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(DOSSIER) Previous text: MATHEMATICS AS A TOOL TO SUPPORT CREATION
Following text: OTHER CREATIVE IDEAS
ABSTRACT ART WITH A GEOMETRIC FLAVOR
Then he took his paraphernalia out of his case and drew a frame around the face, squinting his eyes to estimate the effect. He was proud of his idea: to present geometric figures like painter's paintings!
Denis guedj
The parrot theorem
In some abstract works, mathematics is the main subject of creation. The artists use various geometric shapes: squares, triangles, circles… They also use different types of lines: broken lines, curved lines, oblique lines… They play with the size of the figures, the thickness of the lines, the textures and the colors to produce amazing contrasts.
It may be interesting to explore certain titles of works that reveal the mathematical subject highlighted in the composition.
Here are some examples.
|
Title of the work ... |
Artist |
| Tribute to the square (1964) | Josef albers |
| Suprematism (with blue triangle and black rectangle) (1915) | Kasimir Malevich |
| Thirteen rectangles (1930) | Vassily kandinsky |
| Heavy circles (1927) | Vassily kandinsky |
| Lines and dots (1950) | Carmelo Arden-Quin |
| Turbulent circles (1934) | Sophie Taeuber-Arp |
| 6 random distributions of 4 black and white squares according to the even and odd digits of the number PI (1958) | Francois Morellet |
Some artists arrange shapes, lines and colors in such a way as to create visual perception games. They have fun with our eyes! We then speak of optical art.
Resources
| Resources | Elements to be deepened |
 Open Books Site |
Explore shapes in works of art ...
This book is interested in forms in abstract works, but also in figurative works. It can awaken the gaze to the forms present in the environment. Thus, it is possible to find squares in the "checkered tablecloths, grids, mosaics, black and white checkerboards of shiny floors, or even those of the checkers game ..." (Extract from Of all shapes) |
 Open Books Site |
Deepen the concept of optical illusion and better understand optical art ...
What elements must the artist play with to bring his illusions to life? Mathematical elements:
Other elements:
|
Abstraction: Homage to Kandinsky
Creative intention
Create an abstract work that juggles shapes, lines and colors, taking inspiration from Kandinsky.
| Vassily kandinsky (1866-1944) |
Information taken from ... |
| Kandinsky is one of the founders of abstract art.
“Painting is for him the language of sensitivity: it says with shapes and colors what words fail to express. " (Extract of Kandinsky, the ways of abstraction) For this artist, colors are used to arouse emotions. “The contemplation of color causes a vibration of the soul. "(Word of the artist taken from Journey into a Kandinsky painting) Kandinsky uses different types of lines to create impressions of movement. Some of his creations are built "from geometric elements, shapes drawn with a ruler and a compass". (Extract of Kandinsky, the ways of abstraction) In his work entitled Yellow-red-blue (1925), Kandinsky exploits the contrasts:
A composition of the most meticulous! |
|
Examples of works by Vassily Kandinsky |
|
 Yellow-red-blue (1925) Wikipedia |
 Composition # 9(1936) Wikipedia |
 On white no 2 (1923) Wikipedia |
 Dominant curve (1936) Wikipedia |
Inspiration
| Actions | Digital exploitation |
| Present the creative intention: to create an abstract work that juggles shapes, lines and colors. | |
| Be inspired by the works of Vassily Kandinsky. | Project the works on the TNI. |
Identify the characteristics of the works:
|
Create a digital collective memory to preserve and enrich ideas. This collective memory can take different forms:
Example |
| Artistic reflection Take advantage of this initiation to experience a process of appreciation. |
Production
| Actions | Digital exploitation |
| Create an abstract work that juggles shapes, lines and colors. Artistic reflection Explore visual language according to the needs of creation:
|
Use a vector drawing application:
Use an application of geometric shapes:
Use a drawing application:
Use drawing tools:
Digital and artistic reflection
Tips
|
| Choose a revealing title. Mathematical thinking Explore the language of mathematics to find inspiring titles. |
|
| Create a montage with the work and its title. | Use an application that allows you to combine text and image: |
Examples of creations
Creation made with Pattern Shapes
Creation made with Framavectoriel
(with minimal exploration of the application)
Creation made with Framavectoriel
(with further exploration of the app)
Return
| Actions | Digital exploitation |
| Observe and compare the works of your peers. | Project the works on the TNI. |
| Discuss the characteristics of the works and the effects produced on the observer. Artistic reflection Take advantage of this discussion to experience a process of appreciation. |
|
| Identify the mathematical elements present in the works. Mathematical thinking Classify the mathematical elements used in the works. Example: create a graphic organizer of the geometric figures used. |
Enrich the collective memory initiated during the observation of the artist's works. |
Diffusion
| Actions | Digital exploitation |
| Collect all the works of the students. | Create a book:
Create a slideshow:
|
| Share the works on the Internet. | Use a media of your choice:
* Accompany publications with the hashtag #artsetmaths. |
Possible variant
You can live this same process by being inspired by another artist of abstraction like Piet Mondrian.
