Vandermonde was brilliant

I rate these two relationship due to Vandermonde as brilliant.  Wow !! Fantastic sir !!

The first is called Cauchy-Vandermonde identity.  The second one is called Vandermonde identity.

I have product formula for combination(2n,n) and combination(2n+1,n).

I shall be working on your identity Vandermonde sir. The second one.

Have a nice day !!

Five elements to my art

I wanted to make the relationship between n(n+1) and n ! continuous; I wanted to make better the relationship between phi and pi in infinite series.

But am unable to. I tried collaboration with big institutes; but no initiative from them.

I have left mathematics for a while.

I am now into art. Concentrating on art.

I have defined five elements for art. Pi, phi, triangles,  shadings and textures.  These elements have to be realized every instant. The brain has to realize. The mind has to realize.  The hand has to realize. 

Of course you talk of art in terms of proportions,  perspective,  position too. But these are physical actions. The above five are psychology. 

So that's what it is that I plan to do.

Phi and Pi

 

Newton was far too good

In this lifetime, I managed to give consecutive number model. Based on Rational Number Series. These are my coined terms. These are good in infinite series. These can give a better world.

But Sir Isaac Newton was so far ahead. Cannot believe it. He gave functions. He gave calculus. He made Force laws. He explained the mechanism of the working of things. Most Amazing !! Words cannot describe his contributions. Far, far ahead. Simple models. Explained it all.

Nature works on infinite series. But do not know whether this is the truth. Maybe, relativity is the truth. Still I would say to understand working of nature in gravity based earth, consecutive number model based on rational number series is a good bet.

India do need nature principles which are gravitational earth based. To take better judgement, to try better social solutions, to dream of uniform methods.

Have a nice day !!  

phi minus 1 in infinite sum

I have made now (phi-1) in infinite sum method.

Here it is

Hope you like it. Have a nice day !!

Phi and pi both from product and sum methods

 Using product method and using sigma method I along with Wolfram Alpha have obtained phi and pi formula. 

Product 

Sum

Hope you like these!!

Khinchin constant

I have managed to express Khinchin constant too with my consecutive number model. I am not too sure about the meaning of Khinchin constant. Only thing I know is numbers are expressed in geometric mean and the coefficients form a continued fraction giving us Khinchin constant.

Here is Khinchin Constant in consecutive number model.

All of these expressions are an offering from my side to Lord above and the lovely nature he has given to us.

I hope you like it. Have a nice weekend guys. 

Some of the titled constants expressed in consecutive number model