Zoriana came up to my office to invite me to a concert Saturday night. OK. Who will be there? Just us. Where will it be? Downstairs. When? In half an hour. I was busy, but had to say yes.
She had it well arranged. A row of kitchen chairs for the audience of three (Oksana, Eddie and me), an array of her mother's drums, cymbals, triangles and other percussion instruments, and an improvised stage.
She played quite a few numbers. She got as much variety as one can achieve with such a limited assortment of instruments: different tempos, different tones from the different drums, different moods. After 15 minutes, just as it was getting old, she had a finale and took a bow. It was a success and I went back upstairs.
20 minutes later I got another invitation. Another concert! She assured me that this time it would be just singing and pretty short. I watch closely as she sang her few songs in Ukrainian. She carries a tune and projects fairly well for a six-year-old. She has stage presence. Her voice balanced out that of her mother when the two of them sang a couple of duets.
I remarked to Oksana that she had done a pretty good job of pulling it together. She had the instruments conveniently arranged so that she could move among them very easily and she seemed to have planned her program. Nope. Mom assured me it was all extemporaneous.
Sunday, at Eddie's seventh grade math Olympiad, there was a short concert in which the students played and performed. A boy play the guitar, a girl played the violin, after which another girl sang a vocal number pretty well to the accompaniment of computer audio of a popular song. Then one of the fathers got up and did a pretty good rendition of a Ukrainian patriotic song which everybody joined in. And then, to my surprise, Zoriana dragged her mother up to accompany her singing some of the songs she had done Saturday. Once again, they did pretty well.
Eddie had dragged me into this math Olympiad. It's a very Ukrainian thing. Two teams – parents and children. They give the teams the same problems and by some complex set of rules that I still don't understand they take turns.
Each team had two hours to prepare the answers. I'm listing my translation of the eight questions at the bottom of this blog. They are challenging!
As I learned by observing and asking afterwards, a representative of one team presents the answer to one of the eight problems and a member of the other team critiques the answer. It isn't just whether the answer is right, but how rigorous is the proof. In my schooling we encountered proofs primarily in geometry, and the 10th grade.
Eddie was the first one up on the kids’ team. He had to critique the answer that the parents' team gave to question six below. I thought that the parent did a good job of explaining it. Apparently so did Eddie – he didn't have any critical questions about the proof. And the parents seem got 12 points and the kids got none.
For the next question, a kid presented the kids' team answer to another of the geometry questions. I thought, piece of cake. The kid got it right. However, the parent was able to come up with so many questions concerning the proof that the parents team got the bulk of the points for that one. I still don't understand why.
And so it went, back and forth. The parents predominated. What really impressed me was the presence of these seventh grade kids. Chirpy little guys speaking with great confidence, conviction, and knowledge of what they were doing. And I say guys! All of the parents participating were men, and if there was a girl among the kids' participants I don't remember her. I sat watching in admiration, with a sense of great satisfaction that the rising generation in Ukraine is going to be self-assured and well-educated.
I understand most questions in Eddie's homework, but I didn't understand any of these questions in Ukrainian below except for number one. I was happy to have the excuse of language. As I translate them today, I find that I could not have answered them anyhow. I spent all of my time trying to solve problem number one with simultaneous equations, while a tickle in the back of my brain told me there was an easier way. Yes there was! Can I blame the fact that I didn't see it on the stuffy head resulting from my cold? That would be comfortable, but I'm not sure it would be right.
That was how we spent the weekend. There comes a time when the older generation has to step back and give the younger generation their place in the sun. I may not be up to this stuff, but I'm glad that the kids are.
The temperature remains in the mid-20s and one member of the family or another always seems to be sick. I'm getting over my third cold of the season – that's kind of a record – and Zoriana seems to have caught hers. What can it be? Virus shedding as a consequence of recent mRNA jabs is getting a lot of press in the United States, but I don't think it applies here. Most people didn't get vaccinated even three years ago, and nobody we know has talked about getting the boosters. I think it is just the consequence of a cold winter. The mainstream media (amazingly) recently showed a map to the effect that the northern hemisphere snow cover is at a recent record. That's certainly the case here. I don't know which is the stronger refutation of global warming: the snow cover, the thick ice, or the temperatures hovering in the mid teens Fahrenheit and dipping into is the single digits periodically.
That's the news from Lake WeBeGone, where the strong man has completed collecting, categorizing and uploading all of his book reviews that Amazon deleted. Along the way I found close to 100 reviews that they had either orphaned by discontinuing the books or refused to post. That gives me something to write about next time.
7th Grade Math Olympiad Problems
250 people live on the island - Truth-tellers and Liars. Each of them is a supporter of either the God of Fire or God
Water or Air God. Each resident was asked three questions:
Are you a fan of the God of Fire?
Are you a fan of the God of Water?
Are you a fan of the God of Air?
The first question was answered "Yes!" by 140 residents. 120 answered "Yes!" to the second. 110 answered "Yes!" to the third. How many Liars are there on the island?
Mathematicians A and B, as well as Baron Munchausen, played several games of table tennis in this sport: the loser gives way to the player who did not take part in this game. It turned out that A played 8 games, and B - 17 games. Who and to whom lost in the fifth game?"
When Pirate Joe was 3/8 of the way across the bridge, he noticed a police car speeding towards him at 60 km/h. If Joe starts running back, he will meet the car at the beginning of the bridge. If he starts running forward, the car will catch up with him at the end of the bridge. How fast is Joe running?
The numbers 1, 2, 3, 4, 5, ... 20 are written down one by one. In one operation, you can delete any two numbers a and b and write down a number equal to ab + a + b in their place . What number can remain after 19 such operations?
Friends come to the birthday of a famous mathematician. The birthday boy cut the triangular cake along the bisectors. The last of the Friends was Baron Munchausen. He got a piece in the shape of a right triangle, after which the Baron said that originally the triangular cake was in the form of an isosceles triangle. Is Baron right?
(M. Plotnikov) A circle with the center at point O is circumscribed around the acute triangle ABC. The bisector of angle A, when extended, intersects the circumscribed circle at point W. It is known that OW=6W-A6. Find all angles of triangle ABC.
On the continuations of sides AC and AB of triangle ABC (for points C and B), points K and T are taken, respectively, in such a way that points A, T, Ia, K belong to the same corner (Ia is the center of the externally inscribed circle touching the side BC and continuations of the other two sides).|
In this case, the equality is fulfilled: VT + SC = ВС. Prove it!
A cloak was arbitrarily painted in three colors. Is it true that there will always be two points of the same color at a distance of exactly 1 m?
Wow, lovely scenes of your life Graham. Impressive in multiple ways. Thanks for the view.
A man couldn't be any richer than to have a family like this!