. A straight line divides a plane in which it lies into two congruent parts—;this, of course, has no real meaning, since we are dealing with infinite areas, but such is the argument—;and two rays from a point enclose an (infinite) area which is less than half the whole plane. ...
And this is not just the case with geometry-on-a-sphere. It’s the whole “non-Euclidean” game. Take a set of internally consistent formulas from “Euclidean” geometry, shuffle the terms around in a carefully consistent way, and guess what: The formulas don’t develop inconsistencies they...
This is because all curvature is relative. A curve in a curved field is not necessarily a curve. The word “curve” only has meaning relative to a straight line. The only way to know how much a curve is curving is to put it next to a straight line. This is why all curved geometry...
KANT'S SYNTHETIC A PRIORI IN GEOMETRY AND THE RISE OF NON-EUCLIDEAN GEOMETRIES This article first explores the meaning that attaches to the flexibility in the choice of technology and defines the concept of equity in the distribution of income. It then proceeds to demonstrate how the ability to...
2048Accesses Abstract Very generally speaking, statistical data analysis builds on descriptors reflecting data distributions. In a linear context, well studied nonparametric descriptors are means and PCs (principal components, the eigenorientations of covariance matrices). In 1963, T.W. Anderson derived ...
Now, choosing α and β values we have to keep the λ˜ value within the physical meaning of the Lame parameter and it is convenient to express the λ˜ value as a proportion of the λ value. In this paper, parameters α and β have been chosen to provide the disintegration ...
In this paper, using the classical methods of differential geometry, we define invariants of non-developable ruled surfaces in Euclidean 3-space, called structure functions, and show kinematics meaning of these invariants. We also generalize the notion of the angle of pitch of a closed ruled surfa...
While it is not uncommon to find claims that the very existence of non-Euclidean geometry refutes Kant's theory, such a view fails to take into account the meaning of the term "synthetic," which is that a synthetic proposition can be denied without contradiction. Leonard Nelson realized that...
. A straight line divides a plane in which it lies into two congruent parts-this, of course, has no real meaning, since we are dealing with infinite areas, but such is the argument-and two rays from a point enclose an (infinite) area which is less than half the whole plane. Hence,...
(1999). Supporting the evolution of mathematical meanings: The case of non-euclidean geometry. International Journal of Computers for Mathematical L earning, 3, 229-254.Stevenson, I J and Noss, R (1999) 'Supporting the evolution of mathe- matical meaning: the case of non-Euclidean geometry...