[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 126
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And I have a neat solution to a geometric problem, if anyone remembers it ("There are two circles and a point. Construct a segment whose ends lie on the given circles and whose middle is at the given point"). Well, here's half an hour ago.
Interesting. Come on. :-)
Interesting. Spill it. :-)
I figured it out. Yes, it's a beautiful solution.
Interesting that this method not only detects if there is a solution, but also finds all possible ones at once.
Подсказка: решение всплыло в голове как раз после того, как увидел решение alsu.
Uh-huh, beautiful :), decided, saw the clue and made sure the same way :)
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ZS: now you can really get stoned :)
Well, maybe other maths enthusiasts want to solve it too. The solution is really beautiful - especially when you remember that it was given a few days ago, and I've been torturing her all these days. So, do I need a shot?
P.S. Well, spit it out, then...
OK, here's my solution: we choose a circle (say, 2) and construct its centrally symmetric image relative to our point. One of the intersection points of the circle 2' with 1 (there are at most two, minimum zero) defines one end of our segment.
I was a simpler person and was looking at something like a stripe or stripe system. But it's a little more deliberate. Kudos for the imagination :)
P.S. But why multiples of Pi? Maybe odd multiples of Pi/2?
P.P.S. Next: Is the exact square of a number whose decimal notation consists of 1999 threes?
Pardon, again very simple :(
the exact square cannot end in 3 :)
can we move on to 7th grade?:)))))
Speaking of aeroplane: google "Myth busters" and "taking off an aeroplane" -- these lunatics put it to the test.
The plane took off. :)
Thank you, Sveta. This is a decisive contribution to the struggle for truth. The final and final verdict. Not subject to appeal. :-)
Especially for Farnsworth.
Here http://dic.academic.ru/dic.nsf/ruwiki/922900 is a fairly competent analysis of all the details of the problem, as well as the incongruities and contradictions in the various formulations and interpretations of its condition.
And here the criterion of truth is practice. The takeoff of the plane from the conveyor belt.
Episode 1: https://www.youtube.com/watch?v=KSBFQOfas60
Episode 2: https://www.youtube.com/watch?v=YORCk1BN7QY&feature=related
Oh, I hadn't thought of that. I had a different solution.
Next: Prove that the number 4n + 15n - 1 is divisible by 9.
I was a simpler person and was looking at something like a stripe or stripe system. But it's a little more deliberate. Kudos for the imagination :)
P.S. But why multiples of Pi? Maybe odd multiples of Pi/2?
It's like pi, as far as I'm concerned. The CSs would be the points of maxima and minima, i.e. 0 and pi. And where pi/2 there is no symmetry even locally. The cosines are displaced, after all.