intrinsic metric of sphere
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I am going through this particular topic "intrinsic metric of sphere" . What i have learned so far is that the intrinsic metric is the infimum of all the arclengths of the curves(paths) joining two points . Now for a sphere this metric is defined to be a segment of some great circle . Here i am stucked to understand this . Can we discuss this or if you have some books or notes about this ?
geometry
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
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add a comment |
$begingroup$
I am going through this particular topic "intrinsic metric of sphere" . What i have learned so far is that the intrinsic metric is the infimum of all the arclengths of the curves(paths) joining two points . Now for a sphere this metric is defined to be a segment of some great circle . Here i am stucked to understand this . Can we discuss this or if you have some books or notes about this ?
geometry
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
$endgroup$
add a comment |
$begingroup$
I am going through this particular topic "intrinsic metric of sphere" . What i have learned so far is that the intrinsic metric is the infimum of all the arclengths of the curves(paths) joining two points . Now for a sphere this metric is defined to be a segment of some great circle . Here i am stucked to understand this . Can we discuss this or if you have some books or notes about this ?
geometry
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
$endgroup$
I am going through this particular topic "intrinsic metric of sphere" . What i have learned so far is that the intrinsic metric is the infimum of all the arclengths of the curves(paths) joining two points . Now for a sphere this metric is defined to be a segment of some great circle . Here i am stucked to understand this . Can we discuss this or if you have some books or notes about this ?
geometry
geometry
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
asked Jan 11 '17 at 6:01
Mathslover shahMathslover shah
110110
110110
add a comment |
add a comment |
1 Answer
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A great circle is intersection of the sphere with a plane that goes through its origin. You can also think of it as the "cutting line" for any division of the sphere into two hemispheres. The equator of the Earth (if the Earth were a sphere) is a great circle.
The shortest path between two points on the sphere lies along a great circle connecting the two points. If the two points are not antipodal, there is a unique great circle connecting them.
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
A great circle is intersection of the sphere with a plane that goes through its origin. You can also think of it as the "cutting line" for any division of the sphere into two hemispheres. The equator of the Earth (if the Earth were a sphere) is a great circle.
The shortest path between two points on the sphere lies along a great circle connecting the two points. If the two points are not antipodal, there is a unique great circle connecting them.
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
$endgroup$
add a comment |
$begingroup$
A great circle is intersection of the sphere with a plane that goes through its origin. You can also think of it as the "cutting line" for any division of the sphere into two hemispheres. The equator of the Earth (if the Earth were a sphere) is a great circle.
The shortest path between two points on the sphere lies along a great circle connecting the two points. If the two points are not antipodal, there is a unique great circle connecting them.
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
$endgroup$
add a comment |
$begingroup$
A great circle is intersection of the sphere with a plane that goes through its origin. You can also think of it as the "cutting line" for any division of the sphere into two hemispheres. The equator of the Earth (if the Earth were a sphere) is a great circle.
The shortest path between two points on the sphere lies along a great circle connecting the two points. If the two points are not antipodal, there is a unique great circle connecting them.
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
$endgroup$
A great circle is intersection of the sphere with a plane that goes through its origin. You can also think of it as the "cutting line" for any division of the sphere into two hemispheres. The equator of the Earth (if the Earth were a sphere) is a great circle.
The shortest path between two points on the sphere lies along a great circle connecting the two points. If the two points are not antipodal, there is a unique great circle connecting them.
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
answered Jan 11 '17 at 6:06
angryavianangryavian
40.7k23380
40.7k23380
add a comment |
add a comment |
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