NATURE OF MATHEMATICS

Question 1

~ Born in Pisa, Italy in 1175 AD
~ Met with many merchants and learned their systems of arithmetic
~ Realized the advantages of the Hindu Arabic system
~ Introduced the Hindu-Arabic number system into Europe
~ Europe previously used the Roman number system
~ Consisted of Roman numerals
~ Persuaded mathematicians to use the Hindu-Arabic number system
~ Based on ten digits and a decimal point

Answer 1

Leonardo Pisano

Question 2

~ Were introduced in The Book of Calculating
~ Series begins with 0 and 1
~ Next number is found by adding the last two numbers together
~ Number obtained is the next number in the series
~ Pattern is repeated over and over

Answer 2

The Fibonacci Numbers

Question 3

can be found in the shape of playing cards, windows, book covers, file cards, ancient buildings, and modern skyscrapers.

Answer 3

Golden Rectangles

Question 4

• The ancient Greeks considered this to be the most aesthetically pleasing of all rectangular shapes.
• It was used many times in the design of the famous Greek temple, the Parthenon.

Answer 4

Golden Rectangle

Question 5

~ Represented by the Greek letter Phi
~ Phi equals ± 1.6180339887 … and ±
0.6180339887 …
~ Ratio of Phi is 1 : 1.618 or 0.618 : 1
~ Mathematical definition is Phi2 = Phi + 1
~ Euclid showed how to find the golden section of a line

Answer 5

The Golden Ratio

Question 6

Limit is the positive root of a quadratic equation and is called the

Answer 6

golden section/ratio

Question 7

The golden section arises from the

Answer 7

fibonacci numbers

Question 8

Obtained by taking the ratio of successive terms in the Fibonacci series

Answer 8

the golden ratio

Question 9

The Fibonacci numbers arise from the

Answer 9

golden section

Question 10

used the golden section to place the f-holes in his famous violins

Answer 10

Stradivari

Question 11

used the golden section to construct the contour and arch of violins

Answer 11

Baginsky

Question 12

Golden Mean Gauge: Invented by

Answer 12

Dr. Eddy Levin DDS