#PythaShastri ( #PythaShastri is Ganesan Kirtivasan) is advocating a constant P.
P is similar to golden ratio. A very slight change.
P occurs in nature.
P is irrational.
1,3,6,10,15,21,28,36,45 . . . . is the real number series.
1/2,3/4,5/6,7/8,9/10, . . . is the rational number series.
3/4-1/2 = 1/(4×1). 1 of 1,3,6,10,15 . . .
5/6-3/4 = 1/(4×3). 3 of 1,3,6,10,15 . . .
7/8-5/6 = 1/(4×6). 6 of 1,3,6,10,15 . . .
. . . . .
. . . . .
P is calculated similar to golden ratio.
3/1 then 6/3 then 10/6 then 15/10 and so on.
I have calculated and it converges at 1.02.
P is approximately 1.02.
P is similar to golden ratio. A very slight change.
P occurs in nature.
P is irrational.
1,3,6,10,15,21,28,36,45 . . . . is the real number series.
1/2,3/4,5/6,7/8,9/10, . . . is the rational number series.
3/4-1/2 = 1/(4×1). 1 of 1,3,6,10,15 . . .
5/6-3/4 = 1/(4×3). 3 of 1,3,6,10,15 . . .
7/8-5/6 = 1/(4×6). 6 of 1,3,6,10,15 . . .
. . . . .
. . . . .
P is calculated similar to golden ratio.
3/1 then 6/3 then 10/6 then 15/10 and so on.
I have calculated and it converges at 1.02.
P is approximately 1.02.
Why should P be accepted?
ReplyDelete1+3 =4. Short of 6 by 2. -2.
3+6 =9. Short of 10 by 1. -1.
6+10=16. High than 15 by 1. +1.
10+15=25. High than 21 by 4. +4.
....
....
-2,-1,1,4, . . . .
is 1,2,3,.....
The above is Pattern no 2.
ReplyDeletePattern number 1 is the rational number series and real number series pattern.
The following is pattern number 3.
ReplyDeleteSuppose any three consecutive numbers in 1,3,6,10,15 . . . . are y,ny,mny.
Then I have discovered that m has a series 2,5,9,14,20,27 . . . .
So there are 3 patterns in all these.
Question to #PythaShastri
Do you think like this when you think of numbers?
Very deeply I think of numbers as 1,3,6,10,15 . . . Honestly, yes. About two years with numbers and analysis somehow I am able to express my thought of number systems.
I am happy to be with this number series thought because for one it is symmetric both with the difference and the rational numbers. Pattern 3 and Pattern 1. Also the numbers 1,2,3,4,5 . . . . are expressed with Pattern 2.
There was a story about an old man who calls chair a table. And a table as curtains and so on. This was a story by a Russian author. It was a sad story. By saying 1,3,6,10,15 . . . instead of 1,2,3,4,5 .... is it not sad?
No. For one there is not so much of confusion in me. Two anyway one imagines growth by 1 when we say 1,2,3,4,5 . . . .One is only changing the growth pattern in 1,3,6,10, 15 . . . .
You have done a lot #PythaShastri. Taylor, McLaurin type series. Then pi. e. gamma to some extent. Then rational numbers series. Are you happy in sharing over Google blogspot?
Yes, I am happy.
More questions to #PythaShastri.
ReplyDeleteWhat is #PythaShastri's concept of beauty in numbers and number theory?
Think of sin theta. Or cos theta. This by that and that by this. So beautiful.
Or an Euler e series in cosines and sines. Wow series. Great one.
Or the golden ratio. And the continued fraction of golden ratio. Fantastic !!
Or the Taylor and McLaurin. Genius unparalleled !!
Or the work of Sir Andrew Wiles. Age old problem of Fermat's last theorem. And a proof. Masterly !! Magnificent.
So I have given 5 instances of beauty in numbers and mathematics. I think of these and say to myself how beautiful !!
Is #PythaShastri in the above category ?
No. But I do believe it is in two category below the above. Bronze category.
Thank you, #PythaShastri.
Is there any pattern in 1 squared, 3 squared, 6 squared, 10 squared, 15 squared etc.?
ReplyDeleteYes there's a pattern.