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- Title
Unit shapes and a wealth of calculus problems.
- Authors
Donnelly, Robert G.; Thome, Alexander F.
- Abstract
For a given family of similar shapes, what we call a "unit shape" strongly analogizes the role of the unit circle within the family of all circles. Within many such families of similar shapes, we present what we believe is naturally and intrinsically unital about their unit shapes. We present a number of calculus problems related to extremal questions about collections of unit shapes, and we recapitulate some isoperimetric problems in terms of unit shapes. We close by presenting some problems (some of which are open) and by proffering perhaps a new perspective on the π vs. τ debate.
- Subjects
ISOPERIMETRICAL problems; PYTHAGOREAN theorem; WEALTH; ISOPERIMETRIC inequalities
- Publication
Mathematics Enthusiast, 2021, Vol 18, Issue 1/2, p10
- ISSN
1551-3440
- Publication type
Article
- DOI
10.54870/1551-3440.1510