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Richie, I'm not going to get into an argument with you in an area where everything is solved by practical experience. I don't know the answer. And what I offered was more of a reflection than an answer.
OK, I'll withdraw myself from answering your questions. There are many problems that have a precise, unambiguous solution. I like them much better.
P.S. About the nail in the concrete: there is a hypothesis, but I will not state it here.
in which everything is solved by practical experience
Probably more of a trick. OK, for you there will be problems from the field of mathematics and geometry. I have to be honest, I don't really like maths, although I've done a lot of e-calculus, many of them with an A. I don't like it because most of my maths teachers were not very nice people, to put it mildly.
I'll tell you about hammering a nail into concrete and a diamond a little later.
Не люблю по тому, что большинство моих преподавателей математики оказались не очень хорошими людьми, мягко говоря.
You are just unlucky. In all the places I studied, there was a maths teacher(s), a master of his subject and a good person at the same time.
(Да и сейчас с трудом соображаю как её лепить.) Потому понадеялся на интуицию, которая активно проголосовала за окружность... :)))
Very simple here, with complex numbers solved in mind :)
Let point A be the origin of coordinates and point O, centre Y, be at a distance D to the right of the x-axis (it corresponds to point D = D+i*0 on the complex plane). Any point on the circle (the second vertex of a regular triangle) is the complex number s = D + R*exp(i*fi). The third vertex of the right triangle is the point D rotated clockwise around the origin by Pi/3, i.e. s*exp(-i*Pi/3) = D*exp(-i*Pi/3) + R*exp(-i*Pi/3)*exp(i*fi).
The first term is a constant, and the second term is still a circle.
But were there Americans on the moon?
Can you explain it to me on your fingers?
Geometry question:
There is a ball bearing:
The outer ring of the bearing is stationary.
How many revolutions did the inner ring of the bearing make if the cage made 12 full revolutions? Write the formula.
Consider that the bearing is serviceable and does not spin.
Вопрос из области геометрии:
Есть шарикоподшипник:
Наружное кольцо подшипника неподвижно.
Сколько оборотов сделало внутреннее кольцо подшипника, если сепаратор сделал 12 полных оборотов? Напишите формулу.
Считать, что подшипник исправный и не прокручивает.
V2 = 2*V1
The path taken by the centre of the ball is 12*Pi*D separator.
The path covered by the point on the outer surface of the inner ring in the same time is twice as long.
All that is left is to divide it by the length of the circumference.
2*12*Pi*D separator / Pi*D ring = 24 * (separator/D ring)