The combination formula binomial(n,r) is now made continuous. This means that one need not go back and forth or up and down but keep moving ahead.
Here is the formula and an example with it.
That is why binomial distribution are so natural. It is continuous.
I feel ecstatic. I hope you like the expression.
Below is the Wolfram Alpha screenshots for binomial(7,2) and binomial(8,3)
Have a nice day !!
Right from my childhood I would wonder why there is no formula for a^n-b^n and a^n+b^n.
I have fulfilled this dream of mine yesterday. It took me whole Sunday to do that. 😄. My mathematical prowess is weak. But my intuitions are okay, I guess.
Here are the formulas.
They are not exactly a^n-b^n and a^n+b^n. But the values can be computed.
Have a nice day, guys !!
Here are two more binomial results
And the Wolfram Alpha results to confirm they are correct
My three consecutive number model fetch all the major constants.
I hope you like the expressions. Have a nice day !!
This result is the combination of the results posted in my last two blog posts.
This result is interesting because children often wonder there is a formula for (a+b)^n but no formula is there for a^n-b^n. Now these children have something to feel happy about.
The formula is
And the Wolfram Alpha screenshot to confirm above is true.
Have a nice day !!
The following expression is similar to the expression in my earlier blog post.
And the Wolfram Alpha screenshots to confirm the above is correct.
Have a nice day !!
Most of my mathematics was developed from intuition. I would have an intuition. And I would type them in Wolfram Alpha. And the results were obtained.
Many, many thanks to Wolfram Alpha for I was able to express my intuitions mathematically.
The following result is also one from my intuition.
Here are the Wolfram Alpha expressions to confirm that the above expression is correct. I have used a equal to 5, b equal to 7, m equal to 4 and k equal to 6.
Did you like the expression ? There are two standard binomial statements on RHS multiplied by two algebraic expressions. The numerator binomial statement starts from 1. The denominator binomial statement start from 0.
Have a nice day, guys !!
KAAL number is a memory of a few months.
Yesterday, I did an expression and got 1 by e. Today, I tried the same expression with alternate negation. I got 0.216. And inverse of 0.216 is about the same value as KAAL number.
This is interesting.
I was thinking about something, when the expression on the LHS, came into my mind. I wanted to find out whether the expression on LHS results in something good.
Yes, the expression results in 1 by e.
And below is the Wolfram Alpha screenshot to confirm that the expression is indeed 1 by e.
Have a nice day. Have a nice weekend !!
There are three ways to look at my drawing objectives which are to be achieved in 2 years time.
First way - To draw like masters
Second way - To achieve perfection in pencil control
Third way - To reach art level 80 in the eyes of AI.
Of course, I shall be working on still life drawings, outdoor drawings, comic drawing and cartoons and portraits. But above are the improvement plans.
I hope you have understood my expectations from myself.
Weekend is nearing. Have a great weekend, guys !!
This is my present best shaded hand.
Art Improvement needed (in one year)
1. Exercises for form Bending
2. Exercises for form carving
3. Exercises for form agglomeration
4. Exercises for form mannequining common creatures, humans, objects
5. David Finch shading. Giovanni Civardi shading. Both
Mathematics Improvement needed (life long)
1. Hypergeometry self learning
2. Digamma self learning
3. Bessel functions self learning
4. Whether complex functions too ? ( wondering!!)
Music Improvement needed (short term - 2 months)
1. Finger movements and playing in harmonium
Personality Improvement needed (as much possible, daily)
1. Regularity in 15 minute Vipassana
2. Regularity in prayers, sandhyavandanam
Have a nice day, guys !!
My foldable chair will take time to arrive. Then I shall begin Ranchi township sketching.
I am presently using my sketch book, pencils for indoor drawing.
Here is one I did.
I shall follow the same style for outdoor sketching too.
To have clarity
To boldly use pencils.
There is a door. There is a refrigerator. There is a curtain. There is a clock. There are two switch boards. It is a section of my main hall in my quarters.
I hope you like the drawing. Have a nice day !!
Frank Rines in landscape
Proko in anatomy shading
Kim Jung Gi in comic drawing
In this blog post, I am outlining my drawing art plans.
1. Drawing Exercises
Mirroring
Drawing alphabets extrusions on planar surfaces
Drawing alphabets extrusions on spherical surfaces
Extrusions and Intrusions. Addition and subtraction of drawing alphabets.
Carvings
2. Actual Drawing Practices
Still life drawings inside
Ranchi township drawings
Human Anatomy shading
Comic drawings
3. Time Frame of 2 years
Above is the drawing notebook for Ranchi township drawings.
And below are the foldable chair for outdoor drawings and human anatomy book ordered by me from Amazon.
My blog posts are mainly autobiographies. I write about my plans, action plan and steps taken towards action plan.
This blog post is no different.
