Maths in social and cultural life

1. Maths in cultural and social life
Γιάννης Παλαμάς
Ben Heine

2. Mathematics from the Greek word
“μάθημα” = learning, study
Geometry = Geo + meter = Γη + μετρο =
Earth & measurement

3. The School of Athens by Raphael
(Vatican)

4. Euclid with a
compass
( a detail
from “The
school of
Athens”)

5. A short story........
Joannes Stobaeus (Ιωάννης Στοβαίος ) 5 century
AD, was the compiler of a valuable series of
extracts from Greek authors.
He has written:
One day a young man visited Euclid and asked him to
teach him Geometry. When he learnt the first theorem, he
turned to the famous mathematician and asked him “and
now which is the profit of what I learnt?”
Euclid called a servant and said to him :” Give to this young
man 3 δεκάρες (cents), so he will have a profit from what
he was taught”.

6. Use of
mathematics
Many times during every school year, students
ask me why they have to learn mathematics.
I tell them to take a paper and a pencil and
write down in which cases they use
mathematics during the day.
The students' comments are:

7. Use of
mathematics
When
● we buy a car
● when Irene follows a recipe to make a cake
● when Vasilis goes on foot to his school in the morning following
the shortcut,
● when we decorate our home or our classroom
we are using math principles.
People have been using these same principles for
thousands of years, across countries and continents.

8. Time

9. Money

11. Measurement

12. Probabilities

13. Logic games
Almost all of the logic games are based on
mathematics
● Chess :the most challenging game of all
● The tower of Hanoi
● Sudoku
● cards

14. Symmetry

15. Symmetry

16. In TV Shows....
Sometimes you must know Maths...

17. In a TV SHOW
http://www.youtube.com/
watch?v=BbX44YSsQ2I

18. Finally......
● A photo, sent by Dominique Maucourant (graffiti on a wall in Santa Lucia
-Caribbean)

19. … across the centuries and
countries...

20. 2000 BC
Babylonians used Algebra and Geometry to
construct buildings. Also they used them in
Astronomy. They created a type of calendar
and they were able to predict solar and lunar
eclipse.
Reconstruction of the ziqqurat
of Babylon

21. 1500 BC -Egypt
Nile!! the longest river in the world.
Every year the flood brought disaster and problems in the fields.
● Simple geometry fields' borders
● Simple metric system to study the Nile's flow and flood
every year.

22. Geometric period
The period of the ancient Greek history
between the 11th and 8th century BC is known
as Geometric period, and took its name from
the geometric shapes on the ceramics.

23. Geometric period

24. Mathematics and Art
Mathematics and Art have a long historical
correlation.
Many artists have been inspired by
mathematics from the ancient years until today.

25. Golden ratio and Architecture
The Golden Ratio appeared in ancient architecture.
The examples are many, such as the Great Pyramid
in Giza, Egypt which is considered as one of the
Seven World Wonders of the ancient world, and the
Greek Parthenon . It was also used by the
Renaissance artists, who used the Golden Ratio in
the design of Notre Dame, etc.

26. Pyramids and φ (φ from Φειδίας-
ancient Greek sculptor - 5th century BC)

27. Parthenon
Parthenon is a temple dedicated to the Greek
goddess Athena, built in the 5th century BC. In
its facade and on the floor the golden rectangle
is applied (a rectangle whose length to width
ratio is the golden ratio)

28. Ancient Theater of Epidaurus 340-330
BC
a/b=(a+b)/a = φ=1.62
b
a

29. Golden ratio
The astronomer Johannes Kepler (1571-
1630) wrote, "Geometry has two great
treasures: one is the theorem of Pythagoras,
the other one is the division of a segment into
mean and extreme ratios, which is, the Golden
Mean. The first theorem may be compared to
a measure of gold, the second one to a
precious jewel."

30. Maths and Painting
It is suggested that mathematics and painting
are so closely related and have so many
similarities that it is reasonable to consider
them simply as two different but complementary
ways of visualizing the world.
Mathematics have influenced many art
movements, such as Cubism, Constructivism,
Linear perspective, Surrealism.

