## Monday, December 25, 2006

## Thursday, December 21, 2006

## Tuesday, December 19, 2006

## Sunday, December 17, 2006

## Friday, December 08, 2006

### Listening to...

**Beautiful World by Take That**

Here standing in the rain

The sun has gone again and nothing's gonna change

Time, I need a little time as you slip out of sight

And nothing heals the pain.

And I know that it's you that's stopping me from falling

Crashing down, losing ground til I see you again

And you know...

The sun will shine, and we will see there's nothing standing in our way

Love will stand and never break

Never thought this could be me

Do you feel what I feel?

Everytime that you are near it's a beautiful world

A beautiful world

Words are hard to keep inside

Even though I've tried, impossible to hide.

And you know that it's me that's stopping you from falling

Crushing down, losing ground til I see you again

And you know...

The sun will shine, and we will see there's nothing standing in our way

Love will stand and never break

Never thought this could be me

Do you feel what I feel?

Everytime that you are near it's a beautiful world

A beautiful world

I'll be the stars guiding you

I'll be the place that you hide

I'd run a thousand miles, a thousand miles to be by your side.

**You Are Loved (Don't Give Up) by Josh Groban**

Don't give up

It's just the weight of the world

When your heart's heavy

I...I will lift it for you

Don't give up

Because you want to be heard

If silence keeps you

I...I will break it for you

Everybody wants to be understood

Well I can hear you

Everybody wants to be loved

Don't give up

Because you are loved

Don't give up

It's just the hurt that you hide

When you're lost inside

I...I will be there to find you

Don't give up

Because you want to burn bright

If darkness blinds you

I...I will shine to guide you

Everybody wants to be understood

Well I can hear you

Everybody wants to be loved

Don't give up

Because you are loved

You are loved

Don't give up

It's just the weight of the world

Don't give up

Every one is to be heard

You are loved

**I Got Nerve by Miley Cyrus/Hannah Montana**

We haven't met

And that's okay

Cause you will be askin' for me one day

Don't wanna wait

In line

The moment is mine, believe me

Don't close your eyes

Cause it's a chance worth takin'

And I think that I can shake you

I know where I stand

I know who I am I would never run away when life gets bad

It's everything I see, every part of me

Gonna get what I deserve

I got nerve

Electrified

I'm on a wire

Gettin' together and we're on fire

What I said

You heard

Now I got you spinnin'

Don't close your mind

The words I use are open

And I think that I can show you

I know where I stand I know who I am

I would never run away when life gets bad

It's everything I see, every part of me

I know I can change the world

I know what you like

I know what you think

Not afraid to stare you down until you blink

It's everything I see, every part of me

Gonna get what I deserve

I got nerve

You... you need to discover

Who can make you feel free

And I... I need to uncover

The part of you that's reaching out for me

Hey!

I know where I stand I know who I am

I would never run away when life gets bad...

It's everthing I see every part of me

I know I can change the world

I know what your like

I know what you think

Not afraid to stare you down until you blink

It's everthing I see, every part of me

Gonna get what I deserve

I got nerve

I'm what you want, I'm what you need, I'm what you want, I'm what you need...

I know what your like

I know what you think

Not afraid to stare you down until you blink

It's everthing I see every part of me

Gonna get what I deserve I got... I GOT NERVE!

## Wednesday, December 06, 2006

### Heroes again!

This show just gets better and better. I am speechless.

And yes, it's even better than parabolas!

I absolutely cannot wait until January 22, 2007! Proof: this show almost made me forget about Oxford's reply, which will be in less than eight days! Ahh... adrenaline rush!

### Parabolas

What is a parabola? How is it defined?

What is the standard parabola equation? Most people I ask would say y = x^2. Wrong!

Before I get into the mathematics of this, imagine a point and a line. Draw a locus which is equidistant (equally distant) from the point and the line, and voila you get a parabola! That point is known as the

Imagine a parabola which opens to the right and has its vertex at (0,0). Let the focus of the parabola be the point (a, 0), and the directrix the equation x + a = 0. Since the distance of the line from the directrix to the parabola is equal to the distance from the focus to the parabola, then

√[(x - a)^2 - y^2] = x + a

Squaring both sides,

(x - a)^2 - y^2 = (x + a)^2

x^2 - 2ax + a^2 - y^2 = x^2 + 2ax + a^2

x = at^2, y = 2at --- these are the parametric equation of the parabola.

Using implicit differentiation and simple coordinate geometry, you can work out the tangent of the parabola at any point.

An exercise for you:

Find an equation of the normal at P(4t, 4t^2) on the parabola with equation 4y = x^2. The normal meets the y-axis at the point Q. Find, in cartesian form, an equation of the locus of the point M, the mid-point of PQ, as t varies.

Loving further maths!

What is the standard parabola equation? Most people I ask would say y = x^2. Wrong!

Before I get into the mathematics of this, imagine a point and a line. Draw a locus which is equidistant (equally distant) from the point and the line, and voila you get a parabola! That point is known as the

**focus**of the parabola, and the line,**directrix**. This property is often called the**focus-directrix property**of the parabola.Imagine a parabola which opens to the right and has its vertex at (0,0). Let the focus of the parabola be the point (a, 0), and the directrix the equation x + a = 0. Since the distance of the line from the directrix to the parabola is equal to the distance from the focus to the parabola, then

√[(x - a)^2 - y^2] = x + a

Squaring both sides,

(x - a)^2 - y^2 = (x + a)^2

x^2 - 2ax + a^2 - y^2 = x^2 + 2ax + a^2

**y^2 = 4ax**--- this is the cartesian equation of the parabola.x = at^2, y = 2at --- these are the parametric equation of the parabola.

Using implicit differentiation and simple coordinate geometry, you can work out the tangent of the parabola at any point.

An exercise for you:

Find an equation of the normal at P(4t, 4t^2) on the parabola with equation 4y = x^2. The normal meets the y-axis at the point Q. Find, in cartesian form, an equation of the locus of the point M, the mid-point of PQ, as t varies.

Loving further maths!

## Tuesday, December 05, 2006

### A reminder of how infinitesimal we are

The observable universe is **78 billion light years** in diameter...

Don't fear if you feel lonely. We will find another civilisation in this universe... someday.

## Monday, December 04, 2006

### Christmas gift?

I really want this set of earphones for Christmas!

"Ergonomic and lightweight sound isolating earphones offer the most accurate audio reproduction from both portable and home stereo audio sources—for the ultimate in precision highs and rich low end..."

But it's more expensive than the iPod!

"Ergonomic and lightweight sound isolating earphones offer the most accurate audio reproduction from both portable and home stereo audio sources—for the ultimate in precision highs and rich low end..."

But it's more expensive than the iPod!

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