A preface to the reader
A recovery of Brouncker's proof for the quadrature continued fraction.
350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...
About one problem of Bernoulli and Euler from the theory of statistical estimation.
We consider some results by D. Bernoulli and L. Euler on the method of maximum likelihood in parametric estimation. The statistical analysis is made by considering a parametric family with a shift parameter.
Binomial coefficients' tabulation system or Pascal's triangle: A numerical model rips the loom of time.
Blaise Pascal matematik a myslitel
Brachystochrona
Caustics in Greek antiquity
The word caustic was introduced by Tschirnhausen in 1686, in the Latin expression caustica curva. We show that the study of the optical caustics goes back well before, at least to the hellenistic period. We present a small Greek text, whose author is perhaps Geminus (1st cent. B.C.), describing an optical phenomenon called achilles. We show that the term achilles, which has appeared only once, to our knowledge, in the literature, means caustics by reflection. We complete the description of the achilles...
D’Artagnan mezi matematiky - pocta Pierru Fermatovi k 400. výročí narození
Das Problem der drei Würfel in der Vorgeschichte der Stochastik.
Descente infinie et analyse diophantienne : programmes de travail et mises en œuvre chez Fermat, Levi, Mordell et Weil
Elementargeometrische Integrationen von Pascal.
En el quinto centenario del nacimiento de Copérnico (1473-1543).
Factor tables 1657–1817, with notes on the birth of number theory
The history of the construction, organisation and publication of factor tables from 1657 to 1817, in itself a fascinating story, also touches upon many topics of general interest for the history of mathematics. The considerable labour involved in constructing and correcting these tables has pushed mathematicians and calculators to organise themselves in networks. Around 1660 J. Pell was the first to motivate others to calculate a large factor table, for which he saw many applications, from Diophantine...
Fermat et les prémices d’une mathématisation du hasard
Fermat’s method of quadrature
The Treatise on Quadratureof Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, , or under a higher hyperbola, —with the appropriate limits of integration in each case—has a second part which was mostly unnoticed by Fermat’s contemporaries. This second part of theTreatise is obscure and difficult to read. In it Fermat reduced the quadrature of a great number of algebraic curves in implicit form to the quadrature of known curves: the...
Galileo en el largo campo di filosofare.
Glücksspiel und Markovketten.
History of mathematics in China: A factor in world history and a source for new questions.
Huygensův spis „De ratiociniis in ludo aleae‟ (K 300. výročí úmrtí Christiana Huygense)
I baricentri trovati da Torricelli.