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Affine and Projective Planes
Published in C. C. Lindner, C. A. Rodger, Design Theory, 2017
is a projective plane of order n. (The technique of constructing (P(∞), B(∞)) from (P,B) $ (P, B) $ is called adding a line at infinity, and ∞ is called the line at infinity.)
An integrated machine learning model for automatic road crack detection and classification in urban areas
Published in International Journal of Pavement Engineering, 2022
Abbas Ahmadi, Sadjad Khalesi, Amir Golroo
There will be a line in the parameter space corresponding to each pair () in XY-plane. Therefore, each point in parameter space can represent a specific line in XY-plane. Consider two points () and (). They have two lines in parameter space associated with them. Now, the intersection of these two lines represents the line containing both points () and () in XY-plane. Hence, this principle is used in the Hough transform technique to detect and extract straight lines in binary images. Furthermore, in an XY-plane, the slope of a line approaches infinity for vertical lines. For this reason, Equation (12) is used in this method to represent a line in parameter space (-plane) (Gonzalez and Woods 2008).
Four conceptions of infinity
Published in International Journal of Mathematical Education in Science and Technology, 2022
Magdalena Krátká, Petr Eisenmann, Jiří Cihlář
Kidron and Tall (2015) describe in their study a large group of university students who intuitively work with infinite polynomials, which are limiting objects conceived as having the same properties as the objects in the limiting process (D. O. Tall, 2005). Students thus intuitively formulate ideas that are precisely expressed in the other mathematical disciplines (the theory of ordinal numbers, nonstandard analysis (Robinson, 2016), the Conway theory of games and numbers (Conway, 2000), projective geometry, etc.). Robinson’s nonstandard analysis and Conway’s theory of games deal with infinitely small and infinitely large quantities. In projective geometry, the terms point of infinity and the line of infinity are introduced. These objects are generally called improper objects.