Grundlagen der Geometrie

  title={Grundlagen der Geometrie},
  author={G. B. M.},
THIS fascinating work has long since attained the rank of a classic, but attention may be directed to this new edition, which has various additions, mainly bibliographical, and seven supplements, which are reprints of papers by the author on topics related to that of his famous essay. Two of these can be enjoyed by readers with no exceptional mathematical knowledge. In the one on the equality of the base angles of an isosceles triangle, Dr. Hilbert proves, inter alia, the remarkable fact that… 
Survey of Non-Desarguesian Planes Charles Weibel
T he abstract study of projective geometry first arose in the work of J.-V. Poncelet (1822) and K. von Staudt (1847). About 100 years ago, axiomatic frameworks were developed by several people,
Perspective on Hilbert
  • D. Rowe
  • Art
    Perspectives on Science
  • 1997
As a discipline, the history of mathematics admits a wide variety of styles and methodologies. Even when the subject matter is reasonably well defined and clear, it can be fruitfully investigated in
The last chapter of the Disquisitiones of Gauss
This exposition reviews what exactly Gauss asserted and what did he prove in the last chapter of {\sl Disquisitiones Arithmeticae} about dividing the circle into a given number of equal parts. In
On the Complexity of Hilbert's 17th Problem
It is able to show, assuming a standard conjecture in complexity theory, that it is impossible that every non-negative, n-variate, degree four polynomial can be represented as a sum of squares of a small number of rational functions.
Axiomatizations of Hyperbolic and Absolute Geometries
A survey of finite first-order axiomatizations for hyperbolic and absolute geometries. 1. Hyperbolic Geometry Elementary Hyperbolic Geometry as conceived by Hilbert To axiomatize a geometry one needs
The twofold role of diagrams in Euclid’s plane geometry
The purpose is to reformulate the thesis that many of Euclid’s geometric arguments are diagram-based in a quite general way, by describing what he takes to be the twofold role that diagrams play in Euclid's plane geometry (EPG).
Methods, concepts and ideas in mathematics : aspects of an evolution
ion from the individuals; they are then considered and studied in their totality from certain points of view. A next step is to study abstract totalities (sets). This is perhaps a general
Can one design a geometry engine?
  • J. Makowsky
  • Mathematics
    Annals of Mathematics and Artificial Intelligence
  • 2018
It is shown here using elementary model theoretic tools that the universal first order consequences of any geometric theory T of Pappian planes which is consistent with the analytic geometry of the reals is decidable.
Dense Sphere Packings: A Blueprint for Formal Proofs
The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new