Stevenson, I J and Noss, R (1999) 'Supporting the evolution of mathe- matical meaning: the case of non-Euclidean geometry', International Journal of Computers for Mathematical Learning 3(3), 229-254Stevenson, I., & Noss, R. (1999). Supporting the evolution of mathematical meanings: ...
In this image, all the cells in a 256-by-256 matrix have a D value of zero, except one cell in the approximate middle, which has a D value of ten million. That’s about the simplest starting condition we can come up with to see what happens to a local concentration of D. This p...
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...
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
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...
Why did "curvature" come to have this unusual meaning? Why should we confuse ourselves by saying that "intrinsic" straight lines, geodesics, in non-Euclidean spaces have curvature? This happened because non-Euclidean planes can be modeled as extrinsically curved surfaces within Euclidean space. ...
Finally, stationarity is a typical assumption in GP regression, meaning that the same kernel function is used throughout the entire input space. In many real-world problems such an assumption could be not desirable because the modelled process might exhibit a different variability from one region ...
Stevenson, I J and Noss, R (1999) 'Supporting the evolution of mathe- matical meaning: the case of non-Euclidean geometry', International Journal of Computers for Mathematical Learning 3(3), 229-254Stevenson, I., & Noss, R. (1999). Supporting the evolution of mathematical meanings: ...