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I am an engineer who is in love with math and lifelong math student. I love to learn new things in mathematics for self-satisfaction. My idols are Gauss , Euler , Ramanujan because they were in love with math as I feel.


Jul
9
revised How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?
edited body
Jul
9
answered How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?
Jul
8
accepted Next generation numbers
Jul
6
answered Difference between permutation and combination?
Jul
5
revised Closed form solutions of $\ddot x(t)-x(t)^n=0$
deleted 1 characters in body
Jul
5
answered Closed form solutions of $\ddot x(t)-x(t)^n=0$
Jul
4
awarded  Benefactor
Jul
4
comment Next generation numbers
Now more clear general picture of algebra. If we define different rules for some operators, we have different algebra. I read the remarks in the link below and it mention my question's answer above that $x^2+1=0$ has infinitely many quaternion solutions. Now I feel more stable. I understood how important to define clearly which algebra we use to solve an equation. en.wikipedia.org/wiki/Quaternion#Remarks
Jul
4
revised Next generation numbers
added 11 characters in body
Jul
4
comment Next generation numbers
:If so Quaternions cannot have any relation with algebra. Right?? we just write $x^2+1=0$ and the equation does not have any knowledge about complex plane we define everything while searching solution of it. $(x.x+1=0)$ has just with operators $(. , + )$. I believe it must be more clear definitions of quaternions. Thank you very much for your answers. Really very helpful
Jul
4
comment Next generation numbers
If it is true , Fundamental theorem of algebra should be wrong. According to it that Gauss proved $x^2+1=0$ must have 2 roots. ${+\sqrt{-1},-\sqrt{-1}}$ you mention more than 2 roots can be. Is not it a contradiction? Thanks for answers.en.wikipedia.org/wiki/Fundamental_theorem_of_algebra
Jul
4
comment Next generation numbers
I understand the definition of quaternions. Please consider $i^2+1=0$ thus $i^2=-1$ and then put it in $i^2=j^2=k^2=ijk=-1$. you will get $-1=j^2=k^2=ijk=-1$, and from that if we solve via algebra rules $j=i=\sqrt{-1}$ and $k=i=\sqrt{-1}$ and from last $\sqrt{-1}=-1$. Please explain how to solve that paradox. Is the known algebra wrong? where is the problem?
Jul
4
comment Calculate $\int f(x) f''(x)dx$
@lhf:I do not know any technics to solve $\int f'(x)^2 dx $ without endless series. if you have a closed form solution of $\int f'(x)^2 dx$ and also you would have a closed form of $\int 4x^2e^{2x^2} dx$ when $f(x)=e^{x^2}$ with elemantary functions. They are related to each other. Please see math.stanford.edu/~conrad/papers/elemint.pdf
Jul
4
comment Calculate $\int f(x) f''(x)dx$
To write the solution without an integral is big and deep problem for mathematics.
Jul
4
comment Next generation numbers
When I check hyper complex number links just some number definantions such as $j$,$k$ but no any equation that defines the new number system in an equation of $x$ as we can define for negative numbers,rational numbers,irrational numbers, complex numbers.
Jul
4
comment Next generation numbers
I do not see an equation of $x$ in hyper complex numbers. I wonder exactly this why we cannot write an equation includes $x$ and operators and equality as we wrote for complex numbers $x^2+1=0$. Is there any proof that such equation is impossible to write for hypercomplex numbers? thanks for your answers
Jul
4
revised Next generation numbers
added 19 characters in body
Jul
4
comment Next generation numbers
@anon: Thanks for link. I try to see an equation includes operators and $x$ that we want to find it in new number system. Is it possible?. I noticed this finish in next number system definations after complex numbers.
Jul
4
revised Next generation numbers
added 41 characters in body
Jul
4
revised Next generation numbers
added 41 characters in body