Do you know that.....

Do you know that in Riemann Geometry, sum of the angles of a triangle is not always 180°?

Explanation will come later.

Project Euler

Quite recently, I stumbled upon this so called Project Euler, named after famed German Mathematician. It is a collection of challenging mathematical questions.
Here is the description from the website:

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

Good luck in trying some of the questions XD

Surprising Number Pattern

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

edit : taken from the book Math Wonders to Inspire Teachers and Students.

Interesting Pattern

Have you ever noticed this?

11^2 = 121

111^2 = 12321

1111^2 = 1234321

11111^2 = 123454321

...

111111111^2 = 12345678987654321

1111111111^2 = 1234567900987654321

and so on.

edit : taken from the book Math Wonders to Inspire Teachers and Students.

How true is this?

When I was bored enough during maths lesson, I jotted down some prime number and find something rather surprising. Prime number that is larger or equal to 7 can be re-represented as the sum of three prime numbers. in short, d = a+b+c where a,b,c and d are prime number and d≥7.

Some example up to prime number that is less than 100 would be :
7=2+2+3
11=2+2+7
13=3+3+7
17=5+5+7
19=7+7+5
23=11+5+7
29=23+3+3
31=23+3+5
37=31+3+3
41=31+5+5
43=31+5+7
47=37+5+5
53=43+5+5
59=53+3+3
61=31+13+17
67=61+3+3
71=61+5+5
73=67+3+3
79=73+3+3
83=73+5+5
89=79+5+5
97=41+37+19

Enough of spamming out of the blue.

Thanks to Mr Chew for correcting the mistake.

A Quiz

There is a frog fall inside a 30 meter deep well. The frog can climb 3 meter per day and drop 2 meter per night. Assuming the frog fall on the beginning of the day, how many days needed for the frog to get out of the well.

Pascal triangle and number 11

When I was playing with number 11, I find a rather familiar number pattern for 11^x
we all know that 11^2 = 121 and 11^3 = 1331
121 and 1331 remind me of the polynomial (a+b)^x which leads me to pascal triangle.



Look at the number rows above. The first represent 11^0 which is 1, the second represent 11^1 which is 11 and soon on.
does this mean that 11^5 = 15101051? of course not. It should be calculated this way.


So, the answer is 161051

This method could be applied for 11^x for any value of x due to the nature of no.11

11 = 10+1

Just replace the x with 10 and the y with 1, we will get



since will always be one,




notice that can be derived from pascal triangle.

The last digit of 11^x will always be 1 when the second last will always be the last digit of x

edit: I just realised that the long equation is being cut. Since it does not affect that much, I'll just leave it that way.


last edited on : 15th of May 2010