Difference between revisions of "Leonhard Euler"

Latest revision as of 22:28, 1 November 2024

Leonhard Euler (1707-1783, pronounced Oiler) was a famous Swiss mathematician. He made numerous contributions to many fields of mathematics and science. Euler is often considered to be one of the greatest mathematicians of all time, along with Isaac Newton, Archimedes, and Carl Friedrich Gauss.

Biography

Euler was born on April 15, 1707 in Basel, Switzerland. Euler's parents were Paul Euler, a pastor of the Reformed Church, and Marguerite Brucker, a pastor's daughter. He had two young sisters, named Anna Maria and Maria Magdalena. At the age of thirteen he enrolled at the University of Basel.

On January 7, 1734, he married Katharina Gsell. The young couple had thirteen children, only five of whom survived childhood.

After suffering a near-fatal fever in 1735, Euler became nearly blind in his right eye in 1771. Soon after his return to Russia in 1766, he became almost completely blind in his left eye. Despite his horrible eyesight, Euler continued his prolific research.

Even as an old man, Euler was famous for being able to calculate difficult arithmetic quickly in his head.

On September 18, 1783, Euler passed away in St. Petersburg, Russia after suffering a brain hemorrhage. He was buried in the Alexander Nevsky Monastery.

Contributions to Mathematics

In 1735, Euler showed that $\zeta(2) = \frac{\pi^2}6$ where $\zeta$ is the zeta function.
Euler's polyhedral formula states that for any convex polyhedron, with $V$ , $E$ and $F$ denoting the number of vertices, edges, and faces, respectively, $V-E+F=2$ .
Euler's totient theorem is a theorem related to Euler's totient function, or the sum of all numbers relatively prime to a number and less than it.
Euler's identity is a famous identity of complex numbers which states that $e^{i\theta}=\cos(\theta)+i\sin(\theta)$ for all $\theta$ .

Functions

Euler was the first to use the notation $f(x)$ , and also was the first to call such structures functions. This led to great advancements in calculus and algebra.

Analysis

Euler contributed greatly to the expansion of a branch of mathematics called analysis. His achievements often involved power series. He is also credited with discovering Euler's constant, denoted as $e$ . Euler discovered that

$e^x = \sum_{n=0}^\infty {x^n \over n!} = \lim_{n \to \infty}\left(\frac{1}{0!} + \frac{x}{1!} + \frac{x^2}{2!} + \cdots + \frac{x^n}{n!}\right)$

He also discovered the power series for the arctangent, which is

$\lim_{n \to \infty}\left(\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \cdots + \frac{1}{n^2}\right) = \frac{\pi ^2}{6}$

Physics

Euler helped the wave theory of light become the dominant idea for most of the nineteenth century. He also made several other contributions to optics, such as disagreeing with Isaac Newton's theory of light.

In addition, he made several important discoveries in astronomy and mechanics.

External Links

Biography of Euler

@@ Line 1: / Line 1: @@
-{{stub}}
+'''Leonhard Euler''' (''1707-1783'', pronounced ''Oiler'') was a famous Swiss [[mathematician]].  He made numerous contributions to many fields of [[mathematics]] and [[science]]. Euler is often considered to be one of the greatest mathematicians of all time, along with [[Isaac Newton]], [[Archimedes]], and [[Carl Friedrich Gauss]].
-'''Leonhard Euler''' (pronounced ''Oiler'') was a famous Swiss [[mathematician]].  He made numerous contributions to many fields of [[mathematics]] and [[science]]. Euler is considered to be one of the greatest mathematicians of all time.
 == Biography ==
@@ Line 8: / Line 6: @@
 On January 7, 1734, he married Katharina Gsell. The young couple had thirteen children, only five of whom survived childhood.
-After suffering a near-fatal fever in 1735, Euler became nearly blind in his right eye. Soon after his return to Russia in 1766, he became almost completely blind in his left eye. Despite his horrible eyesight, Euler continued his prolific research.
+After suffering a near-fatal fever in 1735, Euler became nearly blind in his right eye in 1771. Soon after his return to Russia in 1766, he became almost completely blind in his left eye. Despite his horrible eyesight, Euler continued his prolific research.
-''More information needed.''
+Even as an old man, Euler was famous for being able to calculate difficult arithmetic quickly in his head.
 On September 18, 1783, Euler passed away in St. Petersburg, Russia after suffering a brain hemorrhage. He was buried in the Alexander Nevsky Monastery.
-Euler lost sight in his right eye in 1735, and in his left eye in 1766. Nevertheless, aided by his phenomenal memory (and having practiced writing on a large slate when his sight was failing him), he continued to publish his results by dictating them.
+== Contributions to Mathematics ==
+* In 1735, Euler showed that <math>\zeta(2) = \frac{\pi^2}6</math> where <math>\zeta</math> is the [[zeta function]].
+* [[Euler's polyhedral formula]] states that for any [[convex]] [[polyhedron]], with <math>V</math>, <math>E</math> and <math>F</math> denoting the number of [[vertex|vertices]], [[edge]]s, and [[face]]s, respectively, <math>V-E+F=2</math>.
+* [[Euler's totient theorem]] is a theorem related to [[Euler's totient function]], or the sum of all numbers relatively prime to a number and less than it.
+* [[Euler's identity]] is a famous identity of [[complex numbers]] which states that <math>e^{i\theta}=\cos(\theta)+i\sin(\theta)</math> for all <math>\theta</math>.
+=== Functions ===
+Euler was the first to use the notation <math>f(x)</math>, and also was the first to call such structures [[function]]s. This led to great advancements in [[calculus]] and [[algebra]].
+=== Analysis ===
+Euler contributed greatly to the expansion of a branch of [[mathematics]] called [[analysis]]. His achievements often involved [[power series]]. He is also credited with discovering [[Euler's constant]], denoted as <math>e</math>. Euler discovered that
+<cmath>e^x = \sum_{n=0}^\infty {x^n \over n!} = \lim_{n \to \infty}\left(\frac{1}{0!} + \frac{x}{1!} + \frac{x^2}{2!} + \cdots + \frac{x^n}{n!}\right)</cmath>
+He also discovered the power series for the [[tangent function|arctangent]], which is
+<cmath>\lim_{n \to \infty}\left(\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \cdots + \frac{1}{n^2}\right) = \frac{\pi ^2}{6}</cmath>
-== Contributions ==
+==Physics==
-* In 1735, Euler showed that <math>\zeta(2) = \frac{\pi^2}6</math> where <math>\zeta</math> is the [[zeta function]].
+Euler helped the wave theory of [[light]] become the dominant idea for most of the nineteenth century. He also made several other contributions to [[optics]], such as disagreeing with [[Isaac Newton]]'s theory of light.
-* [[Euler's polyhedral formula]]
-* [[Euler's totient theorem]]
+In addition, he made several important discoveries in [[astronomy]] and [[mechanics]].
-* [[Euler's identity]]
-* [[Eulerian graph]]
 == See Also ==
 * [[Euler's line]]
+* [[Euler's identity]]
+* [[Euler's constant]]
+==External Links==
+* [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Euler.html Biography of Euler]
-[[Category:Famous Mathematicians]]
+[[Category:Famous mathematicians]]
+[[category:Mathematicians]]

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