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

Catalan Constant

Catalan constant is also now expressed in terms of consecutive number model.

Below is the expression 

Importance of Catalan constant - Even numbers are the number system itself. Just multiplied by two. Odd numbers are different. So odd numbers give brilliant results like Madhava's pi by 4. Now, squares of odd numbers are important because square of a number, I feel are better representations than to the power one of a number. So, the point to know is 1 by squares of odd numbers and alternately negated is very important and is called Catalan constant. And consecutive numbers are able to represent Catalan constant.

Have a nice day !!

Apery Constant

 Apery constant now expressed in terms of consecutive number model.

Here is the expression

You may recollect that I did Euler-Mascheroni constant earlier with consecutive number model.

Hope you like it. Have a nice day !!