happy Easter wishes

First of all happy Easter!!

Today I recollected what I did in August 2018. I did this experiment with dumbbells and I realized I got something worthwhile. 

Here is what I made a blog post of.

Well n by (n+1)! is really a great expression. It gives you any factorial.  Yes. But the answer is not same when compared with Euler e or Logarithmic series answers. Nevertheless the answer is worth noting as it is quite accurate.  Here are the Wolfram screenshots to review.  These are self explanatory. 5 factorial is 120. Factorial of (1/5) is 0.91816. I get 0.91818.

Actually the results are accurate. 

The other great thing is n by (n+1)! and it's series can be calculated using consecutive numbers. 

Jesus has blessed me today. I pray he blesses us you all with his love . May he guide us all to understand oneself and the nature surrounding us.

Good bye !!

wired to walk

One does not realize how one learnt to walk.

One does not realize how one learnt to talk.

I believe there are fields inside you which can make you see the floor and ceiling function. And they see the floor and ceiling function in Taylor series and its applications. When x is between 1 to infinity. And also when x is between 1 to 0. The x^n changes and n! changes.

I request my blog readers to see and appreciate the point that floor and ceiling values of n! can be seen with my method. People argue that the methods are so complex. Yes, that is true. But remember once as a child , you had difficulties even in writing A. Now you write sentences. So it is just practice.

Let peace prevail. May there be happiness.

Have a nice day !!

reading these two Kindle books

 I am reading the following ebooks nowadays.

It is tough to understand deep concepts.

I am reading this book because because I like "the approximate nature of humans" and many times not able to tolerate "the best approach methods of Artificial Intelligence".

This book is fairly easy to me.

I am reading this book because I want to develop cartoon type comics. Something on the lines of Tintin and Archies.

Which books are you reading these days ?

Do share your comments below.

i will be going ahead with approximations

I shall be going ahead with my approximations theory. On my own.

The following results do matter to me a lot. And I shall endeavor to find out why they are so.

Have a nice day !!

consecutive number theory is approximate

I had been working on consecutive number theory. I did not have relevant journals, books or a guru sitting beside me all these time. And I had deep mathematical thoughts. For example, I nearly reached Wallis pi in 2010. So what I did was explore mathematics as consecutive numbers theory. This was the best option. Also because I was alone most of the time.

I applied my thoughts on consecutive numbers. I made rational number series. I made 3 consecutive and 4 consecutive number theory. I got easy pi expressions. Easy because the partial sums were easy. 

It is "strange" that x squared decreases when x is less than 1 and greater than 0. Similarly x cubed, x to the power of 4 and so on. Euler and English mathematicians had expressions for this factor. In their e and log functions. Essentially what came across was decimal factorials. Decimal factorial exists and they "explain" the fact that x^n decreases when x is between 1 and 0.

Is consecutive numbers able to explain this phenomenon? x^n decreases when x is less than 1 and greater than zero? Also the decimal factorials?

In an approximate way, yes.

All in all, a man can truly explain the beauty and logic of the nature. Approximately. With his fingers.

That is all for now.

Have a great day ahead !! 

for nature function n!

 n! is nature blessed. And nature follows it. As gamma functions. 

n! is also used in imaginative problems as in combinations and permutations.

Do not be confused with decimal factorials. They are of gamma functions. 

Below are two expressions that can calculate gamma functions. These can be used for calculating n! as n! is nothing but gamma(n+1).

Keep solving your very own imaginative combinations and permutations problems. And when you think of decimal factorials think these are of gamma functions.

I think this way. And I hope this helps you too !!.

Have a nice day !! And keep smiling !!

floor and ceiling functions

 I asked Google the question "Are answers with floor and ceiling functions mathematical ?". The answer is "Yes".

I have a few expressions which may work well and can be considered mathematical. They however need floor and ceiling functions. 

So, all in all I do have valid mathematical statements. And they use floor or ceiling functions. The results are demonstrated with the help of Wolfram Alpha. Thank you, Wolfram Alpha.

Have a nice day !!

Leibniz calculus

Now that decimal factorial is clear to me, I shall endeavor in further learning. I understood the philosophy of 0.5!.Going  further ahead needs gamma functions,  e functions or log functions. That is because numbers are not simply 1,2,3 etc. 

I plan to learn Leibniz calculus.  I may buy a book on Leibniz calculus.  But for now it will be Wikipedia.

It has been a long journey.  2008 onwards. I kept going.  And today I am in a position to learn Leibniz calculus. 

I am literally worshipping the greats in mathematics.  Here is a photo of my notice board in my office room. 

Newton, Euler,  Gauss,  Abel, Taylor, Wallis.

Have a nice day !!

Factorials can be calculated

Factorials can be calculated with product of consecutive numbers of my type. However, the formula is different for odd and even. Here are the formulae.

So, functions like common permutation, common combination can all be calculated with consecutive numbers of my type.

Have a nice weekend. Don't forget to enjoy !!

This result

 

This approximation expression

 I present the following approximate expression.

Hope you like it.

Have a nice day !!

my theory of binomials

 

Hope you have a nice day !!

My formula

 Here is a formula that not only integrates sigma and product; but also regular binomial of the type combination(n,r) with combination(2n,n).

Hope you have liked the expression.

