Early History Of Mathematics Research Articles

Physical Mathematics and The Fine-Structure Constant

Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington's Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. Arthur Eddington's work leads to a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler's equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found.

Root 2: the early evidence and later conjectures

Historians believe that the discovery of the irrationality of √2, or, as it would have been described in classical Greek mathematics, the incommensurability of the side and diagonal of a square, was made in the period 550–410 bc. None of the early sources, however, includes a proof of the theorem, so historians have found it a happy hunting ground for conjectures. This article is drawn from the monographs of Knorr and Fowler, and was put together to show how much history of early mathematics is from the minds of historians.

Introduction: The History of Early Mathematics – Ways of Re-Writing

Introduction: The History of Early Mathematics – Ways of Re-Writing

Algebra in ancient and modern times

Some history of early mathematics: Eucild-Archimedes-Diophantus Pythagoras and the Pythagorean triplets Aryabhata-Brahmagupta-Bhaskara Irrational numbers: construction and approximation Arabic mathematics Beginnings of algebra in Europe The cubic and biquadratic equations Solution of the cubic and biquadratic equations: Solution of the cubic equation Solution of the biquadratic equation Some themes from modern algebra: Numbers, algebra, and the real world Complex numbers Fundamental theorem of algebra Equations of degree greater than four General number systems and the axiomatic treatment of algebra References Chronology Index.

Episodes from the Early History of Mathematics.

Episodes from the Early History of Mathematics.

New Mathematical Library: Episodes from the Early History of Mathematics . Asger Aaboe. Random House, New York, 1964. x + 133 pp. Illus. Paper, $1.95; cloth, $2.95.

New Mathematical Library: <i>Episodes from the Early History of Mathematics</i> . Asger Aaboe. Random House, New York, 1964. x + 133 pp. Illus. Paper, $1.95; cloth, $2.95.

Reviews

Reviews Get access Episodes from the Early History of Mathematics. By ASGER AABOE. New York: Random House and the L. W. Singer Company. 1964. Pp. x+133. $1.95. Biometrika, Volume 51, Issue 3-4, December 1964, Page 536, https://doi.org/10.1093/biomet/51.3-4.536-a Published: 01 December 1964

Possible Boundaries in the Early History of Mathematics

Possible Boundaries in the Early History of Mathematics

Possible Boundaries in the Early History of Mathematics

Having been invited by the editors of this Memorial Volume to contribute an article upon some appropriate topic in which Professor Slaught would be interested if he were with us at this time, a brief historical topic has been selected. Having known Dr. Slaught for many years, often discussing with him the teaching of mathematics and the types of literature which were best adapted to our work, we were naturally led to considering at various times the story of the origin and development of the subject of our major interest. I well recall that in one of our visits we dwelt upon the possibility of the opening of new regions in the early history of the subject, necessarily in the fields of numbers, and then of geometry, and finally of some crude form of algebra. We were both familiar with the current literature of the subject, but we visualized a much older era to be revealed by earlier material which scholars in the field of archeology might discover. He was greatly interested in the work being done at that time in his own university circle, particularly in the excavations then being carried on in Iraq. It was natural, therefore, that we should be led to discuss the possibility of discoveries in other fields of archeology and even of medieval documents. Recalling that meeting of only a few years ago, I seem to feel again his enthusiasm in discussing the possibility that we were then upon new thresholds of the habitations of ancient mathematics. It seems therefore appropriate to mention a few of the regions which have opened up since that time and a few which have found place in our recent histories. Briefly stated, since my talks with Dr. Slaught these regions have been widely extended and-what is proving to be of even more importance-the cuneiform records have been deposited in many large museums in most of the leading centers of culture. This spread of original material has allowed scholars, conversant with cuneiform, hieroglyphic, Sanskrit, and other alphabets and related languages, to have access to original documents. We pass over the well known list of excavations of some decades along the Euphrates and Tigris; there are others in progress at this time, with which students are not so familiar. For example, excavations are now being carried on in the Tepe Gawra, near Mosul in Iraq, where more than twenty strata (levels) have been found, each revealing a period in the life of a great city. There is also the Sumerian Uruk, the Biblical Erech, in which Level XIII dates from the fifth millennium B.C., and has brought one of the richest finds of recent years, a rare field for the discoveries of mathematical-commercial material. Level XV dates from c. 4500 B.C., and the work upon it is progressing in this very year. The evidence of number values is also being revealed at the present time in the discoveries at Chagar Bazar in northeast Syria, of c. 1900 B.C., and