Unit 8: Recreational Mathematics.

"Equations are just the boring part of mathematics. I attempt to see things in terms of geometry." Stephen Hawking

WARM-UP

1. What is recreational mathematics?

Label the pictures below with the names: Sudoku, Rubik’s cube, tangrams, origami, Towers of Hanoi. Have you ever tried any of these? Which of these do you think is the most difficult to do?

1 4

2 5

3

Sudoku - 5, Rubik’s cube -4, tangrams-3, origami-2, Towers of Hanoi-1.

2. Do you agree with the English puzzlist and mathematician Henry Dudeney who wrote: “A good puzzle, like virtue, is its own reward.”?

3. What do you think about numerology? Do you agree with Sir Thomas Browne who “…admired the mystical way of Pythagoras, and the secret magic of numbers”? Do you believe that numbers have mystical significance?

4. What magic figures do you know? Why are they called magic?

5. Work in small groups. In three minutes, write down a list of things which are usually round and/or square.

6. Look at the two paintings. What do they have in common? Do you like them?

Robert Delaunay Joie de vivre (The Joy of Life), 1930 Georges Pompidou Center, Paris	Pablo Picasso Three musicians, 1921 New York Museum of Modern Art

Info for teachers both paintings are examples of Cubist style.

In Cubism, the subject of the artwork is transformed into a sequence of planes, lines, and arcs. Cubism has been described as an intellectual style because the artists analyzed the shapes of their subjects and reinvented them on the canvas. The viewer must reconstruct the subject and space of the work by comparing the different shapes and forms to determine what each one represents. Through this process, the viewer participates with the artist in making the artwork make sense.

Analytical Cubism is one of the two major branches of the artistic movement of Cubism and was developed between 1908 and 1912. In contrast to Synthetic cubism, Analytic cubists "analyzed" natural forms and reduced the forms into basic geometric parts on the two-dimensional picture plane. Color was almost non-existent except for the use of a monochromatic scheme that often included grey, blue and ochre. Instead of an emphasis on color, Analytic cubists focused on forms like the cylinder, sphere and the cone to represent the natural world.

1 painting. Robert Delaunay (French, 1885-1941), Joie de vivre (The Joy of Life), 1930 , oil on canvas, 200 x 228 cm, Georges Pompidou Center, Paris. See Orphism, also known as Orphic Cubism.

2 painting. This celebrated work, now in the New York Museum of Modern Art, is part of series painted while Picasso was with his young family in the Fontaineblueau in the summer of 1921. It marks a return to high Synthetic Cubism and his enduring Commedia dellArte imaginary, commenced in the early days in Paris.

Three Musicians is a large painting measuring more than 2 meters wide and high. It is painted in the style of Synthetic Cubism and gives the appearance of cut paper.

Picasso paints three musicians made of flat, brightly colored, abstract shapes in a shallow, boxlike room. On the left is a clarinet player, in the middle a guitar player, and on the right a singer holding sheets of music. They are dressed as familiar figures: Pierrot, wearing a blue and white suit; Harlequinn, in an orange and yellow diamond-pattered custome; and, at right, a friar in a black robe. In front of Pierrot stands a table with a pipe and other objects, while beneath him is a dog, whose belly, legs, and tail peep out behind the musician's legs. Like the boxy brown stage on which the three musicians perform, everything in this painting is made up of flat shapes. Behind each musician, the light brown floor is in a different place, extending much farther toward the left than the right. Framing the picture, the floor and the flat walls make the room lopsided, but the musicians seem steady. Music Makers in Harmony; It is hard to tell where one musician starts and another stops, because the shapes that create them intersect and overlap, as if they were paper cutouts. Pierrot, the figure in blue and white, holds a clarinet in his hands; one hand is connected to a long, thin, black arm, while the other hand lacks an arm. Three Musicians emphasizes lively colors, angular shapes, and flat patterns. Picasso said he was delighted when "Gertrude Stein joyfully announced... that she had at last understood what... the three musicians was meant to be. It was a still life!"

READING