Reminescences
Number π from \(Al-Hv\bar{a}rizm\bar{i}ja\) until present day
Franka Miriam Brückler
orcid.org/0000-0002-8410-0476
; Matematički odsjek, Prirodoslovno-matematički fakultet, Sveučilište u Zagrebu
*
* Corresponding author.
Abstract
In this article, we describe the history of the number π from the 9th century to modern times. Until the 18th century, most of the new results were based on increasingly accurate approximations obtained using variants of Archimedes’ idea of inscribing and describing regular polygons on a given circle, and among them we particularly emphasize the results obtained by Al-Kashi at the beginning of the 15th century and Van Ceulen at the turn of the 16th/17th centuries. After the 17th century, approximations will be obtained using series, primarily Gregory’s series of powers for the arctangent function (1671) in combination with Machin’s formula (1706). However, more accurate approximations than van Ceulen’s are not needed in practice, and in the part of the article that relates to the period from the beginning of the 18th century to the present day, we devote our main attention to
new results on the nature of the number π (irrationality and transcendence), and its connection with results outside geometry (Euler’s formula, 1734, and Buffon’s experiment, 1777).
Keywords
Hrčak ID:
341422
URI
Publication date:
1.6.2025.
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