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.

Web links

Commons : Vincenzo Viviani - Collection of images, videos and audio files

John J. O'Connor, Edmund F. Robertson : Vincenzo Viviani. In: MacTutor History of Mathematics archive .
Viviani in the Galileo Project (English)
Entry on Viviani, Vincenzo (1622–1703) in the Archives of the Royal Society , London

Individual evidence

↑ Johann G. Hagen : The two independent proofs of the earth's rotation in Foucault's pendulum experiment. In: Natural Sciences . Vol. 18, No. 38, 1930, pp. 805-807, doi : 10.1007 / BF01492518 .
^ List of former members since 1666: Letter V. Académie des sciences, accessed on March 12, 2020 (French).

personal data
SURNAME	Viviani, Vincenzo
BRIEF DESCRIPTION	Mathematician and physicist
DATE OF BIRTH	April 5, 1622
PLACE OF BIRTH	Florence
DATE OF DEATH	September 22, 1703
Place of death	Florence

[1] Johann G. Hagen : The two independent proofs of the earth's rotation in Foucault's pendulum experiment. In: Natural Sciences . Vol. 18, No. 38, 1930, pp. 805-807, doi : 10.1007 / BF01492518 .

[2] List of former members since 1666: Letter V. Académie des sciences, accessed on March 12, 2020 (French).