"Bibliography of Hyper-Space and Non-Euclidean Geometry
." American Journal of Mathematics 1 (3): 261-276.
was not appropriate to cover within the timeframe and the ordering of the syllabus.
In the second part of this project we look at the same problems with taxicab geometry--a non-Euclidean geometry
system that may be more useful under certain circumstances, for example when movements are constrained by having to follow roads.
Research interests: geometry of navigation, Electronic Chart Display and Information Systems (ECDIS), Electronic Chart Systems (ECS), Integrated Navigation Systems (INS/ IBS), safety of marine navigation, differential and non-Euclidean geometry
It is also known as a type of non-Euclidean Geometry
, being in many respects similar to Euclidean Geometry.
M.: A Simple Non-Euclidean Geometry
and its Physical Basis, Springer, New York--Heidelberg--Berlin, 1979.
Turning to a classical example--The Brothers Karamazov--one encounters a passage that certainly demands a pause for reflection: Ivan's comparison of his theological doubt to the existence of non-Euclidean geometry
. Ivan Karamazov sees his inability to grasp non-Euclidean geometry
as evidence that he can't understand God.
Technically, 'the non-Euclidean geometry
' that was envisioned by him and his contemporaries was way too deep for me to fully comprehend.
Today, the non-Euclidean geometry
of Gauss, Lobachevsky and Bolyai is called hyperbolic geometry, and the term non- Euclidean refers to any geometry that is not Euclidean.
1040) on the foundations of Euclidean geometry, leading him in the process to prove theorems in non-Euclidean geometry
, including a formulation of what is today called the Strong Hilbert Axiom of Parallels.
Modernism in geometry is associated with changing views on the nature of and developments within geometry (non-Euclidean geometry
, projective geometry, Hilbert's axiomatization of elementary geometry, Italian axiomatic geometry) as well as on geometry's relation to science and everyday experience.
Parsons puts the point this way: "the development of non-Euclidean geometry
and its applications in physics were, historically, the main reasons why Kant's theory of geometry and space came to be rejected." (37) However, viewed philosophically rather than historically, in taking them as a unit we run together the considerations motivating Kant's theory of space and those underpinning his conception of geometry.
The Fifth Postulate: How Unraveling a Two-Thousand-Year-Old Mystery Unraveled the Universe Jason Socrates Bardi The story of the discovery of non-Euclidean geometry
. Wiley, 2009, 253 p., $27.95.
Did people have some inkling of non-Euclidean geometry
, some premonition that the parallel postulate might be false?