Archimedes's Tomb

Archimedes's tomb

volume: 1 : 2 : 3

sphere
cylinder

Archimedes asked for a representation of a cylinder circumscribing a sphere on his tomb. Also his result on the ratio of the volumes of the two should be noted. He was proud of his discovery regarding the volume of a sphere, showing that it is two-thirds the volume of the smallest cylinder that can contain it. The volume of a cylinder

C

of radius

r

and height

2r

is

2rπ×

2

r

=2π

3

r

; the volume of a sphere

S

of radius

r

is

4

3

π

3

r

. Furthermore, the volume of a bicone is half that of the smallest sphere that can contain it. Therefore these three volumes behave as 1: 2: 3.

Details

For more information see:

Biography of Archimedes (The MacTutor History of Mathematics Archive)

Tomb of Archimedes (Courant Institute of Mathematical Sciences)

External Links

Bicone (Wolfram MathWorld)

Cone (Wolfram MathWorld)

Sphere (Wolfram MathWorld)

Cylinder (Wolfram MathWorld)

Cylinder Hemisphere Cone

Archimedes' Hat Box Theorem

Biography of Archimedes (ScienceWorld)

Permanent Citation

Ralf Schaper, Wolfram Koepf

"Archimedes's Tomb" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/ArchimedessTomb/
Published: July 1, 2011

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