Leonhard Euler his life, personnality, discoveries and the impact today

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Leonhard Euler- his life, personnality,
discoveries and the impact today
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Leonhard Euler's life
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The four Stations in Eulers life
Basel 1707 - 1727 St. Petersburg
1727 - 1741 Berlin 1941 - 1766 St.
Petersburg 1766 - 1783
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Basel
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Basel 1707- 1727
1707 Born April 15 Baptised April 17,
Church St. Martin 1715 Sent to Latin school (high
school) 1720 - 1726 University of Basel
Johann Bernoulli, reading course 1726 First
mathematical paper published 1727 Second Prize on
the prize question set by the Paris
Academy On the Optimal Position of a
mast of a ship 1727 Applies for
Professorship in physics a the
University of Basel. (lost by lot)
Celebration 20th April 2007
Old University of Basel
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St. Petersburg 1727 - 1741

• 1727 Adjunct of the Academy
• 1730 Professor of physics
• ordinary member of the Academy
• 1733 Daniel Bernoulli returns to Basel and Euler
• succeeds him as professor in Mathematics
• 1734 Marries Katharina Gsell
• - 13 Children (only 5 reached
  adulthood,
• 3 survived him)
• 1738 Euler looses his right eye
• 1741 Euler accepts call of Frederick II to come
  to
• Berlin to set up the Academy

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St. Petersburg 1727 - 1741
Major works Mechanics Analytic theory
of motion 1736 Music theory
1739 Naval science, written 1740-41
principles of hydrostatics,
stability theory, naval
engineering, navigation
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Berlin 1741 - 1766

• 1746 Berlin Academy is opened Maupertius
  Director
• - Euler is director of Mathematics
  Class
• - Euler becomes foreign member of
  the Royal
• Society of London
• 1752 Maupertius returns to Paris. Euler becomes
  de facto
• director of the academy.
• 1755 Elected foreign member of the Paris Academy
• 1763 Relationship with Frederick II starts to
  deteriorate
• 1766 Return to St. Petersburg

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Berlin 1741 - 1766

• Major works
• First exposition ever of calculus of variation
  (Eulers equation, many examples) 1744
• Cometary and planetray trajectories 1744
• Optics 1745
• Artillery 1742
• Introduction to the analysis of the infinite 1748
• Differential calculus 1755
• Integral calculus 1763, 1773
• Mechanics of rigid bodies 1765
• Dioptrics

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St. Petersburg 1766 - 1783
1766 Return to St. Petersburg, triumphant
reception Decline of visual faculty in
his left eye (cataract) 1771 Eye operation, loss
of left eye. 1773 Eulers wife dies 1776 Euler
marries S. Abigail Gsell, sister-in-law of
his first wife 1783 Euler dies on 7th September
(Stroke)
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Leonhard Euler's personnality
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One of the most productive scientists in history
Galileo Galiei
Einstein
Newton
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Personality

• Modesty
• Honesty
• Uncompromising rectitude
• Tremendous curiosity
• No feelings of rancor because of
• - priority issues (Maclaurin)
• - unfair criticism
• Scientific generosity
• - let others take part in his process of
  discovery
• - let Daniel Bernoulli publish his own
  hydrodynamics

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Personality
Willingness and gift to explain things to the
less gifted - Lettres a une Princesse
DAllemagne - His children, grand
children (even on the day of his
death) Ability to concentrate, despite many
children, large household Personal
believes - religious (Father was a
priest) - felt uncomfortable with
free-thinkers. He called them
Freygeister. - Strong feeling that
anything can be done with
mathematics
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Personal style

• Tremendous Curiosity (fearless, reckless,
  persistent,
• revisiting
  old problems)
• Secure instinct (what is ok and what is not)
• Tremendous working power (even on the day he
  died)
• Superb exhibitor
• Clarity (oldest math which we can easily read
  today)

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Personal style
Tremendous sense for excellent notation
f(x) ? p lim
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His productivity
His Work 866 Publications 27 Books (more than 40
?) Wrote about 800 pages/year Euler commission
in Basel Formed 1907 Produced 76 books so
far Each 500 pages Still not finished
M. Unser, Library ETH Zurich
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Euler's discoveries
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What most of us learnt at school 2D
geometry
orthocentre
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What most of us learnt at school 2D
geometry
circumcentre
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What most of us learnt at school 2D
geometry
centroid
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What most of us learnt at school 2D
geometry
Euler's line
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What most of us learnt at school 3D geometry
Eulers Angles
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What most of us learnt at school 3D geometry
Eulerss Angels
Eulers Disk
Ch. Glocker, ETH Zurich
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Analysis complex numbers
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Euler Squares Greco-Latin Squares
Latin/Greek letter
In each row and each column each Latin letter
occurs exactly once. In each row and each column
each Greek letter occurs exactly once.

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Euler Squares Greco-Latin Squares
11 23 34 42 22 14 43 31 33 41 12 24 44 32 21 13
Latin/Greek letter
Black/Red digit gt Sudoku
In each row and each column each Latin letter
occurs exactly once. (black digit) In each row
and each column each Greek letter occurs exactly
once. (red digit)
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Euler Squares Greco-Latin Squares
11 23 34 42 22 14 43 31 33 41 12 24 44 32 21 13
Latin/Greek letter
Black/Red digit gt Sudoku
Shape/color
Height/color
In each row and each column each Latin letter
occurs exactly once. (black digit) In each row
and each column each Greek letter occurs exactly
once. (red digit)
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6 x 6 Euler Square
One has 6 different troups and of each troup 6
different ranks. Question Can one arrange these
36 different persons in a 6 x 6 square such that
- in each row and each column each troup
occurs exactly once. - in each row and
each column each rank occurs exactly once. We
use shapes and colors
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Euler Square

