Other contributions and legacy

Other contributions

The complete list would take up an entire book. Some highlights:

Euler’s straight line: in every triangle, orthocenter, centroid and circumcenter are aligned.
Euler-Mascheroni constant: $\gamma \approx 0{,}5772$, the difference between the harmonic series and the natural logarithm.
Mechanics and fluids: Euler’s equations for fluids and for the rotation of rigid bodies.
Calculation of variations: the Euler-Lagrange equation, the basis of modern physics.
Special functions: the gamma function, which extends the factorial to non-integer numbers.

Euler lived between Basel, Saint Petersburg and Berlin, and produced half of the work while almost blind.
He gave mathematics the notation $f(x)$, $e$, $i$, $\Sigma$ and popularized $\pi$.
Found that $\sum \frac{1}{n^2} = \frac{\pi^2}{6}$ and that $e^{i\pi} + 1 = 0$.
He named the number $e = \lim (1 + 1/n)^n$, which arises from compound interest and is the base of the natural logarithm.
Solved the spring equation with $e^{rt}$ and its formula: the solution is a sinusoid.
With the Königsberg bridges, he created graph theory.
With $V - A + F = 2$, he explained why every classic football has 12 pentagons.
He linked prime numbers to calculation and created the theorem that protects the internet today.