A new formula

 I observed the following.

Then I posted this formula in MathGPT to verify the correctness. The formula appears to be true for all cases of m, where m >= 1.

Have a nice day !!

Did the Christian Golden ratio came first or the Hindu consecutive numbers?

The Christians believe in golden ratio. The continued fraction, fibonacci series are famous expressions of the golden ratio.

Now I have come up with expressions of golden ratio. These are of consecutive numbers.

We, Hindus never really believed that God made number laws. Christians believe it. At least over internet they claim golden ratio is from the holy bible.

Well, well. To me consecutive numbers are ahead in the race.

Have a good day !!

A nature blessed human

In this blog post, I am outlining some mathematics so that a human being is able to lead a nature blessed life. What is nature blessed life? It is not a technological driven life but a life lead on nature's golden ratio and natural electricity. It is more of nature's positives and negatives than a technological induced positives and negatives. It is about sadness and happiness inside mind happening due to nature laws. The day and night of our lives.

Wallis, Newton,  Taylor and Maclaurin have shaped our lives for centuries.  The human about to take a step in the familiar gravity affected earth.

My blog post is on the above paragraphs.  I have utmost respect for English philosophy and I am deeply involved in Sir Roger Penrose thoughts.

First of all, I would like to say that my binomial which start from 1 (one) are indeed nature blessed.

Secondly, I want to say that humans do compare IQ, strength, contentment and other nature blessed traits. These are of binomial distribution.  And therefore these two expressions are important. 

Thirdly, we compare ourselves with the best. With Einstein, Alon Amit, Gates, Barenghi, Jung Gi etc. And therefore this equation is important. 

The fourth point is about our selection. Our contentment. Our happiness.  Our greed. And therefore the below expression. 

This is how I think. And thought let me share my thoughts. 

Have a nice weekend.  Enjoy your days of weekend  !!

The Devil formula for 2n!

I have made a formula for 2n factorial.  I have called it the devil formula because 3.3 can be 3 or 3.33333 . Similarly 0.066 can be 0.06 or 0.0666. And so can 1.3 be 1.33 or 1.3333. This formula can be adjusted and near value of 2n factorial be reached. However this formula works from 100 to above. 

The formula is

Hope you have a fine day !!

2n factorial formula made accurate

You may be aware that I made 2n! formula of the type ((((n+1)(n+2))/2)^(n)). I have made it very approximate. 

The formula for (2n)! is

The Wolfram Alpha results to confirm that the formula is now very approximate. 

Have a nice weekend!!

(Today on September 8th, 2024)

If you are doing a programming in computer, then you may use the following.  The results will be more accurate.

I have been working on ((((n+1)(n+2))/2)^n) since April. 5 months. I derived the formula from Measuring Behavior expression or what I term it to be equivalent to Wallis pi. I was trying to get 0.5 factorial.  While doing that I discovered the above pattern for (2n)!. So a journey of 5 months of intense application ended yesterday night. 

Of course, James Stirling formula for n! is far more superior and has far more fidelity. 

But the expression (((n+1)(n+2))/2) is the sum of first (n+1) numbers. And that is the reason why I persisted with this formula.  Because sum of (n+1) numbers to the power n is related to 2n!. I found that interesting!!

Math GPT Answers

I was not sure whether two of my approximations statements were true or not.

They were

(a/b)^k

the next numbers

Math GPT has done analysis and found out that the statements are true

(a/b)^k

the next numbers

I am feeling satisfied. Have a nice day !!

1 percent error in calculator range

 I have modified my earlier formula and it now fetches result in the calculator range to 1 percent. Given below is the screenshot of the formula

And the Wolfram Alpha screenshot to confirm 1 percent error claim.

Have a nice day !!