Showing posts with label Mathematics. Show all posts

Beauty of Mathematics

Saturday, October 08, 2011

Maths can never be boring

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.. cause it made you laugh..

.. and it made you felt fully in love!

Just a short update. Stay tuned for more soon!


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6÷2(1+2)

Friday, May 06, 2011

I was browsing through the Chinese newspaper days ago, and found an article which titles:


6÷2(1+2) = ??

As a Mathematics major student, the princess started to calculating it in mind and she got 1 as her answer. Without reading more she went to work and when she was back from work that day, she saw the same related news in Facebook. The curiousness increases and therefore she watched that short clip saying that the answer for the mathematical question was 9 instead of 1! Having doubts, she shared the video on her Facebook and she received lotsa feedback:

Some of the feedbacks and proofs by princess's friends~

Clarified also by the princess's mathematical logic's lecturer~

So, actually the answer should be 1 as you got some proofs and explanation from above. Here's a simple explanation from the princess. First of all, you just need to understand and know the order of operations, which are:
  • terms inside parenthesis (meaning the bracket)
  • exponents and roots
  • multiplication and division
  • addition and subtraction
The operator higher on the list above should be applied first. So, now let's solve the equation:

Terms inside parenthesis applied first - (1+2) = 3
Again, terms inside parenthesis applied first - 6÷2(3) = 6÷6 = 1

There you are, a simple example. Actually if you calculate using scientific calculator, you'll get 1 as the answer too! Guess I needa be more confident in my answer since I'm a maths major student. Hahahaha! For more explanation can refer to this web.

Just a short little update! Take care everyone!


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Function

Saturday, February 28, 2009

Weeks ago, while listening in the lectures, Real Analysis lecture, to be more specific, the lecturer taught us this --> Function.

Students in science stream will be exposed to function when they're in Form 4. Well, this should be the first topic of the add maths if I'm not mistaken. ^^

So, function. The definition of function is...

Let A and B be sets. f is said to be a function from set A to set B if and only if for each element x of A there is associated a uniquely determined element f(x) of B. The set A is called the domain of f and the elements f(x) are called the values of f. The set of all values of f is called the range of f.

Notation: f : A --> B and read as f is a function from A to B

-From Real Analysis's lecture notes-

Which means that, a function can be called a function when the f : A --> B are injective (one-one), subjective (onto) or bijective (both injective and subjective). In a simple form, function is a many-to-one and one-to-one relation. A one-to-many relation is not a function.

Some may think is hard to remember. But no worries. Thanks to my friend who came out with an idea on how to memorise it.

Let A (domain) as MEN, and B (range) as WOMEN

Men cannot live without women, but women can live without men.
(This is one-one relation. So, it's a function.)

Two men can have the same woman on the same time...
(This is many-to-one relation. So, is a function too!)

.. but one man cannot have more than one woman at the same time.
(This is not a function cos is a one-to-many relation)

So, can u remember what relation should the function be in order to call a function? ^^


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The Beauty of Mathematics

Thursday, January 15, 2009

It's truly amazing~

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

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

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

Brilliant, isn't it? And look at this symmetry:

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

Now, take a look at this... 101%

From a strictly mathematical viewpoint:

What equals 100%? What does it mean to give MORE than 100%? Ever wonder about those people who say they are giving more than 100%? We have all been in situations where someone wants you to GIVE OVER 100%. How about ACHIEVING 101%? What equals 100% in life?

Here's a little mathematical formula that might help answer these questions:

If
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26,

then,
H-A-R-D-W-O- R- K
8+1+18+4+23+ 15+18+11 = 98%
and
K-N-O-W-L-E- D-G-E
11+14+15+23+ 12+5+4+7+ 5 = 96%

But:
A-T-T-I-T-U- D-E
1+20+20+9+20+ 21+4+5 = 100%

THEN, look how far the love of God will take you:

L-O-V-E-O-F-G-O-D
12+15+22+5+15+ 6+7+15+4 = 101%

Therefore, one can conclude with mathematical certainty that:

While Hard Work and Knowledge will get you close, and Attitude will get you there, It's the Love of God that will put you over the top!


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Pythagorean Theorem

Friday, January 09, 2009

What is Pythagorean Theorem aka Theorem Pythagoras? This may be ask by some people out there? Well, the theorem is as below:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

and it usually summarized as follows:

The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

-Source from Wikipedia-

Let me simplify in a simplest formula:

Sounds familiar for some readers out there? Yes! We'd learn it in high school years where we're given formulas to find the length of the right angle triangle. Now, we just only need to memorise the formula and just applied it. And we're actually forgotten the most important part:

How they find the formula out? How can they proof it? Why they can produce such formula?

We're taking things for granted and sometimes we're actually forgot to appreciate it.

Okay. My main point for this post is to show something very interesting. They're actually many ways to proof this theorem, such as using similar triangles, Euclid's proof, Garfield's proof, Similarity proof, Algebraic proof, Proof by differential equations and Proof by rearrangement.

Today I'll show you how to proof this theorem by using rearrangement proving. This is also just one example among all kinds of arragement proving. It's very easy. Even elementary students can proof it!! ^^

First, measure and draw a some sort of combination of 2 squares like above

Then, cut of the shaded area...

And connect it to the other edge... And you'll find it is actually another bigger square!!

So, what's the connection some may ask?

During the measurement, it is actually a 2 square that I'd just mentioned, where the smaller square's area is 3square whereas the bigger ones is 4 square...

.. and the cut and paste resulting square with it's area of 5 square~ And this leads to...

.. the Pythagorean Theorem!!!

Easy eh? So, what do you think? A very simple thing that sometimes we won't realise but it's actually may lead to some new thing. Interesting eh?

From this simple thing, more people will able to understand to proof the theorem and parents even can teach this theorem by introducing it as a 'game'!!! ^^


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Questions!!!!

Monday, August 06, 2007

Finally finished the presentation!! Now, is just the time to present only. Thank God that today is not our turn to present. But actually I was hoping to be the first to present. Well, now the second assignment needa be pass up next Monday!!! (>.<) But luckily it’s also a group assignment. Like this the burden won’t be so much… =D

Today suppose to be a busy day. But the lecturer was unable to come so I’m kinda free. That’s why you can see me updating now~ =P Something to share with everyone actually. The logic maths lecturer thought us this today…

Let’s see the following statement…

Can you all see the issue here? Hmm… Suppose the first statement is correct. But as you continue to solve the problem… 1 = -1?!!!! It’s impossible right? 1 and -1 is impossible to be the same right?!

So, where could it possible to be the problem? Anyone knows?


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