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- Napkin_ring_problem abstract "In geometry, the volume of a band of specified height around a sphere—the part that remains after a hole in the shape of a circular cylinder is drilled through the sphere—does not depend on the sphere's radius.Specifically, suppose the axis of a right circular cylinder passes through the center of the sphere and the height (defined as distance in a direction parallel to the axis) of the part of the boundary of the cylinder that is inside the sphere is h, and the radius of the sphere is R. The "band" is the part of the sphere that is outside the cylinder.The result is that the volume of the band depends on h but not on R.As the radius R of the sphere shrinks, the diameter of the cylinder must also shrink in order that h can remain the same. The band gets thicker, and that would increase its volume. But it also gets shorter in circumference, and that would decrease its volume. The two effects exactly cancel each other out. The most extreme case, involving the smallest possible sphere, is that in which the diameter of the sphere is the same as the height h. In that case the volume of the band is the volume of the whole sphere: An early study of this problem was written by 17th-century Japanese mathematician Seki Kōwa. According to Smith & Mikami (1914), Seki called this solid an arc-ring, or in Japanese kokan or kokwan.The "Napkin Ring Problem" is called so because after removing a cylinder from the sphere, the remaining band resembles the shape of a napkin ring.".
- Napkin_ring_problem thumbnail Sphere_bands.svg?width=300.
- Napkin_ring_problem wikiPageID "21693427".
- Napkin_ring_problem wikiPageRevisionID "538719895".
- Napkin_ring_problem hasPhotoCollection Napkin_ring_problem.
- Napkin_ring_problem title "Spherical Ring".
- Napkin_ring_problem urlname "SphericalRing".
- Napkin_ring_problem subject Category:Articles_containing_proofs.
- Napkin_ring_problem subject Category:Japanese_mathematics.
- Napkin_ring_problem subject Category:Mathematical_problems.
- Napkin_ring_problem subject Category:Recreational_mathematics.
- Napkin_ring_problem subject Category:Volume.
- Napkin_ring_problem type Abstraction100002137.
- Napkin_ring_problem type Attribute100024264.
- Napkin_ring_problem type Condition113920835.
- Napkin_ring_problem type Difficulty114408086.
- Napkin_ring_problem type MathematicalProblems.
- Napkin_ring_problem type Problem114410605.
- Napkin_ring_problem type State100024720.
- Napkin_ring_problem comment "In geometry, the volume of a band of specified height around a sphere—the part that remains after a hole in the shape of a circular cylinder is drilled through the sphere—does not depend on the sphere's radius.Specifically, suppose the axis of a right circular cylinder passes through the center of the sphere and the height (defined as distance in a direction parallel to the axis) of the part of the boundary of the cylinder that is inside the sphere is h, and the radius of the sphere is R.".
- Napkin_ring_problem label "Napkin ring problem".
- Napkin_ring_problem sameAs m.05msyqv.
- Napkin_ring_problem sameAs Q6964957.
- Napkin_ring_problem sameAs Q6964957.
- Napkin_ring_problem sameAs Napkin_ring_problem.
- Napkin_ring_problem wasDerivedFrom Napkin_ring_problem?oldid=538719895.
- Napkin_ring_problem depiction Sphere_bands.svg.
- Napkin_ring_problem isPrimaryTopicOf Napkin_ring_problem.