Drawing Exercises
I plan to concentrate on spherical and circular paths for drawing exercises. This is because I am strong in constant pi. I also expect to be driven by constant phi and hope to get higher perspective proportions correct.
Music
As I am concentrating on compositions only, I plan to do 4 finger movement exercises only. In my harmonium.
1. Sa, Ri, Ga........ And backwards.
2. Sa Sa, Ri Ri, Ga Ga........ And backwards.
3. Sa Ri Ga, Ri Ga ma, ....... And backwards.
4. Sa Ri Ga ma, Ri Ga ma pa, ..... And backwards.
These exercises are sufficient to improve my finger movements and develop enough competence to play for compositions.
(Ilaiyaraja is playing today and tomorrow in a concert at Chennai. I badly wanted to attend. But money saving is important to me at present due to personal commitments. Not able to spare money for show. Shall watch in Sun TV from 3pm if possible).
Mathematics
I am trying to give R&D angle to my mathematics, currently. I don't want to write more, now. I work in RDCIS, Ranchi.
That's all for now !! Have a great weekend !!
I was confused as to how I should lead my life. With respect to religion. With respect to religious practices downloaded from ancestors. And with respect to my drive. And with respect to world peace.
I want to follow ten commandments.
I want to do Sandhyavandanam. It is not entirely wrong as per ten commandments to do Sandhyavandanam. As you are following your gurus and Rishis. And Gayatri mantras are vibrations of nature only.
I want to do meditation. I found yogic way of doing meditation confusing and difficult. Then quite recently I came to know of Vipassana. The Buddhist way of meditation. I find Vipassana very suitable to me. Vipassana is not against ten commandments as it is of finding peace of mind for yourself and in yourself.
I shall be visiting temples too. Most of the temples have Shiva Linga. And worshipping Shiva Linga is not fully against ten commandments. This is my personal thoughts.
I shall read, study and master Matthew, Proverbs and Psalms from Holy Bible.
So that's me.
Ten commandments. Sandhyavandanam. Vipassana. Shiva Linga. Matthew. Proverbs. Psalms.
For world peace. For better understanding of working of nature and humans and myself.
My Behavo comics over Tapas has now reached 1K viewership. I feel very happy to announce this.
This weekend is coming to an end. Have fruitful weekdays ahead. Good wishes!!
I call the variables man(m), woman(w), kid(k), God(z) and Love(l)
Have a nice day !!
For those who have been reading my blog would know that I managed to express pi, phi, 1,0, root 2, root3, Euler-Mascheroni constant, Apery constant, Gauss constant, Khinchin constant in terms of consecutive numbers model.
Now I have managed to express the cos(x) and sin(x) too in terms of consecutive numbers model.
Here it goes
The first two are the Maclaurin series for cos(x) and sin(x); and the next two are consecutive number series of cos(x) and sin(x).
The consecutive number model is so rich. One is sitting in a bench. One person passes by. Then a second person. Why? A person is waiting in office for lunch. One packet is distributed. Then the second one. Why? A person is choosing potatoes in a vegetable shop. He selects one potato. Then the second one. Why ?
There are so many Whys with consecutive number. One can become a sanyasi too using consecutive number method for meditation and analysis. 😄😄Consecutive numbers are that powerful.
This is nice.
What do we get if we add numbers and divide by their multiplication and add the resultant all the way till infinity ?
We get 3 times e by 2.
And the Wolfram Alpha screenshot to confirm that this is true.
Have a nice weekend guys !!
These days I am practicing frames for comics.
This exercise of practicing frames will be useful in digital drawing as this will be a layer.
Hope you guys are doing fine. Have a nice weekend!!
I feel my golden ratio ability is enough to get special attention from Indian think tank and academicians and government. As I developed proven abilities in mathematics, art and music.
Only God can judge whether I am correct or not.
Here are Google AI thoughts on this issue.
KAAL number is 4.4.
Presently,
You may recall 1+1/x+1/(x^2)=2 is the golden ratio expression.
Then I said if we raise 1 to very small number, 2 to very small number and 3 to small number, one gets LHS of just above expression.
I was talking of raising only the n to some power. Say raising n to q/r.
What if we raise n to q/r, x to n+s/t and start from u/v and end at w/x. Is there an algorithm for this ?
Yes. Wolfram alpha is showing results.
This can give advanced results for KAAL number.
But it is not in my hands. A big research team is required.
Will this idea get materialized?
No. Because it is India.
KAAL number expressions were made. We used 1+2/x+3/(x^2) for p and got 1/2 number positions correct with correctly placed leading 0s.
The following two results from Wolfram Alpha are promising and we may get 2/3 number positions correct with correctly placed leading 0s.
I can check only a little with calculator and Wolfram Alpha. But I shall try.
But real thing is getting a nod from Professors of Mathematics.