| Piet mondrian (1872-1944) |
Information taken from ... |
| This artist uses in his works vertical and horizontal lines that intersect to create square or rectangular spaces.
To color some of these spaces, he juggles the three primary colors: blue, yellow and red. “From one painting to another, the painter organizes the space, the proportions, the color relationships differently, like a musician composes with the notes of the scale. " (Extract of The house under construction) Each composition is carefully thought out. |
The album collection Pont des Arts offers stories that allow you to discover works. These albums can serve as a trigger to discover the work of an artist. |
Website of Éditions de l'Élan vert
Abstraction: The circle in all its forms!
Creative intention
Create an abstract work with circles, taking inspiration in particular from the works presented in the book entitled 30 circles.
| 30 circles | Examples of works in the book |
|
Blue yellow green orange |
|
The Cosmos |
|
|
Examples of works on the Internet |
||
 Construction AL6Laszlo Moholy-Nagy (1933) Wikiart |
 Several circlesVassily kandinsky (1926) Wikipedia |
 Circled circlesVassily kandinsky (1923) Wikipedia |
Variant
Choose another geometric shape for your creation: triangle, square, rectangle, pentagon ...
Inspiration
| Actions | Digital exploitation |
| Using the book 30 circles as a trigger. | |
| Present the creative intention: to create an abstract work with circles. | |
| Be inspired by works in the book or those found on the Internet. | Project the works on the TNI. |
Identify the characteristics of the works:
|
Create a digital collective memory to preserve and enrich ideas. This collective memory can take different forms:
|
| Artistic reflection Take advantage of this initiation to experience a process of appreciation. |
Production
| Actions | Digital exploitation |
| Create an abstract work with circles. Artistic reflection Explore visual language according to the needs of creation:
|
Use a vector drawing application:
To create works with triangles, squares, diamonds, trapezoids or hexagons, use a geometric shapes application:
Use a drawing application:
Use drawing tools:
Digital and artistic reflection
Tips
|
| Choose a revealing title. Linguistic reflection Make a list of adjectives that can accompany the word "circle" in the title. Examples:
Explore the name and its complement.
|
|
| Create a montage with the work and its title. | Use an application that allows you to combine text and image: |
Examples of creations
Creation made with Pattern Shapes
(with minimal exploration of the application)
Creation made with Pattern Shapes
(with a mathematical reflection on the concept of square)
Creation made with Framavectoriel
(with minimal exploration of the application)
Creation made with Framavectoriel
(with minimal exploration of the application)
Creation made with Framavectoriel
(with further exploration of the app)
Creation made with Sumo Paint
(with further exploration of the app)
Return
| Actions | Digital exploitation |
| Observe and compare the works of your peers. | Project the works on the TNI. |
| Discuss the characteristics of the works and the effects produced on the observer. Artistic reflection Take advantage of this discussion to experience a process of appreciation. |
Diffusion
| Actions | Digital exploitation |
| Collect all the works of the students. | Create a book:
Create a slideshow:
|
| Share the works on the Internet. | Use a media of your choice:
* Accompany publications with the hashtag #artsetmaths. |
Optical art: Homage to Vasarely
Creative intention
Create an abstract work that plays with visual perception, taking inspiration from Victor Vasarely.
