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If The Shortest Distance Between Two Points Is A Straight Line


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  1. Between, Distance, Line, Points, Shortest, Shortest Distance, Straight, Straight Line, Two Quotes to Explore Fight for the things that you care about, but do it .
  2. The shortest distance between two points is a straight line. Gary Ryan Blair. It was Archimedes who first articulated that the shortest path between two points is a straight knobimallavaran.tiopusfalenonnuscfatamapnacordre.co: Gary Ryan Blair.
  3. Mar 24,  · No, a straight line isn’t always the shortest distance between two points. The shortest distance between two points depends on the geometry of the object/surface in question. For flat surfaces, a line is indeed the shortest distance, but for spherical surfaces, like Earth, great-circle distances actually represent the true shortest distance.
  4. Proving that the shortest distance between two points is indeed a straight line. Now to Prove: (well known equation for a straight line in Cartesian coordinates) 1) Distance between two points is "L", which in turn is the following integral.
  5. Nov 08,  · When Is a Straight Line Not the Shortest Distance between Two Points? The hypotenuse of a right triangle is not always the shortest distance between the two points that define it By THE EDITORS on.
  6. The first application I was shown of the calculus of variations was proving that the shortest distance between two points is a straight line. Define a functional measuring the length of a curve between two points: $$ I(y) = \int_{x_1}^{x_2} \sqrt{1 + (y')^2}\, dx, $$ apply the Euler-Langrange equation, and Bob's your uncle.
  7. Jul 31,  · They we can take the square root of the equation to get ds = dx(1 + (dy/dx)^2)^1/2 = dx(1 + (y')^2)^1/2. This is the equation we are trying to minimize. We can now use the Euler equation from step 17 (steps 6 though 16 is a proof for it) to find the equation for the shortest distance between two points in flat space, which turns out to be a line.
  8. 2. Use calculus of variations to show that the shortest distance between two points on a plane is a straight line, using the following procedure: The infinitesimal length ds of a curve y(x) is given by the Euclidean metric: dy whereIntegrating from point 1 to point 2 gives the length S of the curve: minimize Sy)]. begin by writin (b) Integrate both sides of the Euler-Lagrange .
  9. $\begingroup$ "The shortest distance between two points on the sphere is not a straight line." It's not straight when embedded in a 3D Euclidean space, but on the surface of a sphere those lines are as straight as it gets. $\endgroup$ – Emil Mar 22 '16 at

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