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Prove that the shortest distance between two points is a straight line segment joining them?
Wiki User
∙ 14y ago
This problem can be solved with the Calculus of Variations. See
http://en.wikipedia.org/wiki/Calculus_of_variations#The_Euler.E2.80.93Lagrange_equation
Wiki User
∙ 14y ago
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What is distance between two points in the plane?
Using the Euclidean metric, it is the straight line joining the two points. However, there are other metrics, some of which are familiar to many people even if they are not aware of it. The shortest distance between two places in a city, for example, is usually not the straight line joining the two points since that would require you to tunnel through buildings! The shortest distance is constrained by the available roads. The best example in this case is the Minkowski metric, also called the taxicab metric. The concept behind it similar to answering the question in a place like Manhattan with roads laid out in a grid-like pattern. The shortest distance is a combination of some moves in the N-S direction and others in the E-W direction. There are many other, less intuitive metrics.
What is the diagonal of square field?
It is the distance between opposite corners and it can be worked by using Pythagoras' theorem.
Why do you prefer straight line while joining points on a graph?
Sometimes you do, sometimes you don't. In the Euclidean plane. a straight line is the shortest distance between two points. Also, the equation of a straight line is simpler than that of curved lines. Finally, there is the Occam Rule which can be put as follows: when there are lots of possibilities to choose from, go for the simplest one. There are infinitely many curves (including a straight line) that can go through a pair of points.
What is the angle between a plane mirror and the straight line joining the object and its image?
90 degrees (That line is the normal to the mirror.)
Diagonals in a Decagon?
They are straight joining vertices to non-adjacent vertices.
What is shortest distance between two points?
If they are in the same plane then it is the length of the straight line joining them. If they are not in a plane then things get complicated. On the surface of the earth (a sphere), the shortest distance is an arc along the great circle. The great circle is a circle whose centre is the centre of the earth and which passes through the two places. This is why New York to Tokyo flights go over the Arctic region. With polyhedra, one way to find the shortest distance is to mark the two points on a net the shape. If you can draw a straight line between the points such that all of it is on the net, then that is the shortest distance. You may need to play around with different nets.
What is the short distance between two points?
An interval. The short distance is the length of a straight line joining the two points.
What does the shortest distance between them have to do with the triangle Inequality Conjecture?
The shortest distance between any two points, A and B, in a plane is the straight line joining them. Suppose, that the distance A to C and then C to B is shorter where C is any point not on AB. That would imply that, in triangle ABC, the sum of the lengths of two sides (AC and CB) is shorter tan the third side (AB). That contradicts the inequality conjecture.
What is distance between two points in the plane?
Using the Euclidean metric, it is the straight line joining the two points. However, there are other metrics, some of which are familiar to many people even if they are not aware of it. The shortest distance between two places in a city, for example, is usually not the straight line joining the two points since that would require you to tunnel through buildings! The shortest distance is constrained by the available roads. The best example in this case is the Minkowski metric, also called the taxicab metric. The concept behind it similar to answering the question in a place like Manhattan with roads laid out in a grid-like pattern. The shortest distance is a combination of some moves in the N-S direction and others in the E-W direction. There are many other, less intuitive metrics.
What is the diagonal of square field?
It is the distance between opposite corners and it can be worked by using Pythagoras' theorem.
Why do you prefer straight line while joining points on a graph?
Sometimes you do, sometimes you don't. In the Euclidean plane. a straight line is the shortest distance between two points. Also, the equation of a straight line is simpler than that of curved lines. Finally, there is the Occam Rule which can be put as follows: when there are lots of possibilities to choose from, go for the simplest one. There are infinitely many curves (including a straight line) that can go through a pair of points.
Definition of distance between two points?
Depends on the metric defined on the space. The "normal" Euclidean metric for the distance between two points is the length of the shortest distance between them - ie the length of the straight line joining them. If the coordinates of the two points (in 2-dimensions) are (a,b) and (c,d) then the distance between them is sqrt([(a - c)2 + (b - d)2] This can be generalised to 3 (or more) dimensions. However, there are other metrics. One such is the "Manhattan metric" or the "Taxicab Geometry" which was developed by Minkowski. For more information on that, see http://en.wikipedia.org/wiki/Manhattan_metric
How many miles are there between Dublin and London?
A straight line joining O'Connell Street, Dublin to Trafalgar Square, London is 464 Km long. Taking a car and ferry, the distance is 583 Km.
What is the equation to get displacement?
Simple measurement is the only way to get displacement. shortest distance between source and destination which is nothing but a straight line joining the two :) The displacement of a vessel is the weight of a vessel. It will displace its own weight of the fluid in which it is floating. There is no common equation for this, as it will be governed by the hull shape. On commercial vessels, the calculations need support from tables, which tabulate different waterplane areas with the draught.
What is the angle between a plane mirror and the straight line joining the object and its image?
90 degrees (That line is the normal to the mirror.)
How does the distance moved by an object between its starting point and its ending point compare with the displacement vector between the same point?
Displacement is how far the object is from the starting point, while distance traveled is the how far the object traveled all together. -Eric P
How does the rectangular coordinate system relate to traveling?
For small distances, the two ends of the journey may be represented by points on a coordinate plane. The x-axis will usually face East and the y-axis North although that is not necessary. The shortest journey between the two places is the straight line joining the two points. This ignores the fact that there may be obstacles that you cannot cross but need to go around but that is another matter.Latitudes and longitudes are effectively a coordinate system on the surface of the earth but, because of its shape, they do not form a rectangular system. Also, for longer travels, the shortest distance is along the arc of the great circle.
