Leonhard Euler Tercentennary — 2007 Dr. Margo Kondratieva and Andrew Stewart Leonhard Euler Tercentennary — 2007 – p. 1/47 Overview Leonhard Euler Tercentennary — 2007 – p. 2/47 Overview Introduction Leonhard Euler Tercentennary — 2007 – p. 2/47 Overview Introduction Timeline Leonhard Euler Tercentennary — 2007 – p. 2/47 Overview Introduction Timeline Polyhedral Problem Leonhard Euler Tercentennary — 2007 – p. 2/47 Overview Introduction Timeline Polyhedral Problem Basel Problem Leonhard Euler Tercentennary — 2007 – p. 2/47 Overview Introduction Timeline Polyhedral Problem Basel Problem Conclusion Leonhard Euler Tercentennary — 2007 – p. 2/47 Introduction Some numbers about Euler Leonhard Euler Tercentennary — 2007 – p. 3/47 Introduction Some numbers about Euler 76 years Leonhard Euler Tercentennary — 2007 – p. 3/47 Introduction Some numbers about Euler 76 years 13 children Leonhard Euler Tercentennary — 2007 – p. 3/47 Introduction Some numbers about Euler 76 years 13 children 886 articles Leonhard Euler Tercentennary — 2007 – p. 3/47 Introduction Some numbers about Euler 76 years 13 children 886 articles 72 600 · Leonhard Euler Tercentennary — 2007 – p. 3/47 Introduction Some numbers about Euler 76 years 13 children 886 articles 72 600 = 43200 pages · Leonhard Euler Tercentennary — 2007 – p. 3/47 Introduction Opera Omnia Leonhard Euler Tercentennary — 2007 – p. 4/47 Introduction Opera Omnia Pure Math (29 volumes) Leonhard Euler Tercentennary — 2007 – p. 4/47 Introduction Opera Omnia Pure Math (29 volumes) Mechanics and Astronomy (31 volumes) Leonhard Euler Tercentennary — 2007 – p. 4/47 Introduction Opera Omnia Pure Math (29 volumes) Mechanics and Astronomy (31 volumes) Physics and Miscellaneous (12 volumes) Leonhard Euler Tercentennary — 2007 – p. 4/47 Introduction In Math Leonhard Euler Tercentennary — 2007 – p. 5/47 Introduction In Math Analysis: 60% Leonhard Euler Tercentennary — 2007 – p. 5/47 Introduction In Math Analysis: 60% Geometry: 17% Leonhard Euler Tercentennary — 2007 – p. 5/47 Introduction In Math Analysis: 60% Geometry: 17% Number Theory: 13% Leonhard Euler Tercentennary — 2007 – p. 5/47 Introduction In Math Analysis: 60% Geometry: 17% Number Theory: 13% Algebra: 7% Leonhard Euler Tercentennary — 2007 – p. 5/47 Introduction In Math Analysis: 60% Geometry: 17% Number Theory: 13% Algebra: 7% Other: 3% Leonhard Euler Tercentennary — 2007 – p. 5/47 Introduction Some of Euler’s Topics Here are some simple, but important, results of Euler: Leonhard Euler Tercentennary — 2007 – p. 6/47 Introduction Some of Euler’s Topics Here are some simple, but important, results of Euler: Logarithms: the formula logc(b) loga(b) = logc(a) Leonhard Euler Tercentennary — 2007 – p. 6/47 Introduction Some of Euler’s Topics Here are some simple, but important, results of Euler: Logarithms: the formula logc(b) ln(b) loga(b) = = logc(a) ln(a) Leonhard Euler Tercentennary — 2007 – p. 6/47 Introduction Some of Euler’s Topics Here are some simple, but important, results of Euler: Logarithms: the formula logc(b) ln(b) loga(b) = = logc(a) ln(a) The symbol i to denote √ 1 − Leonhard Euler Tercentennary — 2007 – p. 6/47 Introduction Some of Euler’s Topics Here are some simple, but important, results of Euler: Logarithms: the formula logc(b) ln(b) loga(b) = = logc(a) ln(a) The symbol i to denote √ 1 − The base of the natural number, 2.719281828459 . ., and the symbol e to denote 2.719281828459 . Leonhard Euler Tercentennary — 2007 – p. 6/47 Introduction Some of Euler’s Topics Here are some simple, but important, results of Euler: Logarithms: the formula logc(b) ln(b) loga(b) = = logc(a) ln(a) The symbol i to denote √ 1 − The base of the natural number, 2.719281828459 . ., and the symbol e to denote 2.719281828459 . Euler’s Identity: iπ e +1=0 Leonhard Euler Tercentennary — 2007 – p. 6/47 Introduction Some of Euler’s Topics Here are some simple, but important, results of Euler: Logarithms: the formula logc(b) ln(b) loga(b) = = logc(a) ln(a) The symbol i to denote √ 1 − The base of the natural number, 2.719281828459 . ., and the symbol e to denote 2.719281828459 . Euler’s Identity: iπ e +1=0 (Note that this last formula contains e, i, π, 0, and 1, which are five of the most important symbols in mathematics.) Leonhard Euler Tercentennary — 2007 – p. 6/47 Timeline 1707: Euler was born. Leonhard Euler Tercentennary — 2007 – p. 7/47 Timeline 1707: Euler was born. 1720: University of Basel Leonhard Euler Tercentennary — 2007 – p. 7/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree (talk in Latin about the comparison of philosophies of DeCartes and Newton) Leonhard Euler Tercentennary — 2007 – p. 8/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree (talk in Latin about the comparison of philosophies of DeCartes and Newton) Leonhard Euler Tercentennary — 2007 – p. 8/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree Leonhard Euler Tercentennary — 2007 – p. 9/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. Leonhard Euler Tercentennary — 2007 – p. 9/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. (Receives an award from Paris Academy of Science) Leonhard Euler Tercentennary — 2007 – p. 9/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. 1727: Moves to St. Petersburg, Russia Leonhard Euler Tercentennary — 2007 – p. 9/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. 1727: Moves to St. Petersburg, Russia 1730: Professor of Physics Leonhard Euler Tercentennary — 2007 – p. 10/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. 1727: Moves to St. Petersburg, Russia 1730: Professor of Physics 1733: Chair in Pure Mathematics Leonhard Euler Tercentennary — 2007 – p. 11/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. 1727: Moves to St. Petersburg, Russia 1730: Professor of Physics 1733: Chair in Pure Mathematics Duties: Scientific consultant to the government, prepares maps, advises Russian Navy, tests designs for engines Leonhard Euler Tercentennary — 2007 – p. 11/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. 1727: Moves to St. Petersburg, Russia 1730: Professor of Physics 1733: Chair in Pure Mathematics 1734: Marries Katharina Gsell Leonhard Euler Tercentennary — 2007 – p. 11/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. 1727: Moves to St. Petersburg, Russia 1730: Professor of Physics 1733: Chair in Pure Mathematics 1734: Marries Katharina Gsell 1736: First book — Mechanica Leonhard Euler Tercentennary — 2007 – p. 11/47 Timeline 1707: Euler was born. 1720: University of Basel 1723: Master’s Degree 1726: First Paper — Analysis of the placement of masts on a sailing ship. 1727: Moves to St. Petersburg, Russia 1730: Professor of Physics 1733: Chair in Pure Mathematics 1734: Marries Katharina Gsell 1736: First book — Mechanica 1741: Moves to Berlin Leonhard Euler Tercentennary — 2007 – p. 11/47 Timeline 1748: Introductio in Analysin Leonhard Euler Tercentennary — 2007 – p. 12/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus Leonhard Euler Tercentennary — 2007 – p. 13/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess Leonhard Euler Tercentennary — 2007 – p. 13/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess(over 300 in total) Leonhard Euler Tercentennary — 2007 – p. 13/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess 1766: Returns to St. Petersburg Leonhard Euler Tercentennary — 2007 – p. 13/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess 1766: Returns to St. Petersburg 1768: Book on Integral Calculus Leonhard Euler Tercentennary — 2007 – p. 14/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess 1766: Returns to St. Petersburg 1768: Book on Integral Calculus 1772: Treatise on the motion of the moon Leonhard Euler Tercentennary — 2007 – p. 15/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess 1766: Returns to St. Petersburg 1768: Book on Integral Calculus 1772: Treatise on the motion of the moon 1773: Katharina died Leonhard Euler Tercentennary — 2007 – p. 15/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess 1766: Returns to St. Petersburg 1768: Book on Integral Calculus 1772: Treatise on the motion of the moon 1773: Katharina died 1776: Remarries (his wife’s sister) Leonhard Euler Tercentennary — 2007 – p. 15/47 Timeline 1748: Introductio in Analysin 1755: Books on Differential Calculus 1755: Letters to Princess 1766: Returns to St. Petersburg 1768: Book on Integral Calculus 1772: Treatise on the motion of the moon 1773: Katharina died 1776: Remarries (his wife’s sister) 1783: Died Leonhard Euler Tercentennary — 2007 – p. 15/47 Timeline Gottfried Leibniz (1646-1716) Leonhard Euler Tercentennary — 2007 – p. 16/47 Timeline Jacob Bernoulli (1654-1705) Leonhard Euler Tercentennary — 2007 – p. 17/47 Timeline Johann Bernoulli (1667-1748) Leonhard Euler Tercentennary — 2007 – p. 18/47 Timeline Christian Goldbach (1690-1764) Leonhard Euler Tercentennary — 2007 – p. 19/47 Timeline Daniel Bernoulli (1700-1782) Leonhard Euler Tercentennary — 2007 – p. 20/47 Timeline Leonhard Euler Leonhard Euler Tercentennary — 2007 – p.