Another proof

d/dx e^ix = ie^ix
-----------------
d/dx cosx + isinx
= -sinx + icosx
= i (cosx + isinx)
-----------------
Both functions satisfy the differential equation dy/dx = iy

with initial value (x=0)equal to one

Thus they must be equal ( if two functions are the same at one point and change in the same way, their entire functions must be equal.)

Thus we have again, e^ix = cosx + isinx

fried rice!

my fried rice is good..
The otah bits taste great.

Even darren had 2 servings.

Tian can cook

Haha I've been real into cooking lately. Cancer patients are usually advised from eating hawker food because of cleanliness issues. Restaurant food is okay, but of course home cooked food is the best when you're as good a cook as me XD! You can add extra sumptous ingredients like prawns and scallops.

Anyway tonight i cooked chilli crabs. The recipe is really really simple. But you end up with a good sauce thats better than most of the coffee shops one. No need to buy those so-called pre-made instant chilli crab sauces they're such a waste of money (3 or 4 bucks a pack?!?!!) and way too salty. Homemade is the best. delcious too.

Here are some pictures. XD!

My Dad gave it a 72/100

My mum gave it a 75/100

I give myself 70/100 haha the crabs were not sweet enough. But that wasn't my fault sheng shiong just had lousy crabs.. Next time must buy good ones from wet market.. The sauce was awesome though- anyone who wants the recipe just leave a comment haha.. Yupp and i decided to leave a picture of myself.. Monk head! now can go and lian the iron skull marital art.. Very airy maybe i should get a temporary snakehead tattoo or something.. that'll be cool..

Yupp gotta go watch soccer now. Austria will win Crotia.

The Greatest Identity on Earth

Euler's Identity

The greatest identity on Earth, relating the base of the natural logarithm e, with the elementary trigo functions. substituting pi into the identity immediately yields;An equation relating the five most important numbers in mathematics. Nothing else needs to be said. I will attempt to give a single proof of this today. Which is not really totally formal, but works nonetheless.

Proof.

Consider the function

f(x)=

Differentiating we will have,

f '(x)=f '(x) = 0

Take a moment to think about what this means. This tells us that the gradient of f(x) at Every point of its graph is equal to zero. Thus is we draw the graph it must look like a straight horizontal line. Which means that it must be a constant function.

For every value of x, fx is a constant. Thus we can find out what this value is by substituting any value for x. Lets try zero.

f(x)=constant=f(0)= which reduces to one.

Thus we have shown, f(x)=1 for all x,

is equal to one, for all x

Yupp. Too chio.

Apologies

Ahhh... Finally got my PC restored back to normal.. Been downloading too many illegal psp games from utorrent.. Siao liao la. Half a month never update...-.-'''

Guess its time i talk about how I'm coping with chemotherapy.. Everything's going real fine now. I'm near the end.. Just discharged from hospital yesterday. Side effects this time were minimal too.. Doctor says after two more weeks or so i'll have a two months break from chemo to regain back my health. Then its off to another two more months of chemo and i'll be into a sort of remission state.

Its certainly been a long journey.. Many thanks to my parents and supportive friends.. I could not have gone this far without you all.

I'm also real into cooking now.

My chili crab rocks. When i'm well i'll have a party and we'll snack on chilli crabs and barcardi. XD

Life's good when theres food.