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Actually, this turns out to be more of a debate than you might think. Historically, most of us were taught the shortest distance between two points is a straight line; that is a principle of Euclid's geometry. But not everyone agrees with Euclid, and there are other types of geometry. For example, because the Earth is a sphere, and not flat as distance maps portray it, that is why some scientists say that the shortest distance is actually a sphere or a curve (in other words, the distance would be measured by following the Earth's contours).
What else can I help you with?
Who coined the phrase The shortest distance is between two points is a straight line?
Well, It wasnt exactly coined but here goes. Einstien agrees that the shortest distance b/w 2 points is a staight line but then he says that it depends on your point of view: if you draw a straight line on a piece of paper then fold it, to you it will become curved but to an ant walking along that line it is still straight so it all depends on the observer and the plane of geomety since it can curve. You could say that Einstien proved it but as far as who coined it ... I would say Euclid: for euclidean geometry states those very words.
What is the shortest distance between 2 places on the globe?
a straight line ^Wrong. A straight line is NOT the shortest distance between two places when you're on a globe. http://en.wikipedia.org/wiki/Great_circle This is mathematically proven using calculus. Another way to prove this is to take a globe, and get some string. Pick two points, and make a straight line with the string to measure the distance. Cut off the extra string so you are using the exact amount needed for a straight line. Now, use the great circle, and you will be able to reach the same point, and have extra string left over, proving that the great circle is shorter than the straight line.
What is the physical meaning of the area under the curve of the graph of velocity vs time?
The area under the speed/time graph between two points in time is the distance covered during that time.
How to draw a polar curve?
To draw a polar curve, first choose an angle range (usually 0 to 2π) and a function that describes the distance from the origin for each angle. As you increment the angle and calculate the corresponding radius, plot the points on polar coordinates (angle, radius) to form the curve. Connect the points smoothly to visualize the shape of the curve.
Why is a great circle the shortest distance between two distant places on earth?
Yes, if you are talking about two points on earth's surface. The great circle can be thought of as roughly similar to a circle of longitude, or to the equator. It is the largest circle on the globe that can be drawn containing the two points in question. Why is this important? Consider the fact that the larger a circle becomes, the closer a section of the circle resembles a straight line. If you imagine a circle that is infinitely large, you would not be able to distinguish a section of it from a straight line drawn between the end-points. So when you have drawn the largest circle you can that contains two points on earth, you have come as close as you can to approximating a straight line between them (without digging). To people who are not familiar with this idea, seeing a 'great circle route' drawn out on a Mercator projection seems impossible. Map projections have to sacrifice some important detail, because you cannot map a three-dimensional globe onto a two dimensional surface.
A imaginary line that follows the curve of the earth the shortest distance between two points on a globe?
... is called a Great Circle arc.
What figure do you get if you join two points in cartesian plane?
You get a curve. If you join them along the shortest [Euclidean] distance between them, you get a straight line.
What is an imaginary line that follows the curve of the earth?
An imaginary line that follows the curve of the Earth is called a great circle. It represents the shortest distance between two points on the Earth's surface and is often used in navigation and mapping.
What is the difference between actual distance traveled and straight line distance?
Actual distance travel is the total distance you actually traveled, including all the loops and curves. Straight line distance is the direct distance between the 2 places, in a straight line without a curve
Why is the shortest distance between 2 points a straight line?
When you curve the line you are travelling you are no longer going directly from one point to the other. If you want to go from one point to another you would want to go directly to the second point.
What is a closed curve with all points on the curve an equal distance from a given point?
circle
What is a curve with all its points the same distance from the center?
A circle.
Who coined the phrase The shortest distance is between two points is a straight line?
Well, It wasnt exactly coined but here goes. Einstien agrees that the shortest distance b/w 2 points is a staight line but then he says that it depends on your point of view: if you draw a straight line on a piece of paper then fold it, to you it will become curved but to an ant walking along that line it is still straight so it all depends on the observer and the plane of geomety since it can curve. You could say that Einstien proved it but as far as who coined it ... I would say Euclid: for euclidean geometry states those very words.
What is the shortest distance between a straight line and a curve?
If you translate (move without rotation) a copy of the line towards the curve, the first point where the line touches the curve (the tangent to the curve with the slope of the original line) will be the point on the curve closest to the line. Draw a connecting line from this tangent point to the original line, intersecting that original line at right angles. Measure the connecting segment. It is the shortest distance. Vector analysis will give a mathematically strict solution, I do not have the ability to explain this in sufficient detail.
What is a line in math?
The shortest distance between any 2 points. An ideal zero-width, infinitely long, perfectly straight curve (the term curve in mathematics includes "straight curves") containing an infinite number of points. In Euclidean geometry, exactly one line can be found that passes through any two points.A line in math is a straight line that goes forever on each side.
An imaginary line that follows the curve of the earth and is the shortest route for pilots?
The imaginary line that follows the curve of the Earth and is the shortest route for pilots is called a great circle route. This route is the most efficient way to travel between two points on the Earth's surface, as it represents the shortest path over the Earth's surface, given its spherical shape. Pilots often use great circle routes to save time and fuel during long-distance flights.
Has a curve surface on which all points are at the same distance from its center?
A curved surface on which all points are the same distance from the center is called a sphere.
