# One week of mathematics, #2

Hi,
The second day of mathematics was pretty good and in this post I am going to descreibe it. You can find the first day right here.

It started with triangles and how we can make three pieces from it when we cut on thirds one of the sides. Then the guy explained us how we can find out the area of triangles in rectangle where there is one point and all the vertices connected to it. We continued with the similarity of triangles and then some more complicated shapes. While the lecture was good in the end it started to get really complicating and I was not able to follow everything.

The second presentation was called the AG inequality.
A stands for arithmetic
G stands for geometric

It is about the inequality of arithmetic and geometric average.
Arithmetic average goes like this:
1+2+3+4+5/5
You just divide your numbers by amount of them, this is the standard average while geometric average is the multiplication of those numbers and the n root of them where n is the amount of those numbers as I already mentioned last time.

We made proof that arithmetic average is greater or equal to geometrical average for two numbers otherwise it is more  complicated. Than she taught us another two averages: quadratic and harmonical. We did some problems on that and then we had lunch with free time until dinner and evening presentation.

Me and my friends we went to confectioners and solved some problems which needed to do until the end of the week.

The evening presentation was pretty fun at start, I was able to follow up with most things but then it got extremely hard with some elipses and while he did not use any mathematical operations I would not understand at all but he did so many seemingly random things to get to the result I can bet that I would not be able to do it with hours of free time alone.

That was the end of day while we were playimg some card games until deep night.

Dragallur