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Can the distance formula can be derived from the Pythagorean theorem?
Yes, the formula for the Euclidean distance. But not necessarily other distance metrics.
What is the distance between -2 and 3?
The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.
What term describes all points in a plane that are the same distance from a given point in a plane?
A circle. However, that DOES depend on the Euclidean metric being used for measuring distance.
What are the similarities between euclidean and non euclidean?
nothing
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.
Can the distance formula can be derived from the Pythagorean theorem?
Yes, the formula for the Euclidean distance. But not necessarily other distance metrics.
types of distance covered?
4 Types of Distance Metrics in Machine Learning Euclidean Distance. Manhattan Distance. Minkowski Distance. Hamming Distance.
What is the difference between Euclidean Geometry and non-Euclidean Geometry?
In Euclidean geometry parallel lines are always the same distance apart. In non-Euclidean geometry parallel lines are not what we think of a parallel. They curve away from or toward each other. Said another way, in Euclidean geometry parallel lines can never cross. In non-Euclidean geometry they can.
Does 'never intersect' mean 'the same distance apart'?
In Euclidean geometry, yes it does.
If two distinct lines do not intersect are they parallel?
If they are coplanar in a Euclidean space, then yes. If they are not coplanar or not in Euclidean space, then not necessarily.
What are the properties of parallel line?
In Euclidean geometry, parallel lines are the same distance apart and never meet.
What is the distance between -2 and 3?
The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.The Euclidean distance is sqrt[(-2 - 3)2+ (2 - -2)2] = sqrt[52+ 42] = sqrt[25 + 16] = sqrt(41) = 6.40 approx.
Difference between distance and Euclidean distance?
There are many ways to measure distance in math. Euclidean distance is one of them. Given two points P1 and P2 the Euclidean distance ( in two dimensions, although the formula very easily generalizes to any number of dimensions) is as follows: Let P1 have the coordiantes (x1, y1) and P2 be (x2, y2) Then the Euclidean distance between them is the square root of (x2-x1)2+(y2-y1)2 . To understand some other ways of measuring "distance" I introduce the term METRIC. A metric is a distance function. You put the points into the function (so they are its domain) and you get the distance as the output (so that is the range). Another metric is the Taxicab Metric, formally known as the Minkowski distance. We often use the small letter d to mean the distance between points. So d(P1, P2) is the distance between points. Using the Taxicab Metric, d(x, y) = |x1 - x2| + |y2 - y2|
Does a line go on forever in both directions?
In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.
What is the proof for the distance formula?
There are very many different mathematical definitions of distance: the Euclidean metric, the Minkovski metric are two common examples. The proof will be different.
What term describes all points in a plane that are the same distance from a given point in a plane?
A circle. However, that DOES depend on the Euclidean metric being used for measuring distance.
What are the similarities between euclidean and non euclidean?
nothing
