East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A Study on the Existence of the Solution in the Isoperimetric Problem

등주문제에서 해의 존재성 고찰

  • Lee, Hosoo (Department of Mathematics Education, Teachers College (Elementary Education Research Institute) Jeju National University) ;
  • Choi, Keunbae (Department of Mathematics Education, Teachers College (Elementary Education Research Institute) Jeju National University)
  • Received : 2020.02.03
  • Accepted : 2020.02.20
  • Published : 2020.02.29
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Abstract

The isoperimetric problem is a well-known optimization problem from ancient Greek. Among plane figures with the same perimeter, which is the largest area surrounded? The answer to the question is circle. Zenodorus and Steiner's pure geometric proofs, which left a lot of achievements in this matter, looked beautiful with ideas at that time. But there was a fatal flaw in the proof. The weakness is related to the existence of the solution. In this paper, from a view of the existence of the solution, we investigate proofs of Zenodorus and Steiner and get educational implications.

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References

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