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Following text: MATHEMATICS AS A SUBJECT OF CREATION
VERY USEFUL MATHEMATICAL TOOLS
Geometry is to the plastic arts what grammar is to the art of the writer.
Guillaume Apollinaire
The relationship between mathematics and the arts goes down in history. Over time, artists have benefited from different mathematical tools. We cannot ignore the invention of perspective which made it possible to give the illusion of depth in paintings or the discovery of new geometries which inspired the bursting of forms in the 20th century.e century.
Here are some examples of mathematical tools used by creators of yesterday and today.
- Perspective
- The lines of composition
- The proportions and the golden ratio
- Symmetry and asymmetry
- Geometric transformations
- Algorithms and mathematical formulas
- Ranking strategies
Resources consulted
| Resources | Elements to be deepened |
 Open Books Site |
Observe the links between the evolution of science (and mathematics) and the history of art.
Examples:
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 Open Books Site |
Learn about the evolution of perspective in art:
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 Palette Publishing Site |
Discover the universe of cubism, an artistic movement that upsets the conventions of classical perspective.
"At the beginning of the XXe century, a few young artists, led by Pablo Picasso and Georges Braque, revolutionized the art world. They dare to upset the intangible rules of perspective and thus invent cubism. These pioneers seek to represent reality differently, to show everything, even what one should not see - like the two eyes of a woman in profile - and reduce nature to geometric shapes. A bit like a cube that has been flattened! " (Extract of Cubism, the reinvention of art) With the fragmented objects of cubism, we are witnessing a real explosion of forms! |
 Taschen Publishing website |
Immerse yourself in the graphic work of Maurits Cornelis Escher.
“By exposing my senses to the riddles of the universe, reflecting on these sensations and analyzing them, I am approaching the realm of mathematics. " (Extract of The graphic work) Observe different creations of the artist:
Discover the importance of mathematics in the artist's compositions. “Whoever wants to compose a symmetry on a flat surface must take into account the three principles of crystallography: repeated displacements (translation), pivoting around an axis (rotation), reflection of the image in a mirror (reflection). " (Extract of The graphic work) |
 Editions Gallimard website |
Discover some keys to understanding and appreciating a painting.
Examples of mathematical-flavored keys:
“Cézanne said: 'You have to see cylinders, spheres and cones in nature.' His compositions are often based on a strong geometric structure. " (Extract of The keys to painting) |
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The painter's gaze: The pictorial composition |
Discover different secrets of pictorial composition.
Leon-Battista Alberti “was the first to use the term 'composition' to explain that a painting was subject to clear and harmonious mathematical and geometrical laws following the example of the creation of the world by God. " (Extract of The painter's gaze: The pictorial composition) Explore various composition schemes:
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| Additional Resources |
| Infinity Plots: Walk in Escher's Garden Alain Nicolas Belin editions, 2006 Figurative paving method Cézanne: The father of modern art Introduction to composition and perspective The great book of composition |
EXAMPLES OF EXPLORATION PATHS
| IN GENERAL | |
| Exploration tracks | Digital exploitation |
| Look for information on a particular mathematical tool and use an original means of disseminating the findings. | Organize information with an ideator:
Collect illustrations:
Disseminate information:
* Accompany publications with the hashtag #artsetmaths. |
| THE PERSPECTIVE… SHOCKED! | |
| Exploration tracks | Digital exploitation |
| Transform a realistic photograph into a cubist photograph. | Explore cubism in a fun way (observe some works and transform a photograph):
Create a cubist image from a few photographs:
Examples
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| COMPOSITION LINES | |
| Exploration tracks | Digital exploitation |
| Observe the lines of composition in different works and the effects produced. | Draw the lines of composition on a work and comment:
Examples
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| Take photographs while exploring the rule of thirds. | Use the camera and crop the image as needed.
Example
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| THE SYMMETRY | |
| Exploration tracks | Digital exploitation |
| Live a hunt for symmetry in your environment to be inspired (nature, architecture, various objects). | Photographing the discoveries:
Pooling findings:
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| Create photographic images using symmetry. | Generate symmetry:
Example
Use a kaleidoscope-type application:
Example
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| Explore repeating patterns using symmetry. | Use a kaleidoscope-type application:
Tips
Examples
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| GEOMETRICAL TRANSFORMATIONS | |
| Exploration tracks | Digital exploitation |
| Create pavements with geometric patterns. Mathematical thinking Explore the geometric figures used to pave the plan.
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Use an application of geometric shapes:
Examples
Examples
Example
Possible procedure: |
| Create paving with figurative patterns in the style of Escher.
To be inspired ... Figurative paving method |
Use a vector drawing application:
Use a programming application:
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| ALGORITHMS | |
| Exploration tracks | Digital exploitation |
| Create a digital work using programming software. | Use an application to program:
Examples
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Storage art
Creative intention
Create a two-part photographic work (diptych) inspired by Ursus Wehrli.
| Ursus Wehrli (1969 -) |
Information taken from ... |
| This artist humorously practices the art of storage. This art consists in extracting the elements of an image, classifying them and arranging them differently to create a revisited and original work. “Life is a mess. Luckily, Ursus Wehrli puts it in order. " (Extract of Photos in bazaar) Artist's official website Books Examples of works In his book titled Lart in bazaar, he enjoys arranging the paintings of famous painters such as Paul Klee, Vassily Kandinsky and René Magritte. Video : Ursus Wehrli TED Lecture In the book Photos in bazaar, he puts order in a variety of everyday scenes: a clothesline, a sandbox, a parking lot, a bowl of fruit ... Video : " Behind the scenes ... " Ursus Wehrli explores various classification criteria:
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 Milan Publishing Site
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Inspiration
| Actions | Digital exploitation |
| Using the book Photos in bazaar as a trigger. | |
| Present the creative intention: to create a two-part photographic work (diptych) inspired by Ursus Wehrli. | |
| 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.
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Create a digital collective memory to preserve and enrich ideas.
This collective memory can take different forms:
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| Artistic reflection Take advantage of this initiation to experience a process of appreciation. |
Production
| Actions | Digital exploitation |
| Think about different everyday contexts in which we could put some order: bin of lost objects, pencil box, toy bin, bowl of cereal, bottom drawer ... | Create a graphic organizer to store ideas. |
| Choose your preferred context and collect the objects necessary for the realization of the work. | |
Create the first part of the work:
Trick |
Use the camera and crop as needed. |
Create the second part of the work:
Trick
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Use the camera and crop as needed. |
| Choose a humorous title. | |
| Place the two parts of the work on the same support to show the contrast between the two compositions. | Place the two parts of the work one below the other or side by side and add the title:
Trick
Examples
Sofia, 11 years old |
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. |
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| Identify the classification criteria used to create the second part of the works. | Enrich the collective memory initiated during the observation of the artist's works. |
| Complete the exploration of the artist's works with the book l 'Bazaar art. |
Diffusion
| Actions | Digital exploitation |
| Collect all the works of the students. | Create a book:
Create a slideshow:
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| Share the works on social media. | Publish on the network 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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