Monday, September 22, 2008

my story..


erm...

aku rindu ngan skolah lama ku..

aku rindu teman-temanku...

aku rindu gelak tawa kami...

aku rindu suara mereka...

aku rindu nyanyian mereka...

aku rindu senyuman mereka...

aku rindu teriakkan mereka...

aku rindu nak makan sama-sama ngan mereka...

aku rindu untuk lepak ngan mereka...

aku rindu gurauan mereka...

aku rindu lagu mereka...

aku rindu mereka...

aku rindu untuk dimanja oleh mereka...

aku rindu cikgu-cikguku...

aku rindu gelak tawa guruku...

aku rindu maki hamun guruku...

aku rindu teriakkan guruku...

aku rindu tunjuk ajar guruku...

aku rindu nyanyian guruku...

aku rindu guruku...

aku rindu kelasku...

aku rindu kerusiku...

aku rindu mejaku...

aku rindu lokerku...

aku rindu pentas kami...

aku rindu meja guruku...

aku rindu papan hitamku..

aku rindu kapurku...

aku rindu beranda kelasku...

aku rindu tingkapku...

aku rindu bunga kelasku...

aku rindu skolahku...

aku rindu lagu skolah ku...

aku rindu ikrar skolahku...

aku rindu pelajar skolahku...

aku rindu foyer skolahku...

aku rindu peraturan skolahku...

aku rindu sistem skolahku...


AKU RINDU KEPADA KAMU SEMUA....!!!!

inginku kembali padamu skolah ku...

tapiii........

apakan daya....

semuanya hanya tinggal kenangan...

kenangan manisku...

kenangan yang takkan ku lupakan...

kawanku...kenalanku...guruku...kelasku...skolahku...

KAMU ADALAH HIDUPKU...

U ARE MY LIFE...

TIADA PENGGANTI UTK MU...

KAMU ADALAH SEGALA-GALANYA...






Biar beribu batu ku menjelajah...

biar beribu tahun ku hidup...

biar beribu... apa-apa je lah...

U ARE THE BEST SCHOOL EVER...

Sunday, September 21, 2008

PYTHAGORAS' THEOREM

Hye...okey...let's talk about my favorite subject in school...mathametic...this is one of the many subject that i love...pythagoras theorem...
PYTHAGORAS: FATHER OF NUMBERS

FACTS ABOUT THE GUY
* Born around 570 B.C. on Samos, an island lying off the western coast of Asia Minor
* Founder of the Pythagorean school (surprise, surprise!)
* He was a vegetarian
* Was also a philosopher as well as a pretty good mathematician
* Famous for the Pythagoras'Theorem (who woulda guessed it?)

PYTHAGORAS' THEOREM
This theorem is great due to the fact it can be easily proved and is easy to understand.The theorem basically states that for a right angled triangle, the square of the hypotnuse is equal to the sum of the squares of the other 2 sides:
So if we know any 2 sides, we are able to calculate the length of the remaining side:
By rearranging the formula:
Click here to try this yourself with numbers!PROOF
This is my favourite proof, developed by the Indian astronomer Bhaskara (1114-1185):
The area of the big square with sides a + b = (a + b)²
This is equal to the sum of the area of the internal square (c²) plus the sum of the 4 triangles (4 x ½(a x b))Equating these:
(a + b)² = (4 x ½(a x b)) + c²(expanding)
a² + 2ab + b² = 2ab + c²(subtracting 2ab from both sides)
a² + b² = c²
There are many other proofs, click here to see 72 of them!
A brilliant piece of maths i think you will agree. Much better than Fermat's Last Theorem, of which the proof is only understood by a select few........

USES OF THE THEOREM
We can apply this theorem to many everyday situations:
* Construction workers finding lengths of supports
* Finding the argument of a complex number
* Calculating distances in cartesian coordinates
* Navigation of the sea, land and air
* Finding angles of elevation and depression
* Checking if a traingle is right angledOk, so not really 'everyday' for most of us, but it is still extremely useful.

CONSEQUENCE OF THE THEOREM - PYTHAGOREAN TRIPLESA
Pythagorean triple consists of three positive integers a, b, and c, such thata² + b² = c².
This is commonly written (a, b, c), and a well-known example is (3, 4, 5):3² + 4² = 5²9 + 16 = 25
There are infinitely many Pythagorean triples.
The simpliest proof for this being any multiple of a Pythagorean triple is again a Pythagorean triple, ie, if (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k, therefore there will be infinitely many.
More examples of Pythagorean triples:
(5, 12, 13)
(7, 24, 25)
(9, 40, 41)
(11, 60, 61)

GENERATING PYTHAGOREAN TRIPLES
An effective way to generate Pythagorean triples is by Euclid's formula.
This was recordered in his book Elements around 300BC:
If m and n are two positive integers with m > n, then:
* a = m² - n²
* b = 2mn
* c = m² + n²

PROPERTIES OF PYTHAGOREAN TRIPLES
* Exactly one of a and b is odd, c is always odd
* Exactly one of a and b is divisible by 3
* Exactly one of a, b, c is divisible by 5
* ab is always divisible by 12
* abc is always divisible by 60
* Exactly one of a, b, (a + b), (a - b) is divisible by 7
* Every integer greater than 2 is part of a Pythagorean triple
* There is no Pythagorean triple in which the hypotenuse is equal to either 2a or 2b

Simply amazing!
So thanks a lot Pythagoras, we owe you 1!

a words from me...


" for what is the best choice, for each individual is the highest it is possible for him to achieve.."

hello...

hai everyone.. i'm just finish create my blog.. so it's mean that i'm new here... hehe... wanna know about me..? dun worry u just click on my profile.. hehe...