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Area of Spherical Zones Hahnemühle German Etching Print

Area of Spherical Zones Hahnemühle German Etching Print

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Slice an orange by equally-spaced parallel planes. Which pieces have more zest, those near the middle, those near the ends, or something else? It turns out (in the mathematical abstraction) they all have exactly the same amount!

Mathematically, a zone on a sphere (the region between two parallel planes) has the same area as the cylindrical band on the circumscribed cylinder whose axis is perpendicular to the cutting planes. This theorem, known to Archimedes, has modern generalizations related to "symplectic geometry" and "moment maps." It also points to a beautiful parametrization of a surface of rotation, using as parameter not the distance along the axis or the arc length along the surface, but the zonal area.

Printed on archival quality Hahnemühle German etching paper (310gsm) with a velvety surface.
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