Creating a Geometry Masterpiece

Julie West

Christie Goehring

Kristi Felder

CAMT 2009

http://mathforum.org/~sanders/mathart/

“Possibly for students the most surprising connection to math is art.”

http://msteacher.org/epubs/math/math7/art.aspx

“The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

http://www.ams.org/mathimagery/

Why connect mathematics and art?

“For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.”

- M.C. Escher

“Although intellectually sophisticated, Matisse always emphasized the importance of instinct and intuition in the production of a work of art. He argued that an artist did not have complete control over color and form; instead, colors, shapes, and lines would come to dictate to the sensitive artist how they might be employed in relation to one another.”

- Richard Shiff

“Whoever despises the high wisdom of mathematics nourishes himself on delusion.”

- Leonardo da Vinci

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Mona Lisa

by Leonardo da Vinci

"...no human inquiry can be called science unless it pursues its path through mathematical exposition and demonstration." -Leonardo Da Vinci

Leonardo had for a long time displayed an ardent interest in the mathematics of art and nature.He had earlier, like Pythagoras, made a close study of the human figure and had shown how all its different parts were related by the golden section. Leonardo's unfinished canvas Saint Jerome shows the great scholar with a lion lying at his feet.A golden rectangle fits so neatly around the central figure that it is often said the artist deliberately painted the figure to conform to those proportions. Knowing Leonardo's love of "geometrical recreations" as he described them, this is quite likely

The triangle is the strongest, most rigid shape. This is why the triangle is used so often architecture, from bridges to buildings. Many bridges are built using an engineering concept called the "triangular truss"- a geometric design composed of triangles. The following web page will tell you why triangles are used in construction:

Of course, examples of squares and rectangles appear in most buildings, as it is the most common shape in architecture. Why is this? Because this rectangles, each with its 90 degree angles, fits together perfectly! Doors fit into their frames, windows fit into the walls, and one wing of a building fits up against another wing of the building if all are rectangles:

How to teach a Geometry lesson while connecting to art?

Geometry•Pablo Picasso•Henri Matisse•Andy Warhol•Faith Ringgold

Measurement•Faith Ringgold•Leonardo da Vinci•M.C. Escher•Egyptian Art

Henri Matisse

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Henri Matisse was born in France in 1869, and originally trained as a lawyer. However while recovering from appendicitis he turned to art. Matisse brought together a circle of like-minded artists who became known as the Fauves, holding a sensational exhibition in 1905. Matisse made sculptures, designed sets and costumes and illustrated books. He was also an important graphic artist, who in his bed ridden final year’s, evolved his own method of arranging cut-out paper shapes. He died in France in 1954.

Matisse, The Snail