[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 363
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Те если запрокинуть голову набок так чтоб глаза были по вертикали то зеркало поставит ваше отражение с ног на голову так чтоли?
That's what I was thinking. But it's a brain thing. We know we've turned our heads. I read somewhere about an experiment where they put glasses on people to change what they see. They turned them upside down, if I'm not mistaken. There was a loss of vision, but it was quickly restored. The brain turned the picture upside down as it thought it should be.Еще одна:
У двух братьев было стадо баранов. Они продали его и за каждого барана получили столько рублей, сколько голов было в стаде. Выручку стали делить пополам. Старшему брату – десятку, младшему – десятку и так несколько раз. Потом старший брат взял свою десятку, а младшему несколько рублей не хватило. Тогда старший вынул из кармана нож и отдал брату в компенсацию за недостающую сумму.
Спрашивается, сколько стоит нож?
Surprisingly (to me), all squares of integers with an odd number of tens end in sixes. The total: the knife cost 2 roubles.
Я тоже про это подумал. но там ужеработает мозг. мы же занем что повернули голову. Гдето читал.про эксперимент.людям одевали очки которые изменяли видимое ими. Что то там переворачивали. если не ошибаюсь с ног на голову. Происходила потеряоринтации, но они быстро востанавлиались. мозг переворачивал картинку так как считал правильнымYes there is such effect-vision, if to put on glasses which all overturn that vision will soon get used and all becomes as it was and here if to remove that the person appears walking on a ceiling (even on itself has checked it works), but here to a mirror it has no relation.
The whole point is that the point symmetry (in 2D) tends to flip the image along two coordinates,
but axial only flips one, hence the flip effect.
Same inheritance in 3D, the plane does not flip in one of the coordinates.
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Some time ago (before the date of building communism, which turned out to be the Olympics))) I thought that I had thought up this problem-joke. I asked it to everybody and it sounded like this: Explain to me in a nutshell why in the mirror left-right change, but top-bottom do not.
But apparently, it's impossible to come up with something that hasn't already been invented in this field.)
Все точки плоскости раскрашены в красный или белый цвет. Докажите, что найдутся хотя бы две точки одного цвета, расстояние между которыми равно 1 см.
Proved.
MD, super, both of them are valid (about sheep and about 1 cm).
About the mirror - let's add some wood: the rotation of the DNA helix in all living organisms that have it is reversed. The mirror reflects life, impossible on Earth. And what does this have to do with the human brain and other psychiatry?
P.S. I don't know the right answer myself. But it seems that Urain has found the way to it: mirror makes symmetry relatively to the plane that reverses the rotation: vector product from right-handedness turns into left-handedness. And reversing the top and bottom requires central symmetry, which the mirror does not possess (the lens does).
Next:
Can a cart ride without jolting on a flat surface on non-circular wheels?
Richie, you have a chance to show your erudition in technical matters. Generally speaking, the problem is still essentially mathematical...
One last one:
Suppose there are several aliens. Each has at least two fingers on their hand, with the total number of fingers on all the aliens having the same number of fingers. It is known that they can have different number of fingers on different hands. If you count all the fingers in the room, you can find out how many aliens are in the room. The number of fingers is somewhere between 200 and 300. How many aliens are in the room?
Еще одна напоследок:
Пусть есть несколько инопланетян. У каждого на руке не меньше двух пальцев, причём общее количество пальцев на руках у всех инопланетян одинаковое. Известно, что они могут иметь разное число пальцев на разных руках. Если пересчитать все пальцы в комнате, то можно узнать, сколько инопланетян находится в комнате. Число пальцев где-то между 200 и 300. Сколько инопланетян в комнате?
Next:
Can a wagon drive without shaking on a flat surface on non-circular wheels?
Richie, you have a chance to show your erudition in technical matters. Generally speaking, the problem is still essentially mathematical...
Why not? The whole secret is not the surface, it's the wheels.
What is the erudition here, I know the thing well, as I have had to deal with rotary compressors in my life. The secret lies in the "smoothed triangularity" of the wheel, the same shape of the bearing wheel and the "smoothed squareness" of the bearing cage. Incidentally, there are electromagnetic dampers that allow you to "intelligently" compensate for irregularities, but that's another topic.