Symmetry

You once said you were seeing Math with different eyes. That made me very happy.
Here is a video for your curious mind, as well as for your love of ideas and of symmetry. Just click on View video online.

Take a look when you have time to see how Math can be a red thread in the big maze we're living in. Besides, It's a topic I particularly like, and Galois' theory and the symmetries groups were part of my work for a teaching degree years ago.

The image is one of Escher's symmetry drawings. More of his works here.
Click on Picture Gallery, and then Symmetry.

Good thoughts.

Beditime reading

Actually, it's my English dictionary.
Have a peaceful night.

Beauty

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Ages

Salt

I was unpacking the things I've just bought in the market today, including a pack of salt (although I should stop having salt, but apparently this is very hard to do) and I am wondering how many kilos of salt have we had together in these 25 years and how many more are we going to have.
Salt is one of those small and meaningful things in our every-day life and it was always seen as important. Remember our tradition of welcoming guests with bread and salt? And there is the phrase, mostly used in tales: "if you do that, we will never have bread and salt together", an archaic warning for a close friend who's about to do something really bad. Do you have the belief that spilling salt announces a big quarrel?

Speaking of tales, there is a nice one about salt, you probably know it, as I have learned that there are really no specific things- people are the same everywhere. Here it goes.
A king had 3 daughters and no son. As he was getting old, he decided to choose as his heiress the daughter who loved him the best, so he asked them how precious he was for them. The first one answered that he was as sweet as sugar to her, the second- as sweet as honey, but the third daughter just said: I love you as the salt in my food. The king was angry for being compared to such a meaningless thing, so he banished her from his court.
The girl wandered for a while and arrived to another king's castle (as they are everywhere, right?) and she became a cook helper there. She was kind and trustworthy, so everyone liked her. Fortunately, she was the only one who managed to cure the prince who had been badly wounded in a battle, and because she had saved his life, he decided to marry her. Her father was invited too, as he was the "neighbour king", but he had no idea the bride was his daughter. Strangely for him, during the feast he noticed that all his food was sweet and therefore impossible to eat (we don't eat sweet main courses) while everybody else had normal tasty food. So, he asked for an explanation from the cook. That was the moment when the girl revealed herself and the king understood the message. He humbly apologized and the family was happily reunited and etc etc... ever after.

And finally, look at the geometry in the salt crystals. (The photo is from guardian.co.uk.)
How about small things in our daily life? How small are they really?

what joins people

I'm not a football supporter but I understand that sometimes it can be the unique way to gather people in a common cause.
El Chico Square has changed its traditional architecture to host these tents where you can have a drink and something to eat while you are waiting for the football match to start. I mean, the one today, that's to say: Spain.
There is nobody in the streets, two hours before the match there were already people in El chico.
It's amazing the calling power a football match can have.

Old photos

I can't sleep and I'm going through old photos taken 3 years ago by the Danube, just trying to relax or maybe looking for answers. Here is what they are saying, useless maybe:

There is an end to every storm.

A bridge over precipice.

An end to any loneliness.


A way though any mountain.

...if you just keep afloat!

Good thoughts. Good night.

in nature

Coming back from Valladolid, where we went to take half a life back home, we got this view. The last light of the sun beyond rain curtains over deserted fields.
There's a kind of beauty that alters our feelings, that one of these moments.

Congratulations

You may say it was not demanding, but it was serious work done by you. So, here you have a bunch of roses I have "cut" in my walks. some of them have even water drops from the rain.
Congratulations.

and nevertheless

Despite this kind of feeling, I can also get good moments for doves. Look at these ones: beyond the bars and outside. What do they do it for? What is the one inside thinking about? Ill? tired? Why doesn't the one outside fly away? Company? tired?
I will never know. but there they were as I was walking.

A Visitor

This guy is visiting me tonight. He is quite gentle and a book lover, he's handsome inside and outside, so I'm keeping him as long as my cat can stay away from him. Then, I will carefully send him out, without harming him, I hope. It will be a short affair! :)

Borrowed

Sometimes we "borrow" the hobbies of the ones we love, maybe as an effort to understand them better, maybe in our desire to share.
I have not got as far as to like trains, but I became truly fond of old cars. Perhaps because they stimulate my imagination and take me in times that might have been if not easier to live in, at least less alienating.
Anyway, I do enjoy their grace, their elegance and the stories they tell.
The photos are also borrowed from my son, Sorin was not so well and it was horribly hot to go out. But at 24 years old, 36 degrees are still OK.
I will only post a few, it might not be your cup of tea. Or is it? :)

Holidays

Summer holidays start for us today. Of course, we still have things to do in school for about 2 weeks and I have a short course to attend next week, but no classes. I'm literally "burnt out", I could not have survived if it took longer.
I think you still have a week do go, right? I hope you can cope with it and things are better.
Take care and have an easy school-year end!

No, you can't use the computer!

Please don't insist! It's final.

:) Have a nice day!

An ending

The 8th graders said good-bye today. I was not expecting to survive and see this day all those days when I came out of their classroom a wreck. I came home relieved but with a bitter feeling. Maybe it's my fault.
They had a ceremony with speeches, weeping and bla-bla. I could not even pretend to be touched, nor tell them that I loved them as the others did. Maybe my capacity of forgiving has decreased. I just told them that everything I had to say to them I had said during this school-year, and I'd be happy to know anybody had heard me. Wished them luck and gave a quote. It was the coldest and shortest speech of all their teachers. Just want them out of my life. I did not accept their graduation party invitation. I guess I'm turning into the regular bitter, limited middle-aged female Math teacher with no sense of humour.
How was the strike, any success?
Maybe I should not even ask.
Sorry to keep going with this.

Frustrating

Here is (on my small Maths site) what I have been working on for 3 afternoons and 2 half-nights.
It's an illustration for the formula for adding consecutive numbers (the purple squares) by adding the reversed sum. The 2 staircases form a rectangle whose area is easy to find: n*(n+1), so the sum is half of that.
I tried to make it for the Math group.The illustration is not a success and it requires more work, but it will stay like that because I decided I will not invest more of my life into it. It's very frustrating because what worked up to the 9th row did not work for the 10th. All was well until I closed the file, then the 10th row went mad, making weird shapes. When I tried to undo steps, I did not get to points I had been in, but in other situations. I must be a complete idiot. I gave up and stopped at n=9.
The group moderator was not able to explain how she did- she solved it in another way, but I wanted to do it my way. It took her a whole week to do it. As she was not able to help me embed the html in Blogger, even if she could do it in her blog.
It is very frustrating to follow instructions and get no result. And discussing Math in a foreign language is too much.
I MUST be a complete idiot.