March 25, 2018 Sunday

Bedtime Story 

The First Twenty Numbers of Bernoulli 

Bernoulli numbers are depicted as B_n with the first Bernoulli number B₀ being equal to 1 and the second Bernoulli number B₁ being 1/2.

For all odd n other than 1, B_n = 0.

For all even n, B_n is negative if divisible by 4 otherwise they are positive.

So the first twenty B_n are as follows:

B₀ = 1

B₁ = 1/2

B₂ = 1/6

B₃ = 0

B₄ = -1/30

B₅ = 0

B₆ = 1/42

B₇ = 0

B₈ = -1/30

B₉ = 0

B₁₀ = 5/66

B₁₁ = 0

B₁₂ = -691/2730

B₁₃ = 0

B₁₄ = 7/6

B₁₅ = 0

B₁₆ = -3617/510

B₁₇ = 0

B₁₈ = 43867/798

B₁₉ = 0

B₂₀ = -174611/330

Now how do we get the further Bernoulli numbers?

This is exactly the point when we need to return to Ada Lovelace and her Note G in her translation of the treatise of Luigi Menabrea.

It was on the night of February 16, 2018 Friday that we had digressed from Note G of Ada Lovelace – Part 3 to understand the story behind the Numbers of Bernoulli.

For it is here that this brilliant lady describes the algorithm for generating Bernoulli’s numbers using the engine of Charles Babbage.

This gives Bernoulli numbers the honor of being the subject of the first complex computer program ever to be published. 

In the nights to come, we shall return to the Note G of Ada Lovelace which I must warn with all sincerity will not make for an easy reading; yet I promise to clarify it in much simpler later language in future.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

                              

Good night mon ami and my fellow cousin ape.

                           

  

                

             

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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg