The formula for my pentagon side of a unit circle was root2 minus 3/4 of root3 minus root2.
During the construction I realized that the root3 based arc by the corresponding chord was important. And so was root2 based arc by the corresponding chord.
And wonder of wonders, the above ratios fetch pi. And they are what in the above two expressions.
My intuitions are strong.
But my problem is it is difficult to prove the above formula. However I can demonstrate the results to be true.
Madhava of Sangamagrama pi by 4 can be proved. Arctan of 1. The whole of yesterday was spent on trying to prove the result of mine. But I couldn't.
Can anyone help me?
Have a nice day.
There is a pattern to my pi formulas. Look at the below examples.
(How do you find out Wolfram alpha? Tell me your patents !! )
2 comments:
In fact the proof might be simple.
Circumference by diameter is pi.
Circumference by integer when divided by diameter or its ratio shall also be of pi.
Root 3 and root2 arcs are rational parts of Circumference. And the chords to root2 and root3 are parts of diameter.
Hence proved.
I think it is simple and sufficient.
What do you say dear readers?
Do I make sense?
Sirs,
These pi formulas are of golden ratio formula
n squared plus n minus 1 extension.
What is being done here is m into n squared plus m into n minus m equals say q variety.
The reciprocals of these give pi.
In philosophical terms it means golden ratio is okay with pi and numbers.
But proof?
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