[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 96
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Решение я привёл сверху: https://www.mql5.com/ru/forum/123519/page94,
It's not a solution, Richie. I can give a single identity with trigonometry, which is enough to solve to know the angle to the chosen side, under which we draw the first line. But I can't draw to show what corresponds to what.
2 Candid: of course, we are only talking about the exact solution obtained in a finite number of steps.
That's not the solution, Richie.
Why not? All the unknowns have been found.
No, it is not the unknowns that are found, but only some connections between them.
No, the unknowns are not found, but only some connections between them.
You mean the system can't be solved?
Да нет, в общем случае условия для углов дают прямоугольники, условия для сторон - ромбы, и только их пересечение - квадрат. Это решается графически, вопрос в том, точное решение будет или приближённое. Вот то что я описывал раньше будет точным только если указать способ построения точной траектории вершин промбов. Без этого вершины ромба можно подвести сколь угодно близко к геометрическому месту вершин прямоугольников, то есть к окружностям, но это будет приближённым решением.
I'm afraid you are wrong and so is TheXpert, you don't take into account that the size of a square can change while remaining a square :-)And the dots will still be on the sides of the square.
Хотети сказать систему решить нельзя?
I won't count the number of unknowns. But you haven't solved it.
2 xeon: so far I know of only one case where the square changes while remaining a square. This case, degenerate, was highlighted by TheXpert himself.
Mathemat писал(а) >>
2 xeon: so far I know of only one case where a square changes while remaining a square. This case, degenerate, was highlighted by TheXpert himself.
Yes.
I just have a thought that there may be 2 solutions (in the non-degenerate case), just because of the second order of equations.
However, unambiguous graphical construction of this question probably clears it up.
But where is it... :)
размер квадрата может изменятся, при этом оставаясь квадратом :-)при этом точки будут так-же оставатся на сторонах квадрата.
But it seems not, only orientation can change and only in degenerate case, but not length of sides. Your construction is approximate, even by eye you can see misses of points. However, I will not prove my assertion.
I'd be curious about TheXpert's solution, because I don't think mine is pretty and/or elegant. But he doesn't say anything.
There is also a very simple system of 3 equations - provided we have the lengths of both diagonals and an angle between them that is not larger than a straight line (which we have and it is rigidly defined). By solving this system, we can arrive at a single equation defining the length of the side. But it will be 4th order with respect to the unknown (although solvable with a compass and ruler).
2 Candid: I don't have a compass, my son is drawing one right now. And concentrating on an approximate solution is probably not a good idea - although it may be quite elegant.