# Vincenzo Viviani

Vincenzo Viviani (born April 5, 1622 in Florence , † September 22, 1703 ibid) was an Italian mathematician and physicist .

## Life

In 1639 he became an employee of Galileo Galilei and also wrote the first biography about him. Furthermore, he reconstructed the writings of Archimedes and Euclid and carried out experiments on pendulums. In 1661 he observed a clockwise deflection on long pendulums, which according to current knowledge proves the rotation of the earth (see Foucault's pendulum ). With the scientific means of his time, however, he could not interpret this effect, but only viewed it as a disruption of his attempts, which he was able to eliminate successfully through bifilar suspension. In 1666 he became the court mathematician of Grand Duke Ferdinand II. In 1696 he was elected a member ( Fellow ) of the Royal Society . Since 1699 he was a member of the Académie royale des sciences in Paris.

## Vivian body

The intersection of the unit sphere with the solid cylinder

${\ displaystyle \ left \ {(x, y, z) \ in \ mathbb {R} ^ {3} \, {\ big |} \, x ^ {2} + y ^ {2} \ leq x \ right \}}$ is called a Vivian body. He owns the volume${\ displaystyle V = {\ frac {2 \ pi} {3}} - {\ frac {8} {9}} \ approx 1 {,} 2055,}$ as can be demonstrated by integration in polar coordinates .

## Viviani window

The intersection of the unit sphere with the full half cylinder ${\ displaystyle S ^ {2}}$ ${\ displaystyle \ left \ {(x, y, z) \ in \ mathbb {R} ^ {3} \, {\ big |} \, x ^ {2} + y ^ {2} \ leq x, \ z \ geq 0 \ right \}}$ is called Viviani window . It owns the area${\ displaystyle A = \ pi -2 \ approx 1 {,} 1416}$ and the circumference , where the complete elliptic integral is type 2 . ${\ displaystyle U = 2 {\ sqrt {2}} \ cdot \ mathrm {E} \ left ({\ frac {1} {2}} {\ sqrt {2}} \ right) \ approx 3 {,} 8202 }$ ${\ displaystyle \ mathrm {E} (k)}$ ## Viviani moon crater

The lunar crater Viviani is named after him.