I was thinking about math as usual, so I decided to try to write about it to see if it promotes my understanding any, so bear with me. Group theory proves the behaviour of equations by examining the symmetries of their solutions. For instance an equilatoral triangle has 6 different symmetries: F, R, I, R^2, FR and FR^2. Because it has 3 points and 3! = 6. Any other compostitions of elements, F, R, or I reduce to fall under these 6, because of the following: R^3 = I, F^2 = I and RF = FR^2.

On a different topic: Epsilon - Delta defintition of Limits
The limit as x goes to 2 of x^2 =4. Let E>0 be given(fixed but arbitary) Note that you can always make delta smaller than nessesary by taking the minimum. Hence x1^2 = 4-E, therefore x1=sqrt(4-E), suppose E<4. and x2^2 = 4+E, thereforex2=sqrt(4+E). Let delta be the minimum of {2-x1, x2-2}. Note that delta is always greater than 0. Suppose that abs(x-2) < delta. Now follow through two cases, to find abs(x^2-4)< E.

Nisha,

ई जुस्त वांटेड तो लेट यू क्नोव ठाट यू अरे अ ग्रेट फ्रीएंद ऎंड ठाट ई लोवे यू वैरी मुच.

- सराह

Well, I think its about time I write a new post. I'll dedicate this one to my artwork. I finally finished my Romans project, in which I did a reproduction of a classical Roman fresco, using watercolour. Staring what else but a nude woman (actually two). I can tell you that my mom was a bit surprised when she walked into my room and saw me going through a book of nude paintings. Well this is the work in progress...

and this is the finished product...

These are some of the other water colours that I have done...

I dream of painting and then I paint my dream. - Vincent Van Gogh

Wow, so I ended up trying the best thing ever last night.....artichoke and spinich dip with melted cheese on top, served with homade pita and nacho chips. I got it from the Snooty Fox and yes the reason why I thought it tasted sooo good might just be the fact that it was 11:30 at night. But whatever me and the girls were craving warm greesy food and it was incredible. It turned out to be a good night, I got to show off some really 'funky' dance moves and practice my 'krumping' in front of all of Freddyville.....lol.....

My shadow is the only one that walks beside me.

I walk a lonely road, the only one that I have ever known, don't know where it goes, but it's only me and I walk alone.

I don't want the world to see me, cause I don't think they'll understand. When every thing is made to be broken, I just want you to know who I am.....

Why do kraft macroni and cheese box's have a push and pull on thebox, when it doesn't work? When you push all it does is smash the box...youend up pulling back the lid with your finger nails. Who would invent such a thing...

And now these three remain: faith, hope and love. But the greatest of these is love.
- 1 Corinthians 13:13

This blog is for a special friend in my life, who I haven't seen in a very long time....missy you know who you are. I think you may like to read this, you probably have many times before, but it might just help......

The Road not Taken
Robert Frost

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,
And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I-
I took the one less traveled by,
And that has made all the difference.

Always praying for you......