An approach to area under a curve with a new approach to definite integrals. The 2019 Stack Overflow Developer Survey Results Are In Unicorn Meta Zoo #1: Why another podcast? Announcing the arrival of Valued Associate #679: Cesar ManaraA question regarding the geometry of spheres and circles.Area under a pointHow do I calculate the area under a curve using the midpoints of rectangles?Formula for area under the curveDefinite integral and the antiderviative in relation to area under a curveFinding the area under curve without using rectanglesHow do I find the area of a general closed curve? (And then generalisation to multiple dimensions)Area under parametric curve that loops back around itselfArea under a parametric curve in $mathbbR^3$Area under curve: integrationUncertainty associated with area under curve (integrated) estimates
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An approach to area under a curve with a new approach to definite integrals.
The 2019 Stack Overflow Developer Survey Results Are In
Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraA question regarding the geometry of spheres and circles.Area under a pointHow do I calculate the area under a curve using the midpoints of rectangles?Formula for area under the curveDefinite integral and the antiderviative in relation to area under a curveFinding the area under curve without using rectanglesHow do I find the area of a general closed curve? (And then generalisation to multiple dimensions)Area under parametric curve that loops back around itselfArea under a parametric curve in $mathbbR^3$Area under curve: integrationUncertainty associated with area under curve (integrated) estimates
$begingroup$
I would humbly request you all to please just have a quick highlighted view of my previous question given in the following link:-(not compulsory)
A question regarding the geometry of spheres and circles.
I think that we would be requiring the answers to this question and I think all the respected active researchers would already be knowing the answers to this question.
Now coming back to my own concern I do not want anyone to do homework on what I am going to say but please help me to complete this new approach but I would post my approach as an answer after getting some suggestions that I would really like to get.
I want to say that how can one approach to find area under a curve using a new approach by using the thought that the region under curve is made up of infinitesimally small circles such that their area tends to be zero instead of the successful conventional approach of using rectangles. I am quite impressed by the approach using circles because by geometry we know that any two dimensional figure can't have area greater than that enclosed by a circle. This approach would lead to less errors in finding area as I think most of the area would be covered by these extremely small circles.
As I mentioned earlier I would say that I would definitely post my approach after some time by getting some new suggestions.The approach wouldn't not contain a whole explanation but a quite introductory page.
integration
asked Apr 8 at 7:34
ShreyanshShreyansh
348
$endgroup$
add a comment |
$begingroup$
I would humbly request you all to please just have a quick highlighted view of my previous question given in the following link:-(not compulsory)
A question regarding the geometry of spheres and circles.
I think that we would be requiring the answers to this question and I think all the respected active researchers would already be knowing the answers to this question.
Now coming back to my own concern I do not want anyone to do homework on what I am going to say but please help me to complete this new approach but I would post my approach as an answer after getting some suggestions that I would really like to get.
I want to say that how can one approach to find area under a curve using a new approach by using the thought that the region under curve is made up of infinitesimally small circles such that their area tends to be zero instead of the successful conventional approach of using rectangles. I am quite impressed by the approach using circles because by geometry we know that any two dimensional figure can't have area greater than that enclosed by a circle. This approach would lead to less errors in finding area as I think most of the area would be covered by these extremely small circles.
As I mentioned earlier I would say that I would definitely post my approach after some time by getting some new suggestions.The approach wouldn't not contain a whole explanation but a quite introductory page.
integration
asked Apr 8 at 7:34
ShreyanshShreyansh
348
$endgroup$
add a comment |
$begingroup$
I would humbly request you all to please just have a quick highlighted view of my previous question given in the following link:-(not compulsory)
A question regarding the geometry of spheres and circles.
I think that we would be requiring the answers to this question and I think all the respected active researchers would already be knowing the answers to this question.
Now coming back to my own concern I do not want anyone to do homework on what I am going to say but please help me to complete this new approach but I would post my approach as an answer after getting some suggestions that I would really like to get.
I want to say that how can one approach to find area under a curve using a new approach by using the thought that the region under curve is made up of infinitesimally small circles such that their area tends to be zero instead of the successful conventional approach of using rectangles. I am quite impressed by the approach using circles because by geometry we know that any two dimensional figure can't have area greater than that enclosed by a circle. This approach would lead to less errors in finding area as I think most of the area would be covered by these extremely small circles.
As I mentioned earlier I would say that I would definitely post my approach after some time by getting some new suggestions.The approach wouldn't not contain a whole explanation but a quite introductory page.
integration
asked Apr 8 at 7:34
ShreyanshShreyansh
348
$endgroup$
I would humbly request you all to please just have a quick highlighted view of my previous question given in the following link:-(not compulsory)
A question regarding the geometry of spheres and circles.
I think that we would be requiring the answers to this question and I think all the respected active researchers would already be knowing the answers to this question.
Now coming back to my own concern I do not want anyone to do homework on what I am going to say but please help me to complete this new approach but I would post my approach as an answer after getting some suggestions that I would really like to get.
I want to say that how can one approach to find area under a curve using a new approach by using the thought that the region under curve is made up of infinitesimally small circles such that their area tends to be zero instead of the successful conventional approach of using rectangles. I am quite impressed by the approach using circles because by geometry we know that any two dimensional figure can't have area greater than that enclosed by a circle. This approach would lead to less errors in finding area as I think most of the area would be covered by these extremely small circles.
As I mentioned earlier I would say that I would definitely post my approach after some time by getting some new suggestions.The approach wouldn't not contain a whole explanation but a quite introductory page.
integration
integration
asked Apr 8 at 7:34
ShreyanshShreyansh
348
asked Apr 8 at 7:34
ShreyanshShreyansh
348
asked Apr 8 at 7:34
ShreyanshShreyansh
348
asked Apr 8 at 7:34
ShreyanshShreyansh
348
asked Apr 8 at 7:34
ShreyanshShreyansh
348
348
add a comment |
add a comment |
1 Answer
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$begingroup$
I don't see how this could be any better than the current method. Yes, you can approach any area with extremely small circles, but the same is true for extremely small rectangles, or extremely small triangles, or extremely small almost anything. The reason rectangles are usually used is that they make computation easier than other geometric forms would. Not because they approach good or less good, in the limit they approach the area perfectly, so there is no chance that circles will be better in this sense. If you want to have better approximation already before taking the limit, I don't think that will happen:
Rectangles cover the whole area they are laid on, whereas non-overlapping circles don't, see for example link.
answered Apr 8 at 8:01
DirkDirk
4,658219
$endgroup$
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
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oldest
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votes
$begingroup$
I don't see how this could be any better than the current method. Yes, you can approach any area with extremely small circles, but the same is true for extremely small rectangles, or extremely small triangles, or extremely small almost anything. The reason rectangles are usually used is that they make computation easier than other geometric forms would. Not because they approach good or less good, in the limit they approach the area perfectly, so there is no chance that circles will be better in this sense. If you want to have better approximation already before taking the limit, I don't think that will happen:
Rectangles cover the whole