Question

What is the shape of the closed curve, enclosing a given area, for which the length is stationary. 

   What is the shape of the closed curve, enclosing a given area, for which the length is stationary.
m820 Calculus of variations and advanced calculus
m820 Calculus of variations and advanced calculus
D. Richards 1st Edition
Chapter 12, Problem 17 ↓
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What is the shape of the closed curve, enclosing a given area, for which the length is stationary.
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Transcript

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00:01 Hello everyone here we have a is equal to integral 0 to a y d x and i is equal to integral 0 to a under root 1 plus y dash square into d x so the lagrangian equation will be do h by do y minus d by d by d x into do h by do y dash is equal to 0 this implies lambda minus d by d by d by under root 1 plus y dash square will be equal to 0 and this gives y dash square…
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