The Verb Recognize a verb when you see one.
Introduction[ edit ] The shortest path between two given points in a curved space, assumed to be a differential manifoldcan be defined by using the equation for the length of a curve a function f from an open interval of R to the spaceand then minimizing this length between the points using the calculus of variations.
This has some minor technical problems, because there is an infinite dimensional space of different ways to parameterize the shortest path.
Equivalently, a different quantity may be used, termed the energy of the curve; minimizing the energy leads to the same equations for a geodesic here "constant velocity" is a consequence of minimization.
The resulting shape of the band is a geodesic.
It is possible that several different curves between two points minimize the distance, as is the case for two diametrically opposite points on a sphere.
In such a case, any of these curves is a geodesic. A contiguous segment of a geodesic is again a geodesic. In general, geodesics are not the same as "shortest curves" between two points, though the two concepts are closely related.
The difference is that geodesics are only locally the shortest distance between points, and are parameterized with "constant speed". Going the "long way round" on a great circle between two points on a sphere is a geodesic but not the shortest path between the points.
Geodesics are commonly seen in the study of Riemannian geometry and more generally metric geometry. In general relativitygeodesics in spacetime describe the motion of point particles under the influence of gravity alone. In particular, the path taken by a falling rock, an orbiting satelliteor the shape of a planetary orbit are all geodesics in curved spacetime.
More generally, the topic of sub-Riemannian geometry deals with the paths that objects may take when they are not free, and their movement is constrained in various ways.
This article presents the mathematical formalism involved in defining, finding, and proving the existence of geodesics, in the case of Riemannian and pseudo-Riemannian manifolds. The article geodesic general relativity discusses the special case of general relativity in greater detail.
A geodesic on a triaxial ellipsoid.
If an insect is placed on a surface and continually walks "forward", by definition it will trace out a geodesic. The most familiar examples are the straight lines in Euclidean geometry. On a spherethe images of geodesics are the great circles. The shortest path from point A to point B on a sphere is given by the shorter arc of the great circle passing through A and B.
If A and B are antipodal pointsthen there are infinitely many shortest paths between them. Geodesics on an ellipsoid behave in a more complicated way than on a sphere; in particular, they are not closed in general see figure.
Metric geometry[ edit ] In metric geometrya geodesic is a curve which is everywhere locally a distance minimizer.SCHEME OF WORK / 1 September / 13 comments.
PRESENTATION NATIONAL HIGH SCHOOL, BENIN CITY. SCHEME OF WORK FOR PHE. JSS 1. 1ST TERM. Definition, nature, scope and objectives of physical education. The Verb Recognize a verb when you see one.
Verbs are a necessary component of all srmvision.com have two important functions: Some verbs put stalled subjects into motion while other verbs help to clarify the subjects in meaningful ways.
OLS produces the fitted line that minimizes the sum of the squared differences between the data points and the line. Linear regression, also known as ordinary least squares and linear least squares, is the real workhorse of the regression srmvision.com linear regression to understand the mean change in a dependent variable given a one-unit change in each independent variable.
These free equations and word problems worksheets will help your students practice writing and solving equations that match real-world story problems.
Your students will write two step equations to match problems like “James earned a total of $ last week. This total was $10 less than five times the amount he earned last week. Lesson Summary. In this lesson, you learned how to construct the equation of a plane when given the coordinates of three noncollinear points - or points that aren't on the same line - in space.
In. Number Problems Money Story Problems BASIS CTE Change Views Search Custom Headers.