[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 97
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2 Candid: циркуля нету, сын рисует прямо сейчас. Да и концентрироваться на приближенном решении, наверно, не стоит - хотя оно может быть вполне элегантным.
It is simply hoped that when they are precisely constructed they will suddenly lie on a line or a circle, then there will be extra stimulus to think about where that line or circle arises from.
Let's give it a try. I'll try to rent a circular from my son. Although you can probably do it without him.
В квадрате отметили по точке на каждой стороне, а сам квадрат стёрли. Восстановите его.
Mark points A, B, C, D on the circle.
draw a line parallel to AC through point B,
from this line create a perpendicular line going through point B,
from point B on that perpendicular line, take a line segment equal to AC, on the D side, we will have point E.
The line DE will be one of the sides of the square.
then it is simple, parallel-perpendicular :)
R.S.: quadrilateral ABCD doesn't have to be a square.
Exactly, Swan! It was enough to construct another "diagonal" equal to the AC and perpendicular to it.
Давай попробуем. Я буду пытаться арендовать циркуль у сына. Хотя, наверно, и без него можно.
So, Swan has cancelled it looks like. We'll have to think about his decision some more.
P.S. Yes, that's it, I agree.
Obviously, the construction does not work when the diagonals are perpendicular (the quadrilateral is not a square) - the same AC and BE. Maybe here too the square is any arbitrary rectangle circumscribed around this quadrilateral? Let's check on our equation...
Очевидно, построение не работает, когда диагонали перпендикулярны (четырехугольник - не квадрат) - те же АС и ВЕ.
Yes, parallel is unnecessary, a perpendicular to AC is possible.
What to do if AC is perpendicular to BD remains to be solved.
Так, хоть виде чучела, хоть в виде тушки, но из ветки надо сваливать :)
there, there :-)))Так, Swan отменил похоже. Надо ещё пообдумывать его решение.
Seems about right. Nice. Really compact and witty.