Pushy alright

This is hilar-ious!

Thank God my mum's not like that!

Hydrophobic

This stuff and water really don't get along! Like me and horror movies!

Picnic geometry

To pass time:

For more detailed instructions, click here.

Worst nightmare

Clck to enlarge sketch:


Hope this will never happen!

Poisson distribution

Get it?

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!

Heroes again!

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

And yes, it's even better than parabolas!

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 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!

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.

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!