Intresting Maths

In the group of 23 people the possibility that 2 people have birthday in the same day is about 50%.
First lets count the possibility for the variable group of people.(N-is the number of people in the group)
Let's take one person and remember his birthday. Then let's take second person. The possibility that his birthday won't match with the first person's birthday is (1-(1/365))=364/365.Then let's take third person. the possibility that his birthday won't match the previous two is ((1-(2/365)=363/365. Then the forth....is ((1-(3/365)....The Nth will have ((1-((n-1)/365))=(366-n)/365. So if we multiply all these possibilities we will get that the possibility that all N members of the group have different birthday is
t=(364*363*362*361....(366-n))/(365^n)
[365^n is the equivalent of writing 365 to the power of N)
So the possibility that at least 2 people have birthday on the same day is 1-t
If you count it for t=23 you will see that 1-t is slightly above 50%.

endless Mind Maps

Intresting Maths

Galileo's paradox.One of the famous paradoxes of sets. Let's take two sets of numbers:integers and exact squares. Integers are {1,2,3,4,5,6...} and squares are {1,4,9,16,25,36,49....} so it's easy to see that not all the integers are exact squares so set of exact squares is smaller than a set of integers...But each integer has an exact square {1*1=1,2*2=4,3*3=9,4*4=16......} So the number of integers and squares are the same.

Numerous Mind Maps

numerous mind maps

Russian billiard

It's much more difficult than pool. Pockets are narrow and the difference between ball's diameter and pocket is only 8-10 millimetres.
Here is the trickshotvideo

As promised

As we know there are many kinds of billiard:pool,snooker, cannon(carambol) etc. Each kind may have devision on different games,for example pool can be played as 9-ball,8-ball etc. But in order to play well in any kind of billiard you should know the key points of playing. That includes not only rules, but the way you stand when you strike or the way you hold the cue.
First about the position. There is no stated for everyone, but while making a strike you should place most of your weight in the legs,the position should be balanced and your forearm should be perpendicular to table.
Now about the way you hold the cue. Again there is no stated rule about it. The cue should be parallel to table and should be fixed in x-y plain so it should go forward or backward only in z-axe:).
Usefull exercise for the beginners is to strike in the middle of the ball perpendicular to any cushion. When you make the strike you should leave the cue in the position at the moment of strike. If you do everything right the ball will come back to the top of the cue.

here some videos:

First mind map:)

Intresting Maths

Today,during the maths lesson we were doing some researches in the ICT room. I have found very intresting quiz(at least it seems intresing to me). This quiz is simplified famous game "deal or no deal".
There are 3 doors in these game. Behind 2 of them are goats and behind one is a car.Player chooses one door and after that presenter opens one of the unopened doors with the goat. After that he offers player to change a door he has chosen. The question is if it's reasonable to change doors or not.
The answer is that it's better to change the doors.
The solution
let's devide these 3 doors into 2 groups. First group has only one door that is chosen by the player. The other group has 2 unopened doors. The chance that the car is in the first group is 33%(because there is one car and 3 doors) the chance that the car is in the second groups is 66%. Now the presenter opens one door with a goat in the second group. Some people may think that now chances are 50/50 but they are not. Now second group can be opened at one time(because there is only one unopened door left) but the chance that the car is in the second group is 66% and that the car is the first group is only 33%. So it's reasonable to swap the doors.

Mr.Chris

Mr. Chris, i thought i will just give the book back to you on thursday beacause i didn't want to read it all and wanted just to get rid of it. But it appears to be an intresting one.So i have to keep for at least 4 more days:)please...

To do list:D

Following examples of many a-level students, i've decided to write to-do list. Maybe that will help to organise my time.:)
This week:
1)make a to-do list(almost done)
2)Bring Mr.Chris's book
3)do exercises to increase reading speed
4)do air alarm 2 exercises
5)do economic homework.
6)bring Sairan's paper on YED
7)post an article about playing pool and russian billiard(special for Anastasia)
8)find a place to play basketball
9)quit red bull(DOOONE:D)
10)read 2 random quote pages on the www.bash.org
11)translate my 2 chapters into russian
12)write a blog everyday.
13)make english homework
(By the way these points are not listed in the order of importance or smth)