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BoldRIFT was formed in March 2020 to find useful mathematics applications for information theory:

This is TMT’s second publication: Half angles: sequence of Pi integral formulas (up to date version)
ABSTRACT . Draft V1.3: As part of a transversal Mathematics Trial approach (TMT), this article
combine geometry and calculus, I’ve found a sequence of π formulas based on the subtraction of a
triangular area to the circular curve integral to obtain the area of the top one2 n th of disc quadrant S n (R)
of radius R for n ∈ {2, 3, 4, …}.
This article includes the following content:
(1) Useful beforehand definitions: plane quadrants, disc quadrant, disc quadrqant , circle equation
(2) A reminder about π’s disc quadrant integral formulas
(3) the 2 −n π sequence: applying half angles formulas iteratively to π
(4) π integral formula based on the top half disc quadrant
(5) π integral formula based on the top quarter disc quadrant
(6) π integral sequence based on the top one2 n th of disc quadrant.
(7) Conclusion