E705 -- Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae
(English Translation of Title)
Summary:
Euler shows that arctan t = (1/(1 + t2))[1 + (2/3)(t2/(1 + t2)) + ((2)(4)/((3)(5)))(t2/(1 + t2))2 + ((2)(4)(6)/((3)(5)(7)))(t2/(1 + t2))3 + ...]
With this, and some identities like p = 4 arctan(1/2) + 4 arctan(1/3), he
gets p to many decimal places.
Publication:
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Originally published in Nova Acta Academiae Scientarum Imperialis Petropolitinae 11, 1798, pp. 133-149
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Opera Omnia: Series 1, Volume 16, pp. 1 - 20
Documents Available:
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