Have a nice day !!

here is one sigma product equivalence

 Here is one sigma and product equivalence expression. This is an exact expression. 

The expression

And the Wolfram Alpha expressions to confirm that the expression is true.

Hope you like the above expression.

Have a nice day !!

An approximate expression

 For very large values of k, the following is approximately true

Hope you like it.

Have a nice day !!

The best Sigma and product equivalence

 This one is the best sigma product equivalence

Have a nice day !!

Sigma and Product equivalence

 Here is an expression for sigma product equivalence

Have a nice day !!

A deep desire

 There was a deep desire to make binomial sort of expression with combination(2n,n). I have fulfilled the desire now.

Here is the formula

Here are the Wolfram Alpha screenshots to confirm the above expression

Have a nice day !!

combination(2n,n) from consecutive numbers

I have managed to get combination(2n,n) from consecutive numbers. Here is the formula

Here are the Wolfram screenshots to confirm the above.

So what do we have

1. Consecutive numbers form as sigma gives constants and other numbers.

2. consecutive numbers in products gives combination(2n,n)

3, combination(2n,n) gives constants and other expressions

4. consecutive numbers in another form gives rise to binomials.

5. binomials of form from above gives approximations and other results.

That's all folks. Planning to give up mathematics endeavor from now onwards. Nothing more is left out. Knitted a good theory in above.

I shall check Academia app and try and look for mathematics of Gauss, Euler, Ramanujan and Abel.

My good wishes. Have a nice day !!

New Formula

 

New Number

 I discovered the following.

I have checked up to n = 20 in my calculator. If you have an advanced calculator you can check and see

Maybe there is something significant here.

Have a nice day !!

Stronger Better young Indians

Swami Vivekananda said, "One can realize God by playing football than reading Bhagwat Gita". Swamiji had stressed on the importance of being strong from inside.  To face challenges and also to realize God.

Tomorrow might be difficult for India. Conditions may not be favorable.  We need strong, better young Indians. The world is surging ahead at a faster rate every day. 

So what do I say? What should we be focusing on?

The mathematics we have is of external world working. Calculus,  trigonometry. And of complex numbers with i acting as the sway factor that humans and circular motions make. So all in all our education is about the external world and our endeavoring sway . Be the sway be of eyesight,  of legs, of hands, or of fingers.

But we have had favorable fields during childhood that helped us walk. Helped us talk. Helped us behave. Favorable fields of our parents,  relatives and friends.  It is necessary therefore to understand the field inside us to grow and become stronger and better.  And it is here that my mathematics comes in. 

My mathematics can build a better Indian by better understanding of the field inside us. The consecutive numbers.  The three consecutive numbers.  The four consecutive numbers.  The binomials.  The approximations. And more.

I tried to convince many guys in my lifetime.  But I failed.  And today I am making a post. 

We Indians need to be receptive to ideas. After all by giving in you are not going to loose much. Are you?

My thoughts on mathematics

When I think of mathematics,  I think of English mathematicians all the while.

Brook Taylor was so awesome and so great. His Taylor series is the truth of the world.  It has some influence from Wallis.  Then Maclaurin considered from zero value, the Taylor series.  He gave us trigonometric,  hyperbolic,  logarithmic series.  Newton then considered zero at all places (because of gravity) and gave us calculus.  I get clean bowled by the genius of these four gentlemen.  All the while I keep thinking of these four gentlemen. 

Those are of the external world. 

Now the internal world.  

Internal world working and its relationship with the external mathematics is by the complex number small i. Euler gave us e to the power of I theta. He gave us gamma functions and beta functions.  Truly gems from Euler.  Gauss advocated complex functions.  That's German mathematics. 

All the above are of yesteryears. 

Present day number theories are unknown to me. I am unable to search internet search engines suitably. 

That is all for now. Have a great weekend guys!!

My story

I am a man who think in three spheres in my thoughts. Mathematics,  arts and music.

Not always. There is a very emotional fourth sphere of SAIL.  And I want MY SAIL to improve and grow in MY WAY. MY SAIL and MY WAY are a problem most of the times. And I fail to convince my superiors and get MY WAY.

Well, well. Let's move on.

Mathematics 

Phi and 1 by phi are like consecutive numbers. 1.61803 and 0.61803. Just like 2 and 1. This is the essence of my thoughts. 

I need resources like journals and books. I need an understanding guru. I don't get them.

Since 2010. At least.

Art

I have personality equations.  I have reasonable drawing skills. I have intentions of combining these two and make comics.

PDCA,  PDSA, Edward Deming are my way to improve quality of my illustrations. I have 2 to 3 years of time. Enough free time.

Music

I am a listener. I am a commentator.  I can be an inspiration. 

But my theories are way behind carnatic professionals.  

I have made my Bose 500 presets to completely bollywood songs. Namely 

1. Bollywood 60s.

2. Bollywood 70s.

3. Bollywood 80s.

4. Bollywood 90s.

5. Bollywood 2000s.

6. Bollywood 2010s.

I also listen to Ilayaraja,  Harris Jayaraj,  RDBurman, Arijit Singh, Ponniyin Selvan again and again. 

Chess, software, economy have taken a back seat. 

In chess I make silly mistakes. Software are AI these days. Economy, I don't read Economic Times these days.

Quality interest and Digital art interest are growing. 

That's me. Of present times.

Have a nice day !!