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Generated : 19th August 2017

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Uddiee

Thank ou so much for putting together such a good web page on Differentiation. it made me understand the concepts and more importantly the applications. Thank you so much for a job well done.

KryssTal Reply: Thank you - It is an important branch of mathematics.

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Jordi Mas

You wrote at http://www.krysstal.com/zodiac.html :

Pythagoras' Ideas: The square root of 2 can not be written as a fraction. Only by observing nature can an idea be verified or not.

I wonder, how should I observe nature to verify that the square root of 2 can not be written as a fraction?

KryssTal Reply: "Observing nature" means experiment and proof - the scientific method. A proof exists for root 2 not being writable as a fraction.

OK, Only by experiment and proof can an idea be verified or not. OK, there exists a proof for root 2 not being writable as a fraction.

What's the experiment, then?

KryssTal Reply: The mathematical proof is a type of experiment. In it, an assumption is made wich is shown to be incorrect during the mathematical proof.

### 014

lashiedra horne

I HAVE TRIG HOMEWORK TO DO OVER MY CHRISTMAS / WINTER BREAK AND I DON'T UNDERSTAND HOW TO DO ONE OF THE PROBLEMS. IN OUR CLASS WE ARE CURRENTLY WORKING ON SOLVING TRIGONOMETRIC EQUATIONS. THE EQUATION THAT I AM TRYING TO SOLVE IS AS FOLLOWS:

4 sec x - csc x = 0

IF YOU CAN GIVE ME ANY HELP ON HOW TO SOLVE THIS EQUATION PLEASE LET ME KNOW.

KryssTal Reply: Try converting into sines and cosines and simplifying the resultant fraction.

Good luck.

### 013

Jogen De Almeida

Dear Mr.Krysstal,

I'm an undergraduate who is following a degree in information technology, and i found your site very very usefull for my first year of study specially for mathematics, I hope I can get more information as I go through my second and final year of my studies.if you can send me some information about the following or give a URL which will be usefull to find information about the following.

1.Sets
2.Logic
3.Relations
4.Functions
5.Techniques of Counting
6.Probability

My wishes for your future projects. Thanks

My web site is not professional so I add to it as I feel like it. More Mathematics will come soon.

At present, with the USA about to invade Iraq and drag the UK in with it, the Democracy page is the one being updated almost on a daily basis.

After that I will be travelling to Africa for the December 2002 total solar eclipse so I will be updating my Eclipse pages.

### 012

LaVeta Nutter

Webmaster

In example 2 of your algebra section your example states that "a number is multiplied by itself." A number multiplied by itself is X "squared" not 2X as you have in your solution. (x times x equals x squared)

This changes the equation to (X)2 - 3x + 2 = 0 (x squared) minus 3x + 2 = 0

solution: x=1 and x=2

the example to your solution would be a number multiplied by 2 or a number that doubles itself, but not multiplied by itself.

Yes, "a number multiplied by itself" should read as x squared, or x with a little 2 next to and above it. As far as I can see, that is what is there. Perhaps it's a problem with your web browser?

You seem to have a good grasp of the maths (UK shorthand for mathematics) or math (if you're from the USA).

Hello,

I apologize profusely. I really feel silly now. It is not my browser, the equation is correct. I looked at the wrong solution.

I must add again, your website is wonderful. It simplifies algebra in a method that I have not been able to find in textbooks.

My students will benefit from visiting your site. Thank you again! Have a beautiful day!

