Twin Paradox of Einstein

The Twin Paradox of Einstein is an experiment involving two twins , one of whom sets out on a journey into space and back. Because of the time dilation effect of relativity, the twin who left experiences a slowing down of time and will actually be much younger than the twin that stayed behind. The reason that this is considered a paradox is that Special Relativity seems to imply that either one can be considered at rest, with the other moving. It does, and it doesn't.
The confusion arises not because there are two equally valid inertial rest frames, but (here's the tricky part) because there are three. A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, or involve General Relativity. Not so.
The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.
OK, let's see: Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger.
Important question: what is the relative speed of the two Bob frames? On first glance, it would appear that one is going 3/5c in one direction and 3/5c in the other direction, so that the difference between the two frames is 6/5c! Faster than light? No, special relativity does not add speeds this way. The actual difference is only 15/17c, fast but not faster than light. Why is this important? We'll see.
Now, since special relativity lets us use either rest frame, we assume Bob is the at-home twin. Ann speeds away at 3/5c. No problem so far. But after 4 years of waiting, Bob must change his inertial frame. If we allow Ann to return, we've only restated the problem with the names switched. In the first version, Ann stayed in an inertial frame, and she must stay in an inertial frame in this version. Bob zooms off after Ann at 15/17 light speed (now we know why it was important), and of course catches up. It takes him 4 years, and he has seen 8 years since Ann left. Ann has aged 10 years. Same result. No paradox

Math tricks

The 11 Rule

To multiply any two digit number by 11:
For this example we will use 54.
Separate the two digits in you mind (5__4).
Notice the hole between them!
Add the 5 and the 4 together (5+4=9)
Put the resulting 9 in the hole 594. That's it! 11 x 54=594
The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627

Square a 2 Digit Number Ending in 5

For this example we will use 25
Take the "tens" part of the number (the 2 and add 1)=3
Multiply the original "tens" part of the number by the new number (2x3)
Take the result (2x3=6) and put 25 behind it. Result the answer 625.
Try a few more 75 squared ... = 7x8=56 ... put 25 behind it is 5625.55 squared = 5x6=30 ... put 25 behind it ... is 3025

Recurring Number Magic
EffectYou write down the following 8 digit number on a piece of paper:
1 2 3 4 5 6 7 9
Then ask a friend to circle one of the digits. Say that they circle number 7.
You then ask your friend to multiply the 8 digit number by 63, and magically the result ends up being:
1 2 3 4 5 6 7 9 x

6 3

------------------

7 7 7 7 7 7 7 7 7

with the answer as a row of the chosen number 7.
The SecretWhen your friend circles a number, you need to multiply the chosen number by 9 in your head - if 3 was chosen you would work out 3 x 9 = 27. Then you need to ask your friend to multiply the 8 digit number by the number you have just worked out. In the case of 3 being chosen you ask your friend to multiply 12345679 by 27 and you magically get the answer 333333333.

Cool space !!

Since this is the space week , i have a collection of links and photos of space stamps ...