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What else can I help you with?
What is a line of characteristics?
shortest distance between two points in space
Why is a connected two endpoints to a line segment?
A connected line segment has two endpoints because it represents the shortest path between those two points in a straight line. These endpoints define the limits of the segment, allowing for precise measurement of length and positioning in space. The connection between the endpoints emphasizes the segment's continuity and linearity, distinguishing it from other geometric figures.
Is a segment one dimensional?
Yes, a segment is considered one-dimensional because it has length but no width or height. It can be defined as the shortest path between two points in a plane or space, representing a straight line portion. In mathematical terms, a segment is typically defined within a one-dimensional coordinate system.
How do you prove the shortest line between two points is the segment that joins them on a plane?
The shortest line between two points is NOT always the segment that joins (or jion) them on a plane: the answer depends on the concept of distance or the metric used for the space. If using a taxicab or Manhattan metric it is the sum of the North-South distance and the East-West distance. There are many other possible metrics.The proof for a general metric is the Cauchy-Schwartz inequality but this site is totally incapable of dealing with the mathematical symbols required to prove it.
The shortest path from a starting point to an endpoint what is it called?
The shortest path between two points is called a geodesic. In flat (Euclidean) space it is simply a straight line.
The straight line distance between any two points?
this is supposedly the shortest distance between any 2 points, however if you could bend the space between the two points and fold them together, well then they would be right beside each other
What line segment has two endpoints?
A line segment is defined by two endpoints, which are distinct points in space that mark the beginning and end of the segment. For example, if we have points A and B, the line segment AB consists of all the points that lie on the straight path connecting A and B. Unlike a line, which extends infinitely in both directions, a line segment has a finite length determined by the distance between its endpoints.
Given two points A and B in the three dimensional space what is the set of points equidistant from A and B?
A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.
What is the amount of space between two points?
Amount of space between two Points
What is the longest line segment?
The longest line segment is theoretically infinite, as a line segment can extend indefinitely in either direction. However, in practical terms, the longest line segment within a defined space, such as a circle, is the diameter, which is the longest distance between any two points on the circumference. In a three-dimensional space, the longest line segment would be the diagonal across a given volume, like the diagonal of a cube, which can be calculated using the Pythagorean theorem.
Can the displacment vector for a particle moving in two directions ever be longer than the length thraveled by the particle?
In a Euclidean space, the shortest distance between two points is a straight line, so no.
How can the shortest distance between two points be a curve?
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).
