April 15 – Happy Birthday, Leonhard Euler

nPostednon April 15, 2014

He’snconsidered one of the greatest mathematicians of all times!

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nHe’s considered by most to be THEngreatest mathematician of the 18^th Century (the 1700s)!

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nInnhis own time, Euler was so famous among scientists and mathematiciansnthat one of the greatest, Pierre-Simon Laplace, told students, “Read Euler, read Euler; he is the master of us all.”

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nEulernis also considered a physicist. Here are fields Euler madencontributions to:

ninfinitesimaln calculus

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ngraphn theory

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nmathematicaln analysis

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nmathematicaln terms notation

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nmechanics

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nfluidn dynamics

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noptics

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nastronomy

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nmusicn theory

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nBornnon this date in Switzerland, Euler showed his talent for math early.nHe entered a university at age 13, received his Master of Philosophynat age 16, and completed his doctoral dissertation at age 19. He wasnnot able to get a job at his alma mater, in Switzerland, so he endednup moving to the Russian Empire to work as a physics professor.nEventually he moved to Berlin, in what was then Prussia but is nownGermany, to continue as a professor of mathematics and physics.

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nChecknout Eulerian Diagrams!
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nInhave always called the sorts of illustrations seen here (above and right) VennnDiagrams, but John Venn himself called his diagrams Eulerian Circles.nEuler had diagrammed subsets and disjoints with circles and othernenclosed curves long before Venn was even born. However, Venn pointed outnsome problems with Euler’s diagrams: apparently they are open tonmultiple interpretations rather than just one logical interpretation.

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nSonVenn created a more restricted version of Eulerian diagrams, one innwhich all logically possible sets are represented. That means that,nin a Venn Diagram, there will often be subsets that are empty. In thenexample below, which zone (or subset) of the Venn Diagram will be empty? n

(There are no animals that
are both birds and mammals.)

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nCreatenyour own Euler Diagram. Maybe you could make one that compares andncontrasts insects and spiders, or that illustrates how various typesnof polygons, foods, or mammals are the same and different.