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Why art?Why numbers?
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
7 arts
The seven great arts of the Venetian Republic : 1. Commerce and Textiles 2. Monetary exchange and Banks 3. Production of 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
7 arts
Today’s fundamental Arts : 1. Music
2. Literature 3. Sculpture
4. Teatre and dance 5. Painting
6. Photography 7. Cinematography
Mathematics and mathematical
principles are at the core of art
The Ishango bone was found in 1960 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo
Ishango bone
3:4, then the difference is called a fourth
2:3, the difference in pitch is called a fifth:
Thus the musical notation of the Greeks, which we have inherited can be expressed mathematically as 1:2:3:4 All this above can be summarised in the following.
Another consonance which the Greeks recognised was the octave plus a fifth, where 9:18 = 1:2, an octave, and 18:27 = 2:3, a fifth
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
Also known as: • Golden Ratio, • Golden Section, • Golden cut, • Divine proportion, • Divine section, • Mean of Phidias • Extreme and mean ratio, • Medial section,
a b
a+b
a+b
a =
a
b = φ
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
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
About the
Origin of
Fibonacci Sequence
Fibonacci Sequence was discovered after an investigation on the
reproduction of rabbits.
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?
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
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
Pairs
1 pair
1 pair
2 pairs
3 pairs End 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.
Fibonacci (1170-1250)
"filius Bonacci"
“son of Bonacci“
His real name was
Leonardo Pisano
He introduced the arab numeral system in Europe
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!
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
Entrance number LII (52) of the colliseum
3.14159265359
1,680339887
Try to write these in roman numerals
Terry Jones
The history of 1 Documentary BBC 2005