pacioli, a contemporary of Da Vinci."  The golden ratio is .... " a tool, not a rule, for composition" Contains video analyzing Da Vinci and many paintings using golden mean proportions.

http://meandering-through-mathematics.blogspot.com/2012/02/applications-of-golden-mean-to.html

https://www.goldennumber.net/geometry/ Phi and geometry.

http://www.yorku.ca/christo/papers/Green.golden.Perception-1995.pdf  Extensive review of studies on the subject of the golden rectangle perception as the most pleasing from Fechner to 1995. See below for an example.

https://en.wikipedia.org/wiki/Golden_rectangle#:~:text=Draw%20a%20square.,Complete%20the%20golden%20rectangle.: 


Fractals

https://en.wikipedia.org/wiki/Fractal

https://en.wikipedia.org/wiki/Mathematics_and_art

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3124832/ : Perceptual and Physiological Responses to Jackson Pollock's Fractals


Additional Works - More Mathematical in nature.


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