Symmetry: the dynamical way

This week we present an awesome multilanguage software, written in Flash for Windows, Mac and Linux platforms. It is a modern presentation of symmetry aimed to students of all levels, including children.


As I am sure by now all readers have figured out, I am lazy. I don’t feel like writing reviews, especially as they would be enthusiastically monotous: the material I’m posting about is, obviously, what I have enjoyed and what my children have enjoyed (everything we post about, has been used and studied by us: this blog, in contrast to other websites out there, does what it says and says what it does). I am posting for two reasons: one is to save others the waste of time in locating quality material among oceans of cheap junk (I hope you appreciate my altruistic spirit). The second one is very selfish: I wish to hear your thoughts, and especially, if you try out the material, to know how you’ve been using it. Of course feel free to ask me similar questions, if you’d like.


Lenin and the subway

Comrade Lenin, as President of the Union of Soviet Socialist Republic, has lots of work to do, and his workdays finish late at night. Lenin has been married for decades with a comrade and activist, since the days of clandestinity, and loves her very dearly, they have shared everything and have built together a new world, and President Lenin would never divorce her. She has surely not become arrogant with power, and lives in a modest but dignified apartment. Comrade Lenin is, of course, not bound by the bourgeois morality and the contradictory bourgeois family structure, and he has a very attractive young girlfriend. She, too, is not corrupt with power and lives in a modest but dignified apartment not far away. Comrade Lenin, who is very scrupulous and very upright, has thought at length about the best arrangements, so that he should be fair to both, and they have found his suggestion a perfect solution. When he finishes working – at a random time in the evening – he walks from the Kremlin to the subway station, and boards the first train that arrives. According to the direction of the train, he will spend the night with his wife or his lover, because it happens that the two apartments are located on the same subway line, but one needs to take the train in opposite directions.

However, on average, in a month, he spends a night with his wife and the rest of the time with his attractive girl. How can this be?

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Two peasant ladies go to the market

It looks like nobody wants to be the first one to publish a post!

I’ll do, but the first post won’t be mine either. This is a problem I read somewhere in a book or article by V. I. Arnol’d.

Two peasant ladies leave simultaneously at dawn because they are going to a farmers’ country market: one lady leaves from town A and is going to B, while the other one is on her way from B to A. They walk at constant speed (each one at her own speed). At midday sharp, they greet each others without stopping and continue on their way.

At 16 (that is, 4 p.m.) the faster lady reaches her destination, and at 21 the other lady arrives, too.

Compute sunrise time.

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