View by Category

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Leonhard Euler: His Life and Work PowerPoint presentation | free to view - id: e7ce-NjI0M

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Leonhard Euler His Life and Work

- Michael P. Saclolo, Ph.D.
- St. Edwards University
- Austin, Texas

Pronunciation

- Euler Oiler

Leonhard Euler

- Lisez Euler, lisez Euler, c'est notre maître à

tous. - -- Pierre-Simon Laplace
- Read Euler, read Euler, hes the master (teacher)

of us all.

Images of Euler

Eulers Life in Bullets

- Born April 15, 1707, Basel, Switzerland
- Died 1783, St. Petersburg, Russia
- Father Paul Euler, Calvinist pastor
- Mother Marguerite Brucker, daughter of a pastor
- Married-Twice 1)Katharina Gsell, 2)her half

sister - Children-Thirteen (three outlived him)

Academic Biography

- Enrolled at University of Basel at age 14
- Mentored by Johann Bernoulli
- Studied mathematics, history, philosophy

(masters degree) - Entered divinity school, but left to pursue more

mathematics

Academic Biography

- Joined Johann Bernoullis sons in St. Russia (St.

Petersburg Academy-1727) - Lured into Berlin Academy (1741)
- Went back to St. Petersburg in 1766 where he

remained until his death

Other facts about Eulers life

- Loss of vision in his right eye 1738
- By 1771 virtually blind in both eyes
- (productivity did not suffer-still averaged 1

mathematical publication per week) - Religious

Mathematical Predecessors

- Isaac Newton
- Pierre de Fermat
- René Descartes
- Blaise Pascal
- Gottfried Wilhelm Leibniz

Mathematical Successors

- Pierre-Simon Laplace
- Johann Carl Friedrich Gauss
- Augustin Louis Cauchy
- Bernhard Riemann

Mathematical Contemporaries

- Bernoullis-Johann, Jakob, Daniel
- Alexis Clairaut
- Jean le Rond DAlembert
- Joseph-Louis Lagrange
- Christian Goldbach

Contemporaries Non-mathematical

- Voltaire
- Candide
- Academy of Sciences, Berlin
- Benjamin Franklin
- George Washington

Great Volume of Works

- 856 publications550 before his death
- Works catalogued by Enestrom in 1904 (E-numbers)
- Thousands of letters to friends and colleagues
- 12 major books
- Precalculus, Algebra, Calculus, Popular Science

Contributions to Mathematics

- Calculus (Analysis)
- Number Theoryproperties of the natural numbers,

primes. - Logarithms
- Infinite Seriesinfinite sums of numbers
- Analytic Number Theoryusing infinite series,

limits, calculus, to study properties of

numbers (such as primes)

Contributions to Mathematics

- Complex Numbers
- Algebraroots of polynomials, factorizations of

polynomials - Geometryproperties of circles, triangles,

circles inscribed in triangles. - Combinatoricscounting methods
- Graph Theorynetworks

Other Contributions--Some highlights

- Mechanics
- Motion of celestial bodies
- Motion of rigid bodies
- Propulsion of Ships
- Optics
- Fluid mechanics
- Theory of Machines

Named after Euler

- Over 50 mathematically related items (own

estimate)

Euler Polyhedral Formula (Euler Characteristic)

- Applies to convex polyhedra

Euler Polyhedral Formula (Euler Characteristic)

- Vertex (plural Vertices)corner points
- Faceflat outside surface of the polyhedron
- Edgewhere two faces meet
- V-EFEuler characteristic
- Descartes showed something similar (earlier)

Euler Polyhedral Formula (Euler Characteristic)

- Five Platonic Solids
- Tetrahedron
- Hexahedron (Cube)
- Octahedron
- Dodecahedron
- Icosahedron
- Vertices - Edges Faces 2

Euler Polyhedral Formula (Euler Characteristic)

- What would be the Euler characteristic of
- a triangular prism?
- a square pyramid?

The Bridges of KönigsbergThe Birth of Graph

Theory

- Present day Kaliningrad (part of but not

physically connected to mainland Russia) - Königsberg was the name of the city when it

belonged to Prussia

The Bridges of KönigsbergThe Birth of Graph

Theory

The Bridges of KönigsbergThe Birth of Graph

Theory

- Question 1Is there a way to visit each land mass

using a bridge only once? (Eulerian path) - Question 2Is there a way to visit each land mass

using a bridge only once and beginning and

arriving at the same point? (Eulerian circuit)

The Bridges of KönigsbergThe Birth of Graph

Theory

The Bridges of KönigsbergThe Birth of Graph

Theory

- One can go from A to B via b (AaB).
- Using sequences of these letters to indicate a

path, Euler counts how many times a A (or B)

occurs in the sequence

The Bridges of KönigsbergThe Birth of Graph

Theory

- If there are an odd number of bridges connected

to A, then A must appear n times where n is half

of 1 more than number of bridges connected to A

The Bridges of KönigsbergThe Birth of Graph

Theory

- Determined that the sequence of bridges (small

letters) necessary was bigger than the current

seven bridges (keeping their locations)

The Bridges of KönigsbergThe Birth of Graph

Theory

- Nowadays we use graph theory to solve problem

(see ACTIVITIES)

Knights Tour (on a Chessboard)

Knights Tour (on a Chessboard)

- Problem proposed to Euler during a chess game

Knights Tour (on a Chessboard)

Knights Tour (on a Chessboard)

- Euler proposed ways to complete a knights tour
- Showed ways to close an open tour
- Showed ways to make new tours out of old

Knights Tour (on a Chessboard)

Basel Problem

- First posed in 1644 (Mengoli)
- An example of an INFINITE SERIES (infinite sum)

that CONVERGES (has a particular sum)

Euler and Primes

- If
- Then
- In a unique way
- Example

Euler and Primes

- This infinite series has no sum
- Infinitely many primes

Euler and Complex Numbers

- Recall

Euler and Complex Numbers

Eulers Formula

Euler and Complex Numbers

- Euler offered several proofs
- Cotes proved a similar result earlier
- One of Eulers proofs uses infinite series

Euler and Complex Numbers

Euler and Complex Numbers

Euler and Complex Numbers

Euler and Complex Numbers

- Eulers Identity

How to learn more about Euler

- How Euler did it. by Ed Sandifer
- http//www.maa.org/news/howeulerdidit.html
- Monthly online column
- Euler Archive
- http//www.math.dartmouth.edu/euler/
- Eulers works in the original language (and some

translations) - The Euler Society
- http//www.eulersociety.org/

How to learn more about Euler

- Books
- Dunhamm, W., Euler the Master of Us All,

Dolciani Mathematical Expositions, the

Mathematical Association of America, 1999 - Dunhamm, W (Ed.), The Genius of Euler

Reflections on His Life and Work, Spectrum, the

Mathematical Association of America, 2007 - Sandifer, C. E., The Early Mathematics of

Leonhard Euler, Spectrum, the Mathematical

Associatin of America, 2007

About PowerShow.com

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Leonhard Euler: His Life and Work" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Utexas University and other schools with their online training by sharing educational presentations for free