| Victor Vasarely (1906-1997) |
Information taken from ... |
| This artist is considered to be the founder of Op art (optical art), an art that elicits visual reactions in the observer. “… For many years, Vasarely worked on the composition of his paintings: perspective effects, play of colors, optical illusions… He also filed several patents for his optical combinations. " (Extract of Vasarely, the pure sensation) Vasarely is interested in the relationship between shapes and colors. He arranges these elements in such a way as to play with visual perception. “In front of a work by Vasarely, the gaze can no longer decide between what is in front and what is behind; what is in two or three dimensions; between what is concave (hollow) and what is convex (bump). " (Extract of Vasarely, the pure sensation) Vasarely uses simple shapes (circles, triangles, squares, diamonds) that he combines differently from one work to another. He uses cut-out geometric figures and graph paper to plan this combination. |
Open Books Site
|
Examples of works by Victor Vasarely |
|
 Keple Gestalt(1968) Wikiart |
 Vonal Stri(1975) Wikiart |
 Vega 200(1968) Wikiart |
 Folklore(1963) Wikiart |
|
Other works by Vasarely |
|
Inspiration
| Actions | Digital exploitation |
| Present the creative intention: create an abstract work that plays with visual perception. | |
| Be inspired by the works of Victor Vasarely. | Project the works on the TNI. |
Identify the characteristics of the works.
Examples of effects |
Create a digital collective memory to preserve and enrich ideas. This collective memory can take different forms:
|
| Artistic reflection Take advantage of this initiation to experience a process of appreciation. |
Production
| Actions | Digital exploitation |
| Create an abstract work that plays with visual perception by arranging shapes and colors. Artistic reflection Explore visual language according to the needs of creation:
|
Use an isometric drawing app:
Examples
Use an application of geometric shapes:
Examples
Use drawing tools:
Digital and artistic reflection
Tips
|
| Choose a revealing title. Mathematical thinking Explore the language of mathematics to find inspiring titles. |
Create a montage with the work and its title. Use an application that allows you to combine text and image: Trick Enrich the creation by using certain effects (light, color, sharpness, etc.). |
Examples of creations
Creation made with Isometric Drawing Tool
(with minimal exploration of the application)
Creation made with Isometric Drawing Tool
(with further exploration of the app)
Creation made with Framavectoriel
(with an exploration of depth effects)
Creation made with Framavectoriel
(with an exploration of optical effects)
Creation made with Pattern Shapes
Creation made with Pattern Shapes
(with an exploration of the effects of three dimensions)
Return
| Actions | Digital exploitation |
| Observe and compare the works of your peers. | Project the works on the TNI. |
| Discuss the characteristics of the works and the effects produced on the observer. Artistic reflection Take advantage of this discussion to experience a process of appreciation. |
|
| Identify the mathematical elements present in the works. | Enrich the collective memory initiated during the observation of the artist's works. |
Diffusion
| Actions | Digital exploitation |
| Collect all the works of the students. | Create a book:
Create a slideshow:
|
| Share the works on the Internet. | Use a media of your choice:
* Accompany publications with the hashtag #artsetmaths. |
FIGURATIVE ART WITH MATHEMATICAL FLAVOR
Some artists integrate mathematical-related objects into the composition of their work:
- Measuring instruments (hourglass, ruler, scale)
- Geometric drawing tools (compass, set square)
- Objects related to the history of mathematics (abacus, quipou)
- Math games (dominoes, cards, chess, dice)
- Math puzzles (tangram, pentominoes)
- Solids (polyhedron, sphere)
- Special surfaces (Möbius strip)
- Symbols (number, operation, sequence, formula)
These objects can be found in different environments depending on the artist's style: a surrealist setting, a still life, a realistic universe, etc.
Mathematical photography
Creative intention
Create a work that integrates objects related to mathematics, drawing inspiration in particular from Claude La Rivière or Sylvie Donmoyer.
| Two inspiring artists | |
| Claude La Riviere | Sylvie Donmoyer |
| "Image-maker and composer", this passionate artist manipulates the photographs he takes in different contexts in order to imagine extraordinary productions. He retouches them, merges them, metamorphoses them ...
He designed the illustrations for the youth novel Chaos. This fantastic universe creates bridges between the world of mathematics and the world of words. You can enjoy his works on his site. |
A professional illustrator and painter, this artist uses several pictorial techniques, including airbrushing, oil painting, 2D and 3D digital imagery.
