2006年8月30日 · A general orthogonal coordinate system (u,v,w) will have a line elemet of the form: [tex] ds^2 = f^2 du^2 + g^2dv^2 + h^2dw^2[/tex] I have done a lot of vector calculus, but for some reason I can't figure out what this means! What is a line element? I know about the differential length element and its a vector, but this is a scalar!

2020年11月13日 · Determining the geometry of a line element has many practical applications, including mapping and surveying, creating 3D models and animations, and designing structures and machinery. It is also used in fields such as physics, astronomy, and computer science to analyze and model the behavior of objects in space or virtual environments.

2005年2月10日 · Classical Geometry Line In summary, the problem of finding the number of lines that meet a given set of lines in space has been a topic of interest for over 100 years. If there is only one line to start with, there are an infinite number of lines that meet it.

2011年6月25日 · This means that a line in hyperbolic geometry is "bent" inwards, while a line in Euclidean geometry is straight. How is a line in hyperbolic geometry represented mathematically? A line in hyperbolic geometry can be represented mathematically using the hyperboloid model, which is a three-dimensional surface that can be described using the ...

2014年7月23日 · In summary, the concept of a line in Euclidean coordinate geometry refers to an infinitely long line, while in ordinary Euclidean geometry, it typically refers to a line segment between two points. The equation of a line in n dimensions involves n-1 linear equations, and there is a unique line through every pair of points in n dimensions.

2013年8月26日 · What is a line (coordinate geometry) Apr 12, 2019; Replies 1 Views 6K. Finding the Area Bounded by Two ...

2017年5月21日 · In geometry, it is frequently the case that the concept of line is taken as a primitive. In those situations where a line is a defined concept, as in coordinate geometry, some other fundamental ideas are taken as primitives. When the line concept is a primitive, the behaviour and properties of lines are dictated by the axioms which they must ...

2017年1月25日 · 1. Here is the Problem: A line passes through A(2,3) and B(5,7). Find: (a) the coordinates of the point P on AB extended through B to P so that P is twice as far from A as from B; (b) the coordinates if P is on AB extended through A so that P …

2025年1月1日 · Clearly, that line intersects the circle at two points, as it passes the centre at a distance of ##\frac 1 2##. PS using this geometric approach, you can see that the point on the line closest to the centre of the circle is ##-4 + \frac 3 2 i##. The book's conclusion is truly bizarre!

2015年4月22日 · For part b):- show from part a) that the only common point between any 2 of the 4 lines is the common endpoint.