Euler, Calculus of Variations and Mast on a ship

In summary, Euler entered the 1727 Paris Academy Prize Problem competition where the challenge was to determine the optimal placement of masts on a ship. It is not clear how he approached the problem with today's knowledge, as there is no accessible online paper discussing this question. However, it is believed that he utilized his extensive knowledge of geometry and the Calculus of Variations. The original paper is available online in Latin, but no translation can be found at this time.
  • #1
Trying2Learn
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TL;DR Summary
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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  • #3
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.
 
  • #4
then I do not see a matter of the discussion
 
  • #5

1. What is Euler's contribution to the field of calculus of variations?

Euler is credited with developing the fundamental principles and techniques of the calculus of variations, including the Euler-Lagrange equation, which is used to find the extremum of a functional. He also made significant contributions to the study of differential equations and mathematical physics.

2. How does calculus of variations relate to optimization problems?

Calculus of variations is a mathematical tool used to solve optimization problems, which involve finding the maximum or minimum value of a function. It allows for the optimization of a function over a set of possible paths or curves, rather than just discrete points.

3. What is the significance of the Mast on a ship problem in the study of calculus of variations?

The Mast on a ship problem, also known as the Brachistochrone problem, was one of the first problems to be solved using the calculus of variations. It involves finding the shape of a curve that a bead sliding from one point to another in the shortest amount of time, under the influence of gravity. This problem helped to demonstrate the power and usefulness of the calculus of variations.

4. How is the calculus of variations applied in real-world scenarios?

Calculus of variations has applications in various fields such as physics, engineering, economics, and biology. It is used to optimize processes and systems, such as finding the most efficient path for a spacecraft to travel, or the shape of a bridge that can withstand the most weight. It is also used in the study of optimal control and game theory.

5. What are some limitations of the calculus of variations?

While the calculus of variations is a powerful tool, it has some limitations. It is not applicable to all types of optimization problems, and sometimes the solutions it provides may not be unique. It also requires advanced mathematical knowledge and can be challenging to apply in complex scenarios.

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