Monday, January 8, 2018

More on Vilvam tree

I had already talked on √2 based on vilvam /bael twig and its leaves.
The continued fraction was
[1,1,2,1,2,1,2, . . . . . . ]
It takes an expert to say that √3 is due to wind on √2 leaves.
What will happen when wind blows on a bael twig. The two leaves will make a namaste and come back to the original state.
Therefore the continued fraction of √3 is
[1,1,1,1,2,1,1,1,2, . . . . . .]
Hence proved.

Euler and #PythaShastri

First things first. Most of basic feelings of mathematicians are basic.
Euler talked on primes.
#PythaShastri had vision of measuring behaviour.
Euler was able to utilise primes in numbers in 3 ways. 2 for pi and 1 for Riemann zeta functions. For pi one method was - and + of primes in 1/n Riemann zeta functions.  1 point. Another was as products of primes and divided by nearest multiple of 4s. 1 point. Also he talked of 1/1- (1/P(k)). 1 point. 3 points.
#PythaShastri was able to utilise primes in 1 way. Decimal point. A sort of Riemann zeta functions. 1 point.
Euler gets  3 points and #PythaShastri 1 point.
Euler knew and expressed gamma. 1 point.
So Euler gets 4 points and #PythaShastri 1 point.
#PythaShastri did pi with own methods. 1 point.
Euler 4 points and #PythaShastri 2 points.
Differential are west-tech. They are events. Constant e.
Euler was greatest. I am reasonably ok as events methods usage.
No points to me here in differential, integral or logarithmic.
#PythaShastri has primes and combinations advantage courtesy measuring behaviour.
#PythaShastri can work on Ramanujan and Chudnovsky pi functions.
If at all I take chances. Or get a chance.
This finishes the topic.

Sunday, January 7, 2018

Puzzle 2 - Rice Plate

Raghavan was a bachelor and was an interior designer. He came to Kolkata 40 years back from his village in south leaving behind ages of agricultural practice of rice growing.
Raghavan was asked by his boss to entertain six people with lunch on a Sunday. His boss told him that these six people were important and Raghavan need to serve them biryani and side dishes.
On the day of lunch, the six people arrived. Then they sat for lunch.
Where was the biryani bowl kept in the table ?

Friday, January 5, 2018

Puzzle 1 - Musical Chairs

Tarun was always chided by his wife Jaishree that he did not socialize much and was silent in parties. Jaishree wanted Tarun to be a star of parties.
Tarun realized that to win the heart of Jaishree, he needed to impress people attending these parties. Most of the parties had musical chairs competition and Tarun decided that he needs to win all these musical chair competitions to impress.
Tarun was highly intelligent and had a masters degree in engineering. He decided to make a plan for success in musical chairs competition. What could be the plan?

Wednesday, January 3, 2018

√2 and √3

√2 and √3 were known in earliest of civilizations and have been followed by generations.
0 to 1 (or) Riemann zeta functions is new knowledge.
Though I got involved in Riemann zeta functions, √2 and √3 are close to me and most of the constants are expressed by it, though to one or two places of accuracy only.
  1. (√3+√2)/2 + (√3 - √2)/7 = 1.618 (phi)
  2. 1/(√3 - √2) = 3.1416 (pi)
  3. √2 - 3/4(√3 - √2) = 1.175 (side of a pentagon)
  4. √3 + √2 = 3.146 (pi)
  5. √3/√2 = 72/60 (heart beats)
  6. √2/√3 *10/3 = 2.72 (e)
  7. (√3 + √2)/2  - 1 = 0.57 (gamma)
  8. (√3 + √2)(√3 - √2) =1
I hope to lead a better balanced life in future as far as mathematics is concerned.

Tuesday, January 2, 2018

Most beautiful constant

An increase of 1 from 1 will be an increase 2 times.
An increase of 1 from 10 will be an increase just 1/10.
I used to wonder about it. Is it fair. Is there an explanation.
About a year back, I discovered the answer. After discovery of Riemann Zeta Functions.
The number so aligns that the lower power numbers align with higher values. Euler made this equation. And the constant is called Euler-Mascheroni constant(γ).

γ = 1/2 (1/2²+1/3²+1/4² +. . . . . . )+2/3(1/2³+1/3³+1/4³+. . . . . . . . )+3/4(1/2⁴+1/3⁴+1/4⁴+. . . . . . )+. . .

The value of γ is 0.5772156649015328606065120 . . .