Atticus Rare Books

Die geometrischen Grundlagen der Photogrammetrie (Finsterwalder, pp. 1-43) AND Mechanische Beziehnngen bei der Flachen-Deformation (Finsterwalder, pp. 43-91) WITH Uber eine neue Begrundung der Theorie der algebraischen Zahlen (Hensel, pp. 83-87) in Jahresbericht der Deutschen Mathematiker-Vereinigung 7, 1899 [FOUNDATIONAL CLIMATE RESEARCH TECHNIQUES & DATA STILL IN USE with 1st DESCRIPTION OF P-ADIC NUMBERS]

Finsterwalder, Sebastian WITH Kurt Hensel [Kurt Wilhelm Sebastian]

Leipzig: 1899. 1st Edition. 1st EDITION OF A SEMINAL PAPER BY FINSTERWALDER ON GLACIER PHOTOGRAMMETRY, the science of making measurements from photographs. The input to photogrammetry is photographs, and the output is typically a map, a drawing, a measurement. MODERN SATELLITE POSITIONING TECHNIQUES IN CLIMATE RESEARCH ARE BUILT ON THE PHOTOGRAMMETRY TECHNIQUES & INNOVATIONS FINSTERWALDER RELAYS IN THESE PAPERS. The data and images he gathered are also still in use today.

This volume also contains the 1st EDITION OF THE FIRST DESCRIPTION OF P-ADIC NUMBERS (Hensel). More information about this follows further down. [Note that this paper is sometimes incorrectly cited as having been published in 1897. As confirmed by the journal itself, pagination, title, etc., it was not. The 1899 publication offered here is the first].

FINSTERWALDER: Beginning in 1890, “the Bavarian mathematician and geodeticist Sebastian Finsterwalder started a project to re-photograph Swiss glaciers from balloons, enabling him to observe their advances and retreats and alterations to their mass balance. Such images provide a baseline for today’s measurement of glacier retreat, and [Finsterwalder’s] repeat photography has become a key technique for measuring the effects of global climate change” (Cosgrove, Photography and Flight, 29).

In the paper, Finsterwalder is able to reconstitute topography by using a plethora of photographs taken from balloons. The sheer number of images allow him to connect the coplanar points among them and then use mathematical calculations of the many points in the images to projectively reconstruct an area. Finsterwalder’s paper “gives a clear exposition of the fact that from a set of uncalibrated images, a projective 3D reconstruction is possible and provides an algorithm for the case of two images. The concept of projective reconstruction was re-discovered in computer vision in the early 1990’s” (Berciano, “Computer Analysis of Images and Patterns,” 14th International Conference, CAIP 2011, Proceedings, Part I, 3).

HENSEL: “The p-adic numbers were motivated primarily by an attempt to bring the ideas and techniques of power series methods into number theory. Their influence now extends far beyond this. For example, the field of p-adic analysis essentially provides an alternative form of calculus” (Wikipedia).

During the last decade of the 19th century, the German mathematician Kurt Hensel (1861-1941) started his investigations into p-adic numbers -- in the simplest case, numbers which can be expanded in the form. Rooted in the development of algebraic numbers in power series, the “p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems…. Two p-adic numbers are considered to be close when their difference is divisible by a high power of p: the higher the power, the closer they are. This property enables p-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles” (ibid; Ullrich, The Genesis,163). ALSO INCLUDED ARE PAPERS BY: Mehmke (whose copy this volume was), Boltzmann (2), Muller, Sommerfeld, Brendel, Cranz, Lorenz, Fricke, Hilbert, Pringsheim, Bohlmann. Item #1394

CONDITION, PROVENANCE, DETAILS: Complete. 8vo. Bears the ownership signature of the German mathematician Rudolf Mehmke (who also has a paper in this volume). Mehmke’s contribution to mathematics “were very original and of high quality” Reich, On the Concept and Extent, January 2011). Bound in what appears to be contemporary cloth and boards; gilt-lettered at the spine where some cloth is fraying a bit. Solidly and tightly bound. Shows its age but is very good overall.

Price: $475.00