(Feature) Mathematics as a Tool to Support Creation

(continuation of the file) The relation between maths and the arts is written in the history. Here are concrete examples to use, inspired by creators of yesterday and today.

Published on :

Posted in:
READ THIS ARTICLE IN:

Automated English translation - (sometimes hilarious) mistakes can creep in! ;)

ADVERTISEMENT
Add to favorites (0)

(DOSSIER) Previous text: INTRODUCTION
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.

Click on the infographics thumbnails to see them!

 

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:

  • The invention of perspective and Renaissance painters
  • The golden ratio and Leonardo da Vinci
  • New geometries and cubist painters
  • Hyperbolic geometry and Maurits Cornelis Escher
  • Optical illusions and Victor Vasarely
  • Fractal geometry and "fractalist" artists
Open Books Site Learn about the evolution of perspective in art:

  • The principles of perspective
  • The processes developed
  • The devices invented
  • Outstanding artists and their works
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:

  • Regular or irregular filling of a surface
  • Knots, Möbius ribbons, spirals and polyhedra
  • Reflections
  • Impossible constructions

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:

  • Symmetry and asymmetry
  • The lines underlying the composition
  • The geometry hidden behind the works

“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)

The painter's gaze: The pictorial composition
Sarah kent
Gallimard editions, 1995

Editions Gallimard website

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:

  • The stability of the triangle
  • The movement of the circle
  • The dynamism of the diagonal
  • The harmony of the golden section
  • Etc.

 

Additional Resources
Infinity Plots: Walk in Escher's Garden
Alain Nicolas
Belin editions, 2006

Figurative paving method
(content of Alain Nicolas' book on the Web)

Cézanne: The father of modern art
Angela Wenzel
Palette editions, 2006

Introduction to composition and perspective
Fleurus editions, 2002

The great book of composition
David Sanmiguel Cuevas
Bordas editions, 1995

 

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):

  • The Picasso workshop (ios)
  • The cubist factory with Georges Braque (ios)

Create a cubist image from a few photographs:

  • Fracture (ios $)

Examples

The woman with the hourglass

The burst of time

 

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

Our Lady in the Meadow
Raphael
(1506)
Work uploaded by Yelkrokoyade
Wikipedia

The Card Players
Paul Cézanne
(1892-1896)
Wikipedia

Take photographs while exploring the rule of thirds. Use the camera and crop the image as needed.

Example

Dry Etosha Pan
Alchemist-hp
(2011)
Wikipedia

 

THE SYMMETRY
Exploration tracks Digital exploitation
Live a hunt for symmetry in your environment to be inspired (nature, architecture, various objects). Photographing the discoveries:

  • Camera

Pooling findings:

Create photographic images using symmetry. Generate symmetry:

Example

Use a kaleidoscope-type application:

  • KaleidaCam (ios)

Example

Explore repeating patterns using symmetry. Use a kaleidoscope-type application:

Tips

  • Experiment with the stylus while creating.
  • Enlarge the work surface to increase the accuracy of the plotting.

Examples

Sofia, 11 years old
(2017)

 

GEOMETRICAL TRANSFORMATIONS
Exploration tracks Digital exploitation
Create pavements with geometric patterns.
 
Mathematical thinking
Explore the geometric figures used to pave the plan.

  • Regular polygons
    • equilateral triangle
    • square
    • regular hexagon
  • Irregular polygons (examples)
    • isosceles right triangle
    • parallelogram
    • diamond
Use an application of geometric shapes:

Examples

Use a vector drawing application:

Examples

Use a programming application:

Example

Creation of Spirou 201

Possible procedure:
Nantes Academy

Create paving with figurative patterns in the style of Escher.

To be inspired ... Figurative paving method
(content of Alain Nicolas' book on the Web)

Use a vector drawing application:

Little green monsters

The quadruplets on the collar

Use a programming application:

 

ALGORITHMS
Exploration tracks Digital exploitation
Create a digital work using programming software. Use an application to program:

Examples

Creation of N, 10 years old
Creation code

Creation of L, 14 years old
Creation code

 

 

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:

  • The form
  • The height
  • The colour
  • The amount
  • The type of object
Milan Publishing Site

Open Books Site

 

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.

  • Works in two parts:
    • Before: messy image
    • After: picture in order
  • Classification criteria:
    • The type of object
    • The form
    • The height
    • The colour
    • The amount
  • Organization of elements:
    • Vertically
    • Horizontally
    • Other
  • Humorous aspect of certain works
Create a digital collective memory to preserve and enrich ideas.

This collective memory can take different forms:

  • Board
  • Graphic organizer
  • Annotation
  • Virtual adhesive butterflies
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:

  • Place objects out of order… aesthetically!
  • Photograph.

Trick
Explore different supports for the work (materials, textures, colors).

Use the camera and crop as needed.
Create the second part of the work:

  • Classify the objects according to different criteria and imagine a new composition.
  • Photograph.

Trick
Depending on the theme chosen, it may be interesting to create the second part of the work first.

  • Creating the second part a priori requires more artistic reflection.
  • Creating the first part beforehand sheds more light on the mathematical classification criteria.
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
The Pic Collage application only allows you to save the creation in portrait format.
To place the two parts of the artwork side by side:

  • Place the tablet horizontally to create the photo montage.
  • Save the creation.
  • Open the Photos app.
  • Rotate the photo and save again.

Examples

Sofia, 11 years old
(2017)

 

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 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:

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

INTRODUCTION

  • 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

OTHER CREATIVE IDEAS

  • The spreadsheet
  • The story with a mathematical flavor
  • Illustrations using geometric shapes

CONCLUSION

  • The end of a journey… The beginning of creation
  • Thanks
  • Copyright notice

Your comments about this article

To comment on this article and add your ideas, we invite you to follow us on social networks. All articles are published there and it is possible to comment directly on Facebook, Twitter or LinkedIn.

Do you have news to share with us or would you like to publish a testimonial?

Publicize your educational project or share your ideas via our Opinion, Testimonials or Press Releases sections! Here's how to do it!

Do you like what you read?

Subscribe and receive the next 3 issues of École branchée magazine (print or digital, French or English) in addition to our exclusive online files!

Learn more >

About the Author

Receive the Weekly Newsletter

Get our Info #DevProf and l'Hebdo so you don't miss anything new!





You might also like: