Euler, Calculus of Variations and Mast on a ship

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SUMMARY

Euler's work on optimizing mast placement on ships, first presented in 1727 during the Paris Academy Prize Problem competition, is a foundational topic in the Calculus of Variations. The discussion highlights the need for modern interpretations of Euler's methods, particularly how they would be articulated using contemporary terminology and teaching methods. Participants seek accessible resources, including translations of Euler's original Latin paper, to better understand his approach and its application today. Key references include a PDF detailing Euler's ship theory and an online repository of his works.

PREREQUISITES
  • Understanding of Calculus of Variations
  • Familiarity with optimization problems in physics
  • Basic knowledge of historical mathematical literature
  • Ability to read mathematical Latin or access translation resources
NEXT STEPS
  • Research modern applications of Calculus of Variations in engineering
  • Explore online resources for translations of historical mathematical texts
  • Study optimization techniques in ship design
  • Examine Euler's original works available at scholarly repositories
USEFUL FOR

Mathematicians, engineering students, historians of science, and anyone interested in the application of historical mathematical principles to modern engineering challenges.

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TL;DR
How did Euler use the calculus of variations to place a mast on a ship?
From Wikipedia:

"In 1727, [Euler] first entered the Paris Academy Prize Problem competition; the problem that year was to find the best way to place the masts on a ship."

Does anyone know how he did this?

Is there an on-line paper? (But what that is accessible with today's knowledge).

And by that, I do not mean as he did it (for I fear a paper of his work will be dense with geometry) but more: "how would he do it today, equipped with today's "dialect" of how the Calculus of Variations is taught?"
 
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wrobel said:
how is the problem stated exactly?

I do not have a clue. I am not being facetious. I just don't know. I have read from several sources that he did what the wikipedia article says, but I have not clue as to anything more than that.
 
then I do not see a matter of the discussion
 

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