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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).
The shortest distance between two points can be a curve when the path follows the geometry of the space, such as on a sphere or a curved surface where a straight line is not possible. This is because the curve minimizes the distance traveled while staying within the constraints of the space's geometry.
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Who coined the phrase The shortest distance is between two points is a straight line?
The phrase "The shortest distance between two points is a straight line" is an ancient geometric principle rooted in Euclidean geometry, where a straight line is the shortest path between two points in a flat, two-dimensional space. It is a fundamental concept in mathematics and has been used for centuries in various applications involving distance and efficiency calculations.
What is the shortest distance between 2 places on the globe?
The shortest distance between two places on the globe is a great circle route. This is the path that follows the curve of the Earth's surface and represents the shortest distance between two points. Any straight line drawn on a globe represents a segment of a great circle route.
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?
A great circle is the shortest distance between two points on a sphere because it is the largest circle that can be drawn on the surface of the sphere. Any other path between two points would be longer because it would either be a smaller circle or involve more directional changes along the surface of the sphere.
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 traveled refers to the total distance covered between two points, taking into account any curves, turns, or detours in the route. Straight line distance, on the other hand, is the shortest distance between two points, ignoring any obstacles or changes in direction that may affect the path taken.
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
Who coined the phrase The shortest distance is between two points is a straight line?
The phrase "The shortest distance between two points is a straight line" is an ancient geometric principle rooted in Euclidean geometry, where a straight line is the shortest path between two points in a flat, two-dimensional space. It is a fundamental concept in mathematics and has been used for centuries in various applications involving distance and efficiency calculations.
What is a curve with all its points the same distance from the center?
A circle.
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.
