A Simple Non-Euclidean Geometry and Its Physical Basis: An by Basil Gordon (auth.), Basil Gordon (eds.)

By Basil Gordon (auth.), Basil Gordon (eds.)

There are many technical and well known bills, either in Russian and in different languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, some of that are indexed within the Bibliography. This geometry, also referred to as hyperbolic geometry, is a part of the necessary material of many arithmetic departments in universities and lecturers' colleges-a reflecĀ­ tion of the view that familiarity with the weather of hyperbolic geometry is an invaluable a part of the historical past of destiny highschool academics. a lot consciousness is paid to hyperbolic geometry through university arithmetic golf equipment. a few mathematicians and educators fascinated about reform of the highschool curriculum think that the necessary a part of the curriculum should still contain parts of hyperbolic geometry, and that the not obligatory a part of the curriculum should still contain an issue relating to hyperbolic geometry. I The wide curiosity in hyperbolic geometry is no surprise. This curiosity has little to do with mathematical and clinical purposes of hyperbolic geometry, because the functions (for example, within the thought of automorphic capabilities) are particularly really expert, and usually are encountered by means of only a few of the numerous scholars who carefully learn (and then current to examiners) the definition of parallels in hyperbolic geometry and the certain positive factors of configurations of traces within the hyperbolic aircraft. The important reason behind the curiosity in hyperbolic geometry is the real truth of "non-uniqueness" of geometry; of the life of many geometric systems.

Show description

Read or Download A Simple Non-Euclidean Geometry and Its Physical Basis: An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity PDF

Similar geometry books

Geometry of Complex Numbers (Dover Books on Mathematics)

Illuminating, broadly praised booklet on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries. "This booklet may be in each library, and each professional in classical functionality thought might be acquainted with this fabric. the writer has played a unique provider by way of making this fabric so with ease available in one ebook.

Geometric Tomography (Encyclopedia of Mathematics and its Applications)

Geometric tomography bargains with the retrieval of knowledge a couple of geometric item from facts bearing on its projections (shadows) on planes or cross-sections through planes. it's a geometric relative of automatic tomography, which reconstructs a picture from X-rays of a human sufferer. the topic overlaps with convex geometry and employs many instruments from that region, together with a few formulation from crucial geometry.

First Steps in Differential Geometry: Riemannian, Contact, Symplectic (Undergraduate Texts in Mathematics)

Differential geometry arguably deals the smoothest transition from the normal college arithmetic series of the 1st 4 semesters in calculus, linear algebra, and differential equations to the better degrees of abstraction and facts encountered on the higher department through arithmetic majors. this present day it's attainable to explain differential geometry as "the examine of constructions at the tangent space," and this article develops this viewpoint.

Additional info for A Simple Non-Euclidean Geometry and Its Physical Basis: An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity

Example text

The vector a is assumed constant, it follows, just as before, that VI =vi +a, V2=V;+a, and VI- V2=vi -V;. lIICf. Galileo's "Dialogues" [15], pp. l7l-172. 23 I. What is mechanics? ;;J_ _ _oooO(a(t)) A ...... 21 So far we have concerned ourselves with two-dimensional (more accurately, plane-parallel) motions affecting points A(x,y) of some plane xOy. However, nothing prevents us from restricting ourselves to even simpler, rectilinear motions, where we need only consider motions of points A =A(x) of some fixed line o.

Since the endpoints A', B', C',... belong to the image I' of I, the endpoints Ai,B;,C;, ... belong to the image I; of II' Hence I; is a line parallel to 1'. This proves that the shear (la) maps the line II onto the line I;. (b) The proof of (b) is implicit in the proof of (a). 2 2It is easy to show that if I and l' form (Euclidean) angles a and a', respectively, with the x-axis, then tana'=tana+v. 36 I. Distance and Angle; Triangles and Quadrilaterals Figure 27 (c) The equality C' D' / A' B' = CD / AB follows directly from Figure 27; its proof is left to the reader.

Consequently these quantities are not comparable; knowing that two intersecting lines form an angle of 30 0 , and two parallel lines are 15 cm apart (cf. Fig. 29), we cannot say that one of these two deflections is larger than the other. We also note that the distance (4) between lines is defined only if the angle (3) between them is zero, and that two lines coincide if and only if they form an angle 8 equal to zero and the distance d between them is zero. " '-1 (5) it equals the signed length of the projection PP I of the segmentAAI on the x-axis (Fig.

Download PDF sample

Rated 4.67 of 5 – based on 20 votes