Lesson leu alex numbers_highschool_lvl
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The document discusses the history and evolution of the concept of the seven arts or liberal arts throughout antiquity and different time periods. It traces how the seven arts were conceived of in antiquity, during the early medieval period, in 15th century Venice, in the early 19th century according to Hegel, and in modern times. Mathematics and mathematical principles are also discussed as being at the core of art.
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Lesson leu alex numbers_highschool_lvl
- 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,
- 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