31. Cubism
Cubism was a 20th century avant-garde art
movement, pioneered by Pablo Picasso and
Georges Braque
Pablo Picasso
Pablo Picasso

32. George Braque Juan Gris

33. Constructivism
Constructivism was an
artistic and architectural
movement originating in
Russia from 1919 onward
which rejected the idea of
"art for art's sake" in favour
of a praxis directed towards
social purpose.
1915 Dance by Rodchenko

34. Piet Mondrian Gustav Klutsis

35. Linear perspective
Perspective (from Latin perspicere, to see through) in the
graphic arts, such as drawing, is an approximate
representation, on a flat surface (such as paper), of an
image as it is seen by the eye.
Pietro Perugino's usage of perspective in this
fresco at the Sistine Chapel (1481–82) helped bring the Renaissance to Rome
.

36. Melozzo's usage of upward foreshortening in his frescoes at Loreto

37. Wassily Kandinsky- Abstract painting
He began completely abstract painting. His forms evolved
from fluid and organic to geometric and, finally, to
pictographic

38. Leonardo Da Vinci (1452-1519)
Leonardo incorporated many mathematical
concepts into his artwork despite never having
received any formal mathematical training. He
has often been described as the archetype of
the Renaissance man.

39. Salvador Dalí (1904–1989) incorporated
mathematical themes in several of his later
works. His 1954 painting Crucifixion (Corpus
Hypercubus) depicts a crucified figure upon the
net of an hypercube

40. Salvador Dali

41. Salvator Dali
The Sacrament of the Last Supper (1955)
Christ and his disciples are pictured inside a
giant dodecahedron.

42. M.C. Escher (1898-1972) is known for
his mathematically inspired work.

43. Platonic solids
The Platonic solids (tetrahedron, cube-
hexahedron,octahedron,dodecahedron,icosahe
dron) and other polyhedra are a recurring
theme in Western art.
Floor mosaic in St Mark's Basilica,
Venice by Paolo Uccello

45. Maths and Music
"Music," wrote the great 17th-century German
mathematician Gottfried Leibniz, "is the
sensation of counting without being aware you
were counting."
But there is more to this connection than
counting. The French baroque composer
Rameau declared in 1722:
"I must confess that only with the aid of
mathematics did my ideas become clear."

46. The Pythagoreans of ancient Greece are the
first researchers known to have investigated
the expression of musical scales in terms of
numerical ratios. Their central doctrine was
that "all nature consists of harmony
arising out of numbers". Also ancient
Chinese, Egyptians and Mesopotamians are
known to have studied the mathematical
principles of sound.

47. It is believed that some composers wrote
their music using the golden ratio and the
Fibonacci numbers to assist them.
The golden ratio is apparent in the
organization of the sections in the music
of Debussy's Image, "Reflections in
Water", in which the sequence of keys is
marked out by the intervals 34, 21, 13,
and 8 (a descending Fibonacci sequence),
and the main climax sits at the φ position.

48. Maths and literature
“Pure mathematics is, in its way the poetry of logical ideas”..... Albert
Einstein
From the ancient years until today, many Authors use math in stories, plays or
poems in a variety of different ways.
In producing their art writers may :
1. Call on math to illuminate a theory (Aristophanes-the Birds, Dostoevsky-
The Brothers Karamazov , Tolstoy – War and Peace ).
2. Be inspired by mathematical themes to create a work of art based on the
themes (Denis Guedj -Le theoreme du perroquet, A. Doxiadis -Uncle Petros and
Goldbach's Conjecture, T. Michaelides- Pythagorean crimes, Growney and
Upson).
Meanwhile, the last years a new kind of literature has appeared : Mathematical
fiction.
3. Want to produce an educational work( Enzensberger);
4. Want to write the imagined life of an intriguing mathematician ( Petsinis
-The French Mathematician ).
Topics such as logic, geometry, measurement, number theory, statistics,
topology, set theory, and calculus arose naturally from the readings.

49. th
8 century BC
Homer gives a poetic description of number 700
and a geometric presentation of Sicily in chapter
μ of Odyssey :
«... και φτάσαν στο τριγωνικό νησί της Σικελίας/
όπου του Ήλιου έβοσκαν τα όμορφα θρεφτάρια/
γελάδια σε κοπάδια εφτά, αρνιά σε άλλα τόσα,/
πενήντα το καθένα τους...»
“...and they arrived at the triangular island of
Sicily / where the Sun's beautiful cattles
grazed/the cows in seven herds, and the sheep
in as many/ fifty in each of them...”

