appreciation of the gracious donation of Professor Basil
Gordon (UCLA) to my works, I dedicate the following results
to him. These observations were initiated by his remarks,
about the proportions of the circular Optimal Cylinder,
during the Apostol's 50-year-at-Caltech-celebration-Lunch,
Caltech , Athenaeum, October 4, 2000.
Cylinder provides Maximal Volume
Total Surface Area.
Base, its Height equals the diameter of the Base (Classical
Here is my
"Basilic" generalization of this classical problem:
If the Base
has a given Shape, which is arbitrary, but fixed,
what are the
"proportions" of such Optimal Basilar Cylinder?
Specific cases have
interesting interpretations too: when the
Base is polygon, particularly
circumscribed around a circle.
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