Leonard Euler

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Leonard Euler

• A
• Mathematician
• For all
• Seasons
• By A Chaparral High School Teacher

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Euler was born in Basel, Switzerland on April
15, 1707
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What do we know about Switzerland?

• Full country name Swiss Confederation
• Area 41,295 sq km (16,105 sq mi)
• Population 7.3 million
• Capital city Bern (pop 130,000)
• People 74 German, 20 French, 4 Italian 1
  Romansch
• Language German, French, Italian Romansch
• Religion 49 Roman Catholic 48 Protestant

Since the dominant language is German, can you
guess how his name is pronounced?
(to hear his name correctly pronounced click
here )
You heard right, Oiler!
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Euler

• His father wanted his son to follow him into the
  church and sent him to the University of Basel to
  prepare for the ministry.
• He entered the University in 1720, at the age of
  14, first to obtain a general education before
  going on to more advanced studies.
• Johann Bernoulli soon discovered Euler's great
  potential for mathematics in private tuition that
  Euler himself engineered.

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. Euler's own account given in his unpublished
autobiographical writings, is as follows- ...
I soon found an opportunity to be introduced to a
famous professor Johann Bernoulli True, he was
very busy and so refused flatly to give me
private lessons but he gave me much more
valuable advice to start reading more difficult
mathematical books on my own and to study them as
diligently as I could if I came across some
obstacle or difficulty, I was given permission to
visit him freely every Sunday afternoon and he
kindly explained to me everything I could not
understand ...
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• In 1723 (at the age of 16) he completed his
  Masters degree.
• He finished his studies within the next few
  years.
• In 1727 he began teaching at the St. Petersburg
  Academy of Sciences.
• He became professor of physics in 1730
• He became senior chair of mathematics in 1733

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In 1738 he lost the sight in his right
eye. Eulers comment upon this occurance is
stated to be
"Now I will have less distraction."
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• Euler was director of mathematics and physics in
  the Berlin Academy from 1741-1766 (when he lost
  the sight of his other eye).
• He published over 800 different books and papers
  on pure and applied mathematics, physics and
  astronomy.

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NOW.. Lets look at some of
Eulers accomplishments!
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There is a town in Russia whose name today is
Kaliningrad. In the 1700s, it was in
Prussia and its name was Königsberg.
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Here's a true story. Once upon a time (OK, in
the 18th century), in a place far away (well,
Prussia), there once was a town called
Königsberg. The townspeople enjoyed walking
through their town and passing over the seven
bridges spanning the river which passed through
town. Over the years, a controversy arose and
eventually word of it reached Euler
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The problem is stated as follows In the town of
Königsberg in Prussia there is an island called
Kneiphhof, with the two branches of the river
Pregel flowing around it. There are 7 bridges
crossing the two branches. as shown below The
question is whether a person can plan a walk in
such a way that he will cross each of these
bridges once but not more than once.
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So, what did he find out?

• It was impossible to do that!
• Euler went on to formulate a general theory which
  solved this particular problem and created a new
  branch of mathematics called graph theory.
• To find out more trypaths

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• Euler contributed to every mathematical field
  that existed at the time. He standardized modern
  mathematics notation when he used symbols such as
  f(x), e, i and sin(x). He was the first person
  to represent trigonometric values as ratios and
  prove that e is an irrational number.
• His invention of the calculus of variations led
  to the general method to solve maximum and
  minimum value problems.
• He was also one of the first people to recognize
  that infinite series had to be convergent to be
  used safely.
• In physics, he developed the general equations
  for hydrodynamics and for motion.

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Possibly his most impressive work was his
approximation of the three-body problem of the
sun, earth and moon, which he solved while
completely blind and performing all the
computations in his head.

WOW!
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. Euler was able to relate the number of faces
(F), vertices (V) and edges (E) of a polyhedron
by the following equation, F V E 2
from which one can derive that there are
only five regular polyhdera.
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In fact, Germany created a stamp that
commemorates this formula discovery
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Euler also discovered the formula

• eix cos x i sin x

Which happens to be commemorated on a Swiss stamp
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Eulers importance to society is reflected in his
appearance not just on stamps but on currency as
well!
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So, as you can see Eulers contributions to
mathematics are broad and varied. His impact can
still be felt in algebra, geometry, calculus and
other branches of mathematics such as topology
and graph theory.
Indeed, it is difficult to find a mathematician,
modern or historical, who was as prolific as
Leonhard Euler,
but I challenge you to try!
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Project Assessment PowerPoint Presentation
Layout (15 points possible) q      Is your
presentation easy to view and attractive? (6
points) q      Does your presentation avoid
clutter yet utilize the space on the slide? (3
points) q      Are slide transitions used
appropriately? (3 points) q      Are graphics,
animations, sounds, and other multimedia used for
a purpose? (3 points)   Organization (15 points
possible) q      Do titles and other important
elements stand out on the slide? (3
points) q      Do slides progress in a logical
order? (3 points) q      Do elements of slides
appear in the proper order? (3 points) q      Are
bullets or other organizing aids used
appropriately? (3 points) q      Are there
appropriate title, outline, and conclusion
slides? (3 points)
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Content (15 points possible) q      Does your
presentation effectively summarize important
information? (3 points) q      Are words spelled
correctly and is grammar used properly? (3
points) q      Does your show contain at least 10
content slides? (3 points) q      Does your
presentation contain at least 5 multimedia
images, sounds, animations, videos, etc.? (3
points) q      Is author and source information
included? (3 points)   Classroom Presentation (5
points possible) q      Is the pace of your
presentation a comfortable one for your audience?
(3 points) q      Do the presenters speak
clearly, confidently, and with appropriate eye
contact? (2 points)   TOTAL (50 points possible)