She combines the precision of the scientific illustrator and the artist's imagination in her works. A pleasant combination! “The meeting with a mathematician led me logically towards the exploration of geometry and a visual interpretation of mathematics. " With his work entitled Still life with magic square, this artist won first prize in the Mathematical Art exhibition at the 2012 Joint Mathematics Meetings. You can enjoy his works on his site. |
| Other works that incorporate objects related to mathematics | ||
| Works | Mathematics-related objects | Sources |
| The persistence of memory or Soft Watches Salvador Dali (1931) Wikipedia |
Watches |  Open Books Site |
| Centimeters Francis Picabia (1918) |
Tape measure |  Open Books Site |
| Station L112, 14 km Paul Klee (1920) Artist's official website |
Number
Unit of measure |
|
| Illuminations René Magritte (1934) |
Clock | |
| Pipe, glass, thimble and newspaper Georges Braque (1914) |
Dice |  Palette Publishing Site |
| Still life with a checkerboard Louis Marcoussis (1912) |
Checkerboard
Playing cards Cubes |
|
| Reptiles Maurits Cornelis Escher (1943) Artist's official website |
Polyhedron
Paving Square |
 Taschen Publishing website |
Inspiration
| Actions | Digital exploitation |
| Present the creative intention: to create a work that integrates mathematical objects. | |
| Be inspired by the works of Claude La Rivière and Sylvie Donmoyer. | Project the works on the interactive digital board. |
| Identify the characteristics of the works and list the mathematical objects present. | Create a digital collective memory to preserve and enrich ideas. This collective memory can take different forms:
Example |
| Artistic reflection Take advantage of this initiation to experience a process of appreciation. |
| Examples of works by Claude La Rivière | |
 Symmetry and nature of thingsArtist's official website |
 Wooded with a thousand branchesArtist's official website |
 Possible vanishing pointArtist's official website |
 Mathematical whirlwindArtist's official website |
| Characteristics of the works | Mathematical objects |
|
|
| Examples of works by Sylvie Donmoyer | |
 Tribute to EscherArtist's official website |
 Still life with magic squareArtist's official website |
| Other mathematical works | |
| Characteristics of the works | Mathematical objects |
|
In the above mathematical works:
In other mathematical works:
In Dürer's work:
|
Realization inspired by Claude La Rivière
| Actions | Digital exploitation |
| Gather a collection of mathematical objects that can be inserted into the creations. Collect objects at school or at home. |
|
| Choose your favorite objects from the collection and photograph them. | Use the camera and crop as needed. |
| Take pictures of an environment in which the objects could be integrated. Artistic reflection Possibility of offering a capsule on certain rules of composition in photographic art: the rule of thirds, symmetry, point of view, lines, patterns, etc. Example of a resource to consult 10 rules of composition to know absolutely Photographs for inspiration Unsplash (under license Creative Commons Zero) |
Use the camera and crop as needed. |
| Process the photographs and mix them to create an original composition: integrate the mathematical objects in an inspiring environment. | Cut out the objects in the photos, combine them with the environment and create effects:
Tips
Tip (Photoshop Mix)
Cut out the objects on the photos: Create effects: |
| Choose a revealing title. Mathematical thinking Explore the language of mathematics to find inspiring titles. |
|
| Create a montage with the work and its title. | Use an application that allows you to combine text and image: |
Examples of creation
| Intermediate stages of creation | |
 |
 |
 |
 |
Creation inspired by Sylvie Donmoyer
| Actions | Digital exploitation |
| Gather a collection of mathematical objects that can be inserted into the creations.
Collect objects at school or at home. |
|
| Imagine an original three-dimensional composition with different objects from the collection. Artistic reflection Explore different ways of organizing elements in space: enumeration, juxtaposition, repetition, alternation, layering, symmetry, asymmetry, balance, movement and rhythm. Trick For the “backstage” of the composition, provide certain objects:
|
|
| Photograph the creation.
Tips
|
Use the camera and crop as needed.
Examples
|
| OPTIONAL
Process the photograph by exploring certain effects:
|
Create effects: |
| Choose a revealing title. Mathematical thinking Explore the language of mathematics to find inspiring titles. |
|
| Create a montage with the work and its title. | Use an application that allows you to combine text and image: |
Examples of creations
Return
| Actions | Digital exploitation |
| Observe and compare the works of your peers. | Project the works on the TNI. |
| Discuss the characteristics of the works and the effects produced on the observer. Artistic reflection Take advantage of this discussion to experience a process of appreciation. |
|
| Identify the mathematical objects present in the works. Mathematical thinking Classify the mathematical objects used in the works. Example: create a graphic organizer of the operated solids. |
Enrich the collective memory initiated during the observation of the works of the artists. |
Diffusion
| Actions | Digital exploitation |
| Collect all the works of the students. | Create a book:
Create a slideshow:
|
| Share the works on the Internet. | Use a media of your choice:
* Accompany publications with the hashtag #artsetmaths. |
—
This is a part of a complete dossier.
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
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