### 011

Carl

I need to talk to someone....I have also discovered several of the patterns you have, but I need to know which ones have already been discovered and what mathmatical proofs have been established regarding Pascal's Triangle. I would love to talk to someone for a few minutes to ask a few key questions.

ok...lets start with the simple one....when you take sequencial numbers raised to a power and take their differnece...and the difference of that difference and so on....you eventually end up with a number that is tha same all the way down...and that number is the power factorial.

in other words....2 cubed is 8...3 cubed is 27...4 cubed is 64...5 cubed is 125..6 cubed is 216...7 cubed is 343...etc.

their difference is (27-8)=19...(64-27)=37...(125-64)=61...(216-125)=91...(343-216)=127...etc.

their differerence is (37-19)=18...(61-37)=24...(91-31)=30...(127-91)=36...etc

and finally.....(24-18)=6...(30-24)=6...(36-30)=6....etrc....

you see? the power (3) factorial..(3X2X1) is 6......the same number...and that is true for all numbers raised to any power ...the final differnece is always the factorial of the power....

Have you seen this and is this part of Pascal's Triangle and if it is...what conclusions have been drawn regarding this pattern.

Thanks

I hadn't noticed that before. I'll do some checking.

Appreciate your help...if I publish some earth shattering proof I will be sure to mention your help...lol

### 010

Rahul Ganatra

Dear sir/ma'am,

I'm doing an honors math project on Pascal's Triangle, and I came across your page in my search. The binomial theorum section was especially helpful, I've noticed that it's difficult to come across detailed yet simple explanations of some of the triangle's appllications. Your website has been most helpful =)

However, I would like to point out something that can be fixed (which I'm sure someone has by now). This is assuming that you don't know why 0! = 1, not that you are just not willing to explain it. If you do, then please disregard this paragraph....that was not obvious from reading the line "don't ask me why, but 0! = 1" ;-) Anyway, 0! = 1 because, if you recall the definition of the factorial function, "there are x! permutations of x distinct objects), then the reason is clear. If you have zero objects, there is only one way to select them. In algebraic terms, the solution to x! is zero, or the null set (because there are no elements in the only permutation).

I hope this has been helpful....I felt compelled to complement your page and maybe offer a little bit of help in lieu of the help that you have offered me in my research. Thank you again, and congratulations on a well put together page =)

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Alba C

Hi, i am another one of those american 'ninth graders' who is curious as to how one would do a presentation on this? I took a look at your websitte on pascal's triangle and was almost overwhelmed with the information that i was given. It was very useful but now i have to ask what a did at the beginning, how to present this to my peers? Thank you for your time......

What's a ninth grader? I assume it's your school year and age. It sounds like a USA term. If I know your age I may be able to give you some ideas.

I'm fifteen and so are the other ninth graders in the USA we all are..what is that considered in England?, and How would my age help u find a way for me to present my project?

Your age helps me to gauge my language and tells me the types of things I can assume you may know. If you were 9 years old I would assume you had not yet done algebra but as a 15 year old I know you probably have done that.

A fifteen year old in England would be said to be in the 4th or 5th year of Secondary School (similar to your High school). We just don't use grades. I have a web page that talks a little about the differences in the English spoken in the USA and in the UK. You may find it fun to look at...

www.krysstal.com/ukandusa.html

Back to Pascal's triangle. I'm going to send you a simplified version of my web page without the background colours (sorry "colors") and you can print it out and make copies. That may be the best way to present it to you peers.

The interesting thing is how initially different parts of mathematics are all linked together: Probability and roots; algebraic expansions and Pascal's triangle. Also emphasise how you can obtain the same results by approaching a problem from two different directions: the triangle and the binomial expansion.

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Alan Speigel

I just lucked onto your website about an hour ago (I was looking for the definition of transcendental numbers).

I don't think I.ve ever seen a site showing such a breadth of eclectic knowledge!! And everything I read was explained so simply and directly. I honestly don't know how you manage all those subjects so well, and still have time to travel so extensively. You deserve a big award for everything you've done!!

Thank you very much for your site. It is indeed bookmarked!

KryssTal Reply: Thank you for your kind words. I always try to explain things the way I would have liked them explained to me when I was younger.

### 007

Hi KryssTal,

First, let me congratulate you for this Kaleidoscope of knowledge in your site. My concern is about the origin of the number ZERO. I understand was an Arabic contribution. Could you post an article about this wonderful invention. Thanks