50. Prometheus (of Aeschylus ,460 BC) was chained to the
rocks, punished by Zeus for daring to offer to the mortals
the knowledge which was suitable only for Gods .
Among the gifts that he gave to the people, there are
goods destinated only for immortals: «...και μην αριθμόν,
έξοχον σοφισμάτων, εξηύρον αυτοίς...» …..(«Μα και
τον αριθμό, την πιο τρανή σοφία βρήκα για χάρη τους
εγώ...»)
“I also found out the
number, the most great
wisdom , for them...”

51. Aristophanes- The Birds
In the end of the 5th century BC , Aristophanes refers to the unsolved
problem “circle squaring” , in his comedy “The Birds”.
The astronomer Meton (Μέτωνας) is at the scene of the theater saying:
«με το ορθό ραβδί αρχίζω να μετρώ= I start measuring with my right stick
ώστε να γίνει ο κύκλος τετράγωνος για χάρη σου˙= so that the circle
becomes a square, for your sake
και στο κέντρο του θα είναι η αγορά=and at its center there will be the
market
στην οποία θα οδηγούν όλοι οι δρόμοι= to which all roads will lead
συγκλίνοντας στο κέντρο, όπως σ’ ένα αστέρι,=converging in the center,
the way it happens in a star,
που ενώ είναι κυκλοτερές=which (the star) , although it is circular,
στέλνει παντού ευθείες ακτίνες λαμπρές».= it sends straight bright rays
everywhere
«Αλήθεια, ο άνθρωπος είναι Θαλής!»=Really, the man is Thales!

52. Dostoyevsky-The Brothers Karamazov
During the 19th century, there was a period when a non-
Euclidean geometry appeared throughout Europe
Dostoyevsky used these new mathematical ideas to illuminate
his philosophy.
In a part of the “Brothers Karamazov”, Ivan explains to his
younger brother, Alyosha, that while he believes in God, he has
difficulty believing in the world that God created.
“Even if the parallel lines converge and I actually witness
it, I shall witness it and say they have converged, but all
the same I shall not accept it”.

53. Tolstoy-War and Peace
In War and Peace, Tolstoy provides an
example of the use of ratio and linear equations
to clarify how the disadvantaged (such as the
Russians) can win battles against more
advantaged (such as the French) if they
have enough spirit and energy. Ratio and
proportion can be used to relate the power of
an army to its spirit!

54. Mathematics in movies
http://www.math.harvard.edu/~knill/mathmovies/
Many directors and script writers have been
inspired by mathematics. There is more than
700 movies containing mathematical dialogues
and images.

55. “Flatland” by Edwin Abbott Abbott
Directors:
Dano Johnson, Jeffrey Travis

56. Mathematics.....
A universal language..

57. A lonely trip based on mathematics.....
Back in 1977 , when the voyager spaceship
started its lonely trip into the vast space-void,
the NASA officials placed inside it, a golden
record with recordered political messages,
th
spoken greetings in 55 languages, the 5
symphony of Beethoven and engraved
mathematical symbols on it.

58. The cover of the
Voyager Golden
Record.

59. This diagram defines the location of our sun
utilizing 14 pulsars of known directions from our
sun. The binary code defines the frequency of
the pulses.

60. The way of communication with
unknown civilizations...

61. The greetings in European languages
<< Οίτινες ποτ`εστέ χαίρετε. Ειρηνικώς πρός φίλους
ελαλήσαμεν φίλοι.>>
("Greetings to you, whoever you are. We come in peace
to those who are friends.")
Herzliche Grüße an alle (in German)
Salutări la toată lumea ( in Romanian)
Sayın Türkçe bilen arkadaşlarımız, sabah şerifleriniz
hayrolsun (in Turkish)
Witajcie, istoty z zaświatów (in Polish)

62. Some Famous Mathematical
Quotes

64. Mathematics is like draughts
[checkers] in being suitable for the
young, not too difficult, amusing, and
without peril to the state.
Plato

65. "To imagine the usefulness of
mathematics in our lives, just
imagine life without mathematics "
Lao Tzu. (Chinese philosopher)

66. Leo Tolstoi said:
A man is like a fraction, whose numerator is
what he is and whose denominator is what he
thinks of himself.
The larger the denominator, the smaller the
fraction.

67. A man is......
=

68. Archimedes will be remembered when
Aeschylus is forgotten, because
languages die and mathematical ideas do
not. “Immortality“ may be a silly word, but
probably a mathematician has the best
chance of whatever it may mean....
C.H.HARDY : A mathematician's Apology

69. Thank you for your attention!!!!!