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Are there any links between mathematics and the visual arts? These two seemingly opposed disciplines have several extremely interesting points in common.
by Stéphanie de Champlain and Jennifer Poirier
(Image source presentation of the file, page consulted on April 24, 2017.)
From an artistic angle
Claude La Riviere
(2017)
Unpublished work by the artist for this dossier
In italics: intentions and creative approaches to be experienced in the classroom
SUMMARY OF THE FILE
- The links between mathematics and the visual arts
- Overview
- Proposal
MATHEMATICS AS A TOOL TO SUPPORT CREATION
- Very useful mathematical tools
- Perspective
- The lines of composition
- The proportions and the golden ratio
- Symmetry and asymmetry
- Geometric transformations
- Algorithms and mathematical formulas
- Ranking strategies
- Examples of avenues of exploration
- Storage art
MATHEMATICS AS A SUBJECT OF CREATION
- Abstract art with a geometric flavor
- Abstraction: Homage to Kandinsky
- Abstraction: The circle in all its forms
- Optical art: Homage to Vasarely
- Figurative art with a mathematical flavor
- Mathematical photography
- The spreadsheet
- The story with a mathematical flavor
- Illustrations using geometric shapes
- The end of a journey… The beginning of creation
- Thanks
- Copyright notice
WHEN MATHEMATICAL ENGINEERING MEETS ARTISTIC ENGINEERING ...
The best works of mathematicians are art, a highly perfected art, defying the innermost dreams of the imagination, clear and limpid. Mathematical genius and artistic genius touch each other.
Gösta Mittag-Leffler
We invite you to dive into the heart of this creative encounter and take advantage of the links that unite these two incredibly rich worlds.
THE LINKS BETWEEN MATHEMATICS
AND THE PLASTIC ARTS
Although these two disciplines are apparently opposed, they have several extremely interesting points in common.
The intention… Better understand the world around us and give it meaning.
The process… Implement a creative process to bring to life an original artistic achievement or a novel mathematical solution.
Language… Explore the language of shapes, lines, volumes and space…
Omnipresence... Observe the presence of mathematics and the arts in our environment.
To better understand the relationship that exists between mathematics and the visual arts, we were inspired by a conference by Denise Demaret-Pranville, professor of mathematics and visual artist:
Art and Mathematics
An artistic or scientific vision of the world:
opposition or complementarity?
December 8, 2014
Here is an excerpt from that conference:
| “There are two different ways of encountering mathematics in the field of art, either as a tool helping in the creation of a work, as, for example, with the use of perspective, i.e., on the contrary, when the artist chooses to take mathematical objects as subject, which is very present in geometric art or in fractal art. We can say that, in the first case, mathematics constitutes a tool in the service of artists, and that, in the second case, mathematics becomes a subject art. " |
Mathematics and the arts are therefore two disciplines to be explored in complementarity.
OVERVIEW
To facilitate your navigation through this file, we have designed a graphic organizer inspired by the words of Ms. Demaret-Pranville. It should be noted that the categories suggested are not exhaustive and hermetic. Feel free to imagine other links or other examples.
Click on the graphic organizer to enlarge it.
Note
In this dossier, we use the term “mathematical objects” in a broad sense to allow students of different ages to have experiences within their reach. This expression therefore designates mathematical objects such as polyhedra, but also concrete objects linked to mathematics such as measuring instruments or certain games (cards, dominoes, dice).
(See the list of objects that represent mathematics in the section called FIGURATIVE ART WITH MATHEMATICAL FLAVOR.)
PROPOSAL
To promote the establishment of bridges between mathematics and the arts, we offer you some creative intentions that materialize through a short process of “artistic-mathematical” creation in four phases:
| Inspiration | Production | Return | Diffusion |
| Discover an artist and his mathematical color for inspiration. | Engage in the production of a work. Live a creative process based on artistic and mathematical resources. |
Review the works created from an artistic and mathematical point of view. | Share works with a mathematical flavor. |
You will recognize in this process elements inspired by the dynamic of creation of the field of the arts and the competence "To implement his creative thought".
Computer graphics produced by Andrée-Caroline Boucher,
contact person at national service of the RÉCIT des arts
Inspired by Quebec school training program (secondary)
Arts field
Implement your creative thinking
Quebec school training program (elementary)
Transversal skills
Do not hesitate to modify and enrich these ideas according to your educational intentions and the target clientele.
Here are some possible variations:
- Produce the works on paper and use digital technology to inspire, appreciate or distribute the creations.
- Live the proposed approach to discover another artist or another artistic movement.
- Choose a more or less complex application depending on the age of the students.
- Put more emphasis on the mathematical component or the artistic component.
GOOD EXPLORATION!
Note on applications
Certain applications offered display advertising or require the creation of an account (personal account or class account depending on the age of the students). We have retained them all the same since they are free and intuitive.
When the applications present banner ads or "popup" windows, it is possible to block them using a free tool such as AdBlock.
Note on illustrations
The illustrations that do not include the name of an artist were produced by the authors of this dossier. Please mention the source if you wish to reuse them.
