lesson leu alex numbers_highschool_lvl

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