2 x 2 Euler Square
Arrange these four symbols in a square such that
in each row and each column each
color occurs only once and each
shape occurs only once
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Euler Square

2 x 2 Euler Square
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Euler Square

2 x 2 Euler Square
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Euler Square

2 x 2 Euler Square
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Euler Square

2 x 2 Euler Square
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Euler Square

2 x 2 Euler Square
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Euler Square

2 x 2 Euler Square
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Euler Square

2 x 2 Euler Square

• No
• solution

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Euler Square

3 x 3 Euler Square
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Euler Square

Euler proved There exists an n x n Euler square
for - n an odd
number 1, 3, 5, 7, 9, 11, 13, 15, 17,
- n a multiple of 4 4, 8,
12, 16, 20, Euler could not find a 6 x 6 Euler
square (36 officers problem)
proved 1901
Gaston Tarry No Euler square for 2, 6,
10? Euler conjectured There is no 10 x 10 Euler
square There is no
Euler square for n 2 4 k, k 0,1,2,
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Euler Square
1959 Bose, Shrikhande found counterexamples for n
10 1960 Parker, Raj Chandra Bose, Shrikhande
Euler conjecture wrong for n gt 10
There exists an n x n Euler square for all n,
except n 2, 6
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Euler Square and Sudoku
11 23 34 42 22 14 43 31 33 41 12 24 44 32 21 13
Latin/Greek letter
Black/Red digit gt Sudoku
Shape/color
Height/color
In each row and each column each Latin letter
occurs exactly once. (black digit) In each row
and each column each Greek letter occurs exactly
once. (red digit)
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Euler Square, Latin Square and Sudoku
11 23 34 42 22 14 43 31 33 41 12 24 44 32 21 13
1 2 3 4 2 1 4 3 3 4 1 2 4 3 2 1

• 3 4 2
• 4 3 1
• 1 2 4
• 2 1 3

Black/Red digit gt Sudoku
4 x 4 Latin Square
9 x 9 Latin square with additional
constraints Each of the nine 3 x 3 subsquares is
a Latin square
In each row and each column a black digit
red digit occurs exactly once.
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Euler Square, Latin Square and Sudoku
9 x 9 Latin square with additional
constraints Each of the nine 3 x 3 subsquares is
a Latin square
Solution

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The impact today
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From Euler's thesis to today's fluidynamics,
shape optimisation and operations research
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Thesis what is the difference between vibration
cords' and wind instruments' music?
Globules ??? Speed of sound Influence of shape
the instruments
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Euler's fluid dynamics
Density Conservation
of Momentum Energy
Flow about a cylinder N. Botta, SAM, ETH Zurich
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Todays ApplicationsEuropean Space Shuttle HERMES
Experiment
Theory
Euler Equations Chemistry
Simulation
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Euler's fluid dynamics todays applications Flow
in a heart arteries

Carotide - velocity, A. Quarteroni EPFL Lausanne
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Euler's fluid dynamics todays applications
Americas Cup Alinghi
Navier-Stokes
Alinghi A. Quarteroni EPFL Lausanne
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Example of shapesoptimised usingEuler's
equations of fluid
Gasturbine MS7001
3D optimization of rotor Blades with Eulers
equation and also Navier-Stokes ABB - Alstom
Power - SAM - ETH Zurich
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Example of shapes optimised using Euler's
equations of fluid
World Record 5385 km/l in Ladoux, June 2005
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Example of shapes optimised using Eulers
equations of fluid and Navier-Stokes
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Example of shapes optimised using Eulers
equations of fluid and Navier-Stokes
BMW - Sauber Fromula 1
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From the 7 bridges problem to today's OR
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The seven bridges of Königsberg
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The seven bridges of Königsberg
Problem Do a closed walking tour crossing each
bridge exactly once. Euler 1736 Impossibility
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The seven bridges of Königsberg
Problem Do a closed walking tour crossing each
bridge exactly once. Euler 1736 Impossibility
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The seven bridges of Königsberg
Problem Do a closed walking tour crossing each
bridge exactly once. Euler 1736 Impossibility
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The seven bridges of Königsberg
Start at D cross bridge D - A Problem Do a
closed walking tour crossing each bridge exactly
once.
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The seven bridges of Königsberg
Start at D cross bridge D to A Take any bridge
form A to B Problem Do a closed walking tour
crossing each bridge exactly once.
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The seven bridges of Königsberg
Start at D cross bridge D to A Take any bridge
form A to B Take bridge from B to D Problem Do
a closed walking tour crossing each bridge
exactly once.
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The seven bridges of Königsberg

• Start at D cross bridge D to A
• Take any bridge form A to B No
  solution
• Take bridge from B to D
• Problem Do a closed walking tour crossing each
  bridge exactly once.

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The seven bridges of Königsberg
Graph Vertices A, B, C, D Degree of a vertex
of connections to
other vertices degree A
3 B 5 C 3 D 3 Euler If there is
a vertex of odd degree Then No solution
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The seven bridges of Königsberg
Birth of

• Topology
• Graph theory used also Operations
  Research OR

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OR The so-called "Salesman" and "Chinese
Postman" key problems
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An example of graph theory for railways
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Acknowlegements

Patrick Freymond Students

Nicola Botta Euler lecturers
Andrea Scascighini Robon
Wilson Michael Fey
Gerhard Wanner Andreas
Troxler Walter Gautschi
.. Colleagues
Further Support Lino Guzzella
Dominique Ballarin-Dolphin
Francois Fricker Margit
Unser Rita Jeltsch
Marianne Jeltsch Christoph Glocker
Ralf Hiptmair
Many Websites Alfio Quarteroni
Wikipedia Patrick Jenny
. Hans-Jakob Luethi .
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Thank YOU!

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