Related papers: Adam Adamandy Kocha\'nski's approximations of \pi:…
Annotated parallel text in Latin and English of the classic paper of Adam Adamandy Kocha\'nski "Observationes Cyclometricae", published in Acta Eruditorum 4:394--398 (1685), in which he presented approximate geometric method of…
Annotated parallel text in Latin and English of the paper of Adam Adamandy Kocha\'nski "Solutio Theorematum Ab illustri Viro in Actis hujus Anni Mense Januario, pag. 28. propositorum", Acta Eruditorum, Lipsiae 1682, pp. 230-236, in which he…
Annotated parallel text in Latin and English of the paper of Adam Adamandy Kocha\'nski "Mensurae universales magnitudinum ac temporum", Acta Eruditorum, p. 259--266, May 1687, in which he presents some ideas of how to establish universal…
In his famous work, "Measurement of a Circle," Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern…
The aim of this paper is to review how some approximation results in commutative algebra are being used to construct equisingular deformations of singularities. The first example of such an approximation result appeared for the first time…
Translation from the Latin of "Annotationes in locum quendam Cartesii ad circuli quadraturam spectantem" (1763). The passage Euler is referring to is the "Excerpta" in part 6, p. 6 of Descartes' 1701 "Opuscula posthuma". Before reading this…
A brief overview of publications in approximation theory of functions known to the author and connected with scientific publications by V.~K.~Dzyadyk (1919--1998).
This is a letter to the editor concerning Semjon Adlaj's article "An eloquent formula for the perimeter of an ellipse", AMS Notices 59, 8 (2012), 1094-1099.
The Dutch scientist Christiaan Huygens refined Archimedes' celebrated geometrical computation of $\pi$ to its highest point. Yet the rich content of his beautiful treatise \emph{De circuli magnitudine inventa} (1654) has apparently never…
We provide a commentary on Teichm{\"u}ller's paper "Extremale quasikonforme Abbildungen und quadratische Differentiale" (Extremal quasiconformal mappings of closed oriented Riemann surfaces), Abh. Preuss. Akad. Wiss., Math.-Naturw. Kl.…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
In order to approximate transandental functions, several algorithms were proposed.Historically, polynomial interpolation, infinite series, $\cdots$ and other$+,\times, -$ and $/$ based algorithms were studied for this purpose.The CORDIC…
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide…
The perimeter of an ellipse has no exact closed-form expression in terms of elementary functions, and numerous approximations have been proposed since the eighteenth century. Classical formulas by Fagnano, Euler, and Ramanujan, as well as…
There is little known about the methods used by the ancient Babylonians and Egyptians to arrive at their recorded estimates of the value of Pi. A surprisingly accurate estimate of Pi was recently revealed coded within a verse in the book of…
The early Renaissance artist Albrecht Durer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and mathematical tools for their trade. In the…
This paper is intended to serve two purposes: one, to present an account of the life of Sangamagr\=ama M\=adhava, the founder of the Kerala school of astronomy and mathematics which flourished during the 15th - 18th centuries, based on…
Confocal quadrics capture (encode) and geometrize spectral properties of symmetric operators. Certain metric-projective properties of confocal quadrics (most of them established in the first half of the XIX$^{\mathrm{th}}$ century) {\it…
In this paper we give another proof of the Chudnovsky formula for calculating $\pi$ - a proof in detail with means of basic complex analysis. With the exception of the tenth chapter, the proof is self-contained, with proofs provided for all…
We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is…