The legend of e and π

 The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter. The constant, sometimes written pi, is approximately equal to 3.14159.

 The wonder of π is much more than the definition.

There are much more interesting formula about this constant, and maybe the only constant which can be equal to π is e.

This formula is called the most beautiful formula, you can know how e is important in math.

One piece of the beauty of math is connected together, two totally different definition can be connected inside. 

References: http://en.wikipedia.org/wiki/Pi

            http://en.wikipedia.org/wiki/E_(mathematical_constant)

Can all the 8-puzzle be solved?

   Do you ever play the game below?

   At first, the order of these numbers is in a mess, you can move the number to the blank. If you can place the order you win the game. So if you are given a 8-puzzle can you solve it? At first thought it seems can be solved easily. But it's not true!!!

   Here is the proof:

   Give the note [2 3 1 4 5 6 7 8 9] for the following 8-puzzle:

   Define the inverse order of the sequence. The inverse order of [2 3 1 4 5 6 7 8 9]  is two, for [2,1]，[3,1] is disorder in the sequence.

      The movement when you solve the puzzle never change the even or odd of the inverse order.

      The inverse order of the target order [1 2 3 4 5 6 7 8] is even, Which means if you are given a puzzle, which disorder is odd, you can never solve it.

      You can play the trick on your friend, you already have the magic of math. Math can be the interesting part of life, right?

Math is the best epitaph of mathematician

   Many mathematicians regard math as their whole. They devoted everything to math. Here are some epitaphs of mathematician. We can see a little part of their amazing miracles. 

   Archimedes wanted no other epitaph than a sphere inscribed within a cylinder -- he had determined the sphere's relative volume and considered this his greatest achievement.

   Henry Perigal's tomb in Essex displays his graphic proof of the Pythagorean theorem.

(2)

     Gauss wanted to be buried under a heptadecagon, which he'd shown can be constructed with compass and straightedge. 

(3)

I can't dream about being someone like one these great mathematicians. But I want to get to know these great work done by these great men. If you can design your epitaph now, what do you expect on your epitaph?

References: 

(1).(3)http://www.guokr.com/article/69516/

(2)http://www.futilitycloset.com/2010/04/20/mathematicians-graves/

Wrong proof 2=1, just for fun

We will proof that 2=1!!!

1)	Let a = b
2)	Multiply 1) by a a2 = ab
3)	Add a2 – 2ab to both parts of 2) a2 + a2 – 2ab = ab + a2 – 2ab
4)	3) could be simplified: 2a2 – 2ab = a2 – ab
5)	It is the same as 2(a2 – ab) = 1(a2 – ab)
6)	Reduce 5) by (a2 – ab). 2=1

Where is a mistake?

Mistake is in the 6^th step.
We can not divide by (a² – ab) because a²– ab = 0.
a = b, so a²– ab = 0.

(https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJu25zYMF63kaKc_S0pdjkxPPgxhy7bMDJq55RHJxFsa5hjHaao8EgWm2C0XCR7HkOKgfZgrsuzCpLnX8a21KH3EjFcxAlwYMj7f8FCKim6kVY7Y5i_GIEKR-EYG8woW782zBO68yUwpM/s400/dog+can+laugh.jpg)

 

Beauty of Numbers

Here are some funny math interesting facts. All the below tricks are based around the sequential manipulation of the numbers being used for input and output.

Sequential Inputs of numbers with 8

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

Sequential 1's with 9

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

Sequential 8's with 9

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

Numeric Palindrome with 1's

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

Without 8

12345679 x 9 = 111111111

12345679 x 18 = 222222222

12345679 x 27 = 333333333

12345679 x 36 = 444444444

12345679 x 45 = 555555555

12345679 x 54 = 666666666

12345679 x 63 = 777777777

12345679 x 72 = 888888888

12345679 x 81 = 999999999

Sequential Inputs of 9

9 x 9 = 81

99 x 99 = 9801

999 x 999 = 998001

9999 x 9999 = 99980001

99999 x 99999 = 9999800001

999999 x 999999 = 999998000001

9999999 x 9999999 = 99999980000001

99999999 x 99999999 = 9999999800000001

999999999 x 999999999 = 999999998000000001

......................................

Sequential Inputs of 6

6 x 7 = 42

66 x 67 = 4422

666 x 667 = 444222

6666 x 6667 = 44442222

66666 x 66667 = 4444422222

666666 x 666667 = 444444222222

6666666 x 6666667 = 44444442222222

66666666 x 66666667 = 4444444422222222

666666666 x 666666667 = 444444444222222222

......................................

(http://www.testsherpa.com/images/Numbers1-10.gif)

Miracle of 2519

   Some numbers is very interesting, they have some special properties. Some of them can be very amazing. Here are some funny math interesting facts about this number 2519. Enjoy the Facts.

2519 Mod n means the reminder of 2519/n, here / is the integer division.

2519 Mod n

2519 Mod 2 = 1

2519 Mod 3 = 2

2519 Mod 4 = 3

2519 Mod 5 = 4

2519 Mod 6 = 5

2519 Mod 7 = 6

2519 Mod 8 = 7

2519 Mod 9 = 8

2519 Mod 10 = 9

Sequential Numbers with 2519

1259 x 2 + 1 = 2519

839 x 3 + 2 = 2519

629 x 4 + 3 = 2519

503 x 5 + 4 = 2519

419 x 6 + 5 = 2519

359 x 7 + 6 = 2519

314 x 8 + 7 = 2519

279 x 9 + 8 = 2519

251 x 10 + 9 = 2519

My Mathematics Bioloigy professor

    I am glad to introduce my mathematical biology professor Ronald Shonkwiler to you who devotes his all life to math and teaching, Ronald Shonkwiler.

1.       What makes you choose the mathematics as your lifetime career?

Shonk: My initial interest is engineer, and I have to learn a lot of math to learn engineer well. Then I found that mathematics is much fundamental and fascinating.

2.       What do you think mathematics can bring to our life or develop our life?

Shonk: Well, math is very useful in the daily life, for example forecasting how fast flu spreads, how much loss due to the earthquake.

3.       Well, I heard you hobby is flying, right? When did you have your first plane?

Shonk: Yes, I like to fly. I got my first plane about 10 years ago.

4.       Where do you learn how to fly?

Shonk: Well, I learned how to fly after I moved to Georgia, right in Georgia tech.

5.       How long did it take you to learn?

Shonk: About 10 months, but I didn’t learn every day. I you learn every day you can spend much less time.

6.       I heard you have made a plane by yourself, right?

Shonk: That’s right. It took me a lot of time. But it was very exciting, at first the plane were just pieces, then after the effort you could fly in the sky.

…

“Well if you are interested you can fly with me.” Then:

 

 

 

   Thanks my professor for the interview and the flying. What a nice guy he is , and I want to be a person like him, enjoy your job and enjoy the life. I think that’s the most happy life I have ever heard, I want to be a person like him. So what kind of life do you want in the future?