Erasmus+ arteducation.eu Numbers RO1 Upper secondary

1. Why art?Why numbers?

2. The 7 arts
In antiquity :
1.Poetry
2.History
3.Music
4.Tragedy
5.Writing and panthomime
6.Dans
7.Comedy
8.Astronomy
7 liberal arts : (Around ~730 AD)
1.Grammar
2.Dialectics
3.Rhetoric
4.Arithmetics
5.Music
6.Geometry
7.Astronomy

3. 7 arts
The seven great arts of the
Venetian Republic :
1. Commerce and Textiles
2. Monetary exchange and
Banks
3. Productionof gold objects
4. Wool manufacture
5. Leatherworkers
6. Judges and Notaries
7. Medics,
pharmacists,merchants and
painters
Hegel considers these to be arts :
(year ~1830 AD):
1.Architecture
2.Sculpture
3.Paintings
4.Music
5.Dans
6.Poetry
7.At this list, around 1911,
cinematography is added

4. 7 arts
Today’s fundamental Arts :
1. Music
2. Literature
3. Sculpture
4. Teatre and dance
5. Painting
6. Photography
7. Cinematography

5. Mathematicsand
mathematical
principles are at
the core of art

7. The Ishango bone was found in 1960 by
Belgian Jean de Heinzelin de Braucourt while
exploring what was then the Belgian Congo

8. Ishangobone

41. 3:4, then the difference is called a fourth

42. 2:3, the difference in pitch is called a fifth:

43. Thus the musical notationof the Greeks, which
we have inherited can be expressed
mathematically as1:2:3:4
All this above can be summarised in the
following.

44. Another consonancewhich the Greeks
recognised was the octave plusa fifth, where
9:18 = 1:2, an octave, and 18:27 = 2:3, a fifth

63. The golden ratio is an irrational mathematical
constant, approximately equals to
1.6180339887
The golden ratio is often denoted by the Greek
letter φ (Phi)
So φ = 1.6180339887

64. Also known as:
• Golden Ratio,
• Golden Section,
• Golden cut,
• Divine proportion,
• Divine section,
• Mean of Phidias
• Extreme and mean ratio,
• Medial section,

65. a b
a+b
a+b
a
=
a
b
= φ

66. A golden rectangle is a rectangle where the ratio of its length to width is
the golden ratio. That is whose sides are in the ratio 1:1.618

67. The golden rectangle has the property that it can be further subdivided in
to two portions a square and a golden rectangle This smaller rectangle can
similarly be subdivided in to another set of smaller golden rectangle and
smaller square. And this process can be done repeatedly to produce
smaller versions of squares and golden rectangles

77. About the
Origin of
Fibonacci Sequence

78. Fibonacci Sequence was discovered
after an investigation on the
reproduction of rabbits.

79. Problem:
Suppose a newly-born pair of rabbits (one male, one female) are
put in a field. Rabbits are able to mate at the age of one
month so that at the end of its second month, a female can
produce another pair of rabbits. Suppose that the rabbits never
die and that the female always produces one new pair (one male,
one female) every month from the second month on. How many
pairs will there be in one year?

80. 1 pair
1 pair
2 pairs
End first month… only one pair
At the end of the second month the female produces a
new pair, so now there are 2 pairs of rabbits

81. Pairs
1 pair
1 pair
2 pairs
3 pairs
End second month… 2 pairs of rabbits
At the end of the
third month, the
original female
produces a second
pair, making 3 pairs
in all in the field.
End first month… only one pair

82. Pairs
1 pair
1 pair
2 pairs
3 pairsEnd third month…
3 pairs
5 pairs
End first month… only one pair
End second month… 2 pairs of rabbits
At the end of the fourth month, the first pair produces yet another new pair, and the female
born two months ago produces her first pair of rabbits also, making 5 pairs.

83. Fibonacci (1170-1250)
"filius Bonacci"
“son of Bonacci“
His real name was
Leonardo Pisano
He introduced the arab numeral
system in Europe

84. Thus We get the following sequence of numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34 ,55,89,144....
This sequence,in which each number is a sum of two previous is
called Fibonacci sequence
so there is the
simple rule: add the last two to get the next!

85. 1
1
2
3 1.5000000000000000
5 1.6666666666666700
8 1.6000000000000000
13 1.6250000000000000
21 1.6153846153846200
34 1.6190476190476200
55 1.6176470588235300
89 1.6181818181818200
144 1.6179775280898900
233 1.6180555555555600
377 1.6180257510729600
610 1.6180371352785100
987 1.6180327868852500
1,597 1.6180344478216800
2,584 1.6180338134001300
4,181 1.6180340557275500
6,765 1.6180339631667100
10,946 1.6180339985218000
17,711 1.6180339850173600
28,657 1.6180339901756000
46,368 1.6180339882053200
75,025 1.6180339889579000

100. Entrance number LII (52) of the colliseum

101. 3.14159265359
1,680339887
Try to write these in
roman numerals

102. Terry Jones
The history of 1 DocumentaryBBC 2005