Numbers and arts HS RO1

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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

    Todays 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 (Phi)

    So = 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 =

  • 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