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 · Summary:: Given an arbitrary line element, how does one calculate the geometry of the space that it describes? Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how ...

2011年6月25日 · You can think of Euclidean geometry in different ways. one of them is to say that Euclidean geometry is a group of isometric transformations like translation,rotation and reflection. the other way is to say that Euclidean geometry is the geometry of uncurved spaces. I'm sure people on this forum can help you better than me on this topic.

2020年10月15日 · In Euclidean geometry, a straight line between point A and B is the shortest line from A to B. True but irrelevant to the question at hand, which is about the physical universe we live in, not abstract math.

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 ...

2025年3月16日 · The free body diagram of a block on an incline on the right shows two such angles ##\theta.## The black side of one angle is perpendicular to red side of the other. If you decrease the angle of the incline to zero, the red line that is perpendicular to the incline will be along the vertical and the other angle ##\theta## will also be zero.

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 ...

2018年4月18日 · For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, …

2025年3月13日 · A vector has a length and a direction. A point does not. The coordinate description of points is sufficient to calculate classical problems in Euclidean geometry. But the perspective of a vector as directed line segment rather than a coordinate tuple opens the door to physics. Newtons formula $$ F=m\cdot a $$ becomes an equation of vectors $$

2023年8月1日 · geometry specification function G. It uses a Delaunay triangulation algorithm. The mesh size is determined from the shape of the geometry. G describes the geometry of the PDE problem. See PDEGEOM for details. The outputs P, E, and T are the mesh data. In the point matrix P, the first and second rows contain x- and y-coordinates of the points in ...