Another Indigenous golden ratio transform

Here is another indigenous golden ratio transform.

minus m squared plus m plus one when equated to zero gives the golden ratio.

Hope you have a nice day !!

Indigenous golden ratio transform

My earlier blog post was a golden ratio transform. But it was not fully indigenous.  It had an expression of e^m which was borrowed from foreigners.

As I had e^m indigenous expression,  I decided to make changes in the formula.

Now here is the golden ratio transform. 

It is indeed indigenous.  All the subset expression are mine and the golden ratio transform is indigenous. 

Thank you Wolfram alpha.  You have been wonderful ❤️!!

Golden ratio transform

I have got what I have been dreaming about. An infinite series expressions which fetches the golden ratio equation.

First of all my thanks to Wolfram alpha.  You have taught me how to express.

Here is the golden ratio transform expressions. 

m squared plus m minus one when equated to zero gives golden ratio. 

Have a nice day!!

Width experiment

You may be aware that I have done three experiments with my fingers and hand.

One was lifting dumbbell with left hand. It helped me get an expression for 1 and new expression for e to the power x.

Second one was lifting dumbbell with right hand. It helped me with expression of 2. The most difficult. 

Third one was lifting okras with left hand fingers. This helped me in understanding gamma function.  And because gamma functions were termed equivalent to beta functions it improved my knowledge tremendously. 

Today I did the fourth experiment. 

Measuring width of an object with finger width. 

Distance            No. Of fingers

1 full distance        1 finger width

1/2 distance             2 finger width

1/4 distance             3 finger width 

The third reading was surprising.  I thought it will be 4 finger width but surprisingly it was 3 finger width. 

So 1 by m to the power of n of distance.  And n is the number of fingers.

Simple experiment.  But far reaching learning.

On Golden Ratio

Golden ratio is a seeing constant.  It is present in nature. But needs to be seen.

Here are four screenshots which exhibit Golden ratio equations.

You may be aware that I have three infinite series expressions of golden ratio. 

I also have support of 10 golden ratio expressions for my 3 to 4 consecutive numbers theory. 

Great Expression

Mixing the two expressions from my earlier two blog posts, one can get

You may note that we are dealing with infinite series here. (-n) and (-n+1) follow one another in one step. And combination (n,n-1) and combination (n+1,n) too. So that is the beauty here. And the result is 1.

You may know that e to the power of i into theta has similar properties. cos theta and sine theta follow one another. But the phase difference is 90 degrees.  Step of i to the power n.

Complex numbers are not just a+ib sorts. That is just the beginning. Electrical engineering supports this because magnetism and electricity have a 90 degree phase difference. i.

So complex numbers are much more complex than you would have learnt. Riemann zeta function, Dirichlet beta functions are functions dealing with complex numbers and they have a simple form which is suitable to numbers and number theory.

Did you learn something useful here ?

Another expression on 26-05-2022

The following expression was made possible entirely due to Wolfram Alpha. I am not taking credit for this.

Hope you like it.

Have a nice day !!