I. Match the word with its meaning:

1	ratio	A	exactly, free from error
2	spiral	B	anything that makes clear or proves something
3	clumps	C	anti –clockwise
4	evidence	D	relation between two amounts determined by the number of times one contain the other
5	precisely	E	in the form of advancing or ascending continuous curve winding round central point
6	counterclockwise	F	being or getting near to(in number or quality)
7	nautilus	G	moving in a curve in the same direction as the two hands of watch do
8	clockwise	H	small sea animal of which the female has a very thin shell
9	primordial	I	groups of
10	successive	J	primeval, from the beginning
11	approximately	K	coming one after the other in an uninterrupted sequence

II. Work in pairs. Decide if the sentences 1- 7 are t (true) or f (false)

1. The golden ratio is usually represented by the Latin letter ‘q’.

2. German mathematician Martin Ohm must have introduced the popular name ‘the golden ratio or the golden number’ in 1835.

3. The golden number isn’t considered to be associated with elegance of proportion in art and architecture, and there is much evidence for these claims.

4. The golden number is related to the logarithmic spiral.

5. The spiral of the nautilus has the ratio ϕ.

6. Fibonacci numbers are very common in kingdoms of plants and animals.

7. Fibonacci numbers occur in the seed heads of sunflowers and daisies kingdom.

III. Many aspects of the natural world display strong numerical patterns and strong connection with Mathematics. Think of a fractal or any other phenomenon. Find some information on the Internet and share it with other students

T ext 11

Reading and Speaking

A strong mathematical component

M aurits Cornelis Escher was born on June 17, 1898 in Leeuwarden (Friesland), the Netherlands. His father George Arnold Escher, who was a civil engineer, and his mother Sarah Gleichman Escher, had three sons of which Maurits was the youngest. The Escher family lived in Leeuwarden for the first 5 years of Maurits Cornelius life in a large house called “Princessehof”. 1.___________________________________________________ In 1903 the Escher family moved to Arnhem where Maurits took carpentry and piano lessons until he was thirteen. From 1912 until 1918, Maurits Cornelius Escher attended secondary school. 2._______________

___________________________________________ He never succeeded in his final exam, so M.C. has never officially graduated. Later he started studying at the Haarlem School of Architecture and Decorative Arts. After three years, Maurits decided he had gained enough experience in drawing and woodcutting and left the school.

Escher traveled to Italy regularly in the following years, and it was in Italy that he first met Jetta Umiker, the woman who would become his wife in 1924. 3._____________________________ When the political climate under Mussolini became unbearable, the family moved to Chateau-d’Oex , Switzerland, where they stayed for two years. 4.__________________________________________So two years later, in 1937, the family moved again, this time to Ukkel, a small town near Brussels, Belgium. World War 2 forced them to move a last time in January 1941, this time to Baarn, the Netherlands, where Escher lived until 1970. Most of Eschers better known pictures date from this period. 5. ______________________________. Only in 1962, when he had to undergo surgery, there was a time when no new images were created. Escher moved to the Rosa-Spier house in Laren in the northern Netherlands in 1970, a retirement home for artists where he could have a studio of his own. He died there on March 27, 1972.

Escher and Umiker had three sons.

Well known example of his work include Drawing Hands, a work in which two hands are shown drawing each other, Sky and Water, in which plays on light and shadow convert fish in water into birds in the sky, and Ascending and Descending, in which lines of people ascend and descend stairs in an infinite loop, on a construction which is impossible to build and possible to draw only by taking advantage of quirks of perception and perspective.

Esher’s works has a strong mathematical component, and many of the worlds which he drew are built around impossible objects such as the Necker cube and the Penrose triangle.

6.___________________________________________________________________

For example, in Gravity, multi-colored turtles poke their heads out of a stellated dodecahedron. His work has been referenced in the 1980 Pulitzer Prize-winning

book Godel, Escher, Bach by Douglas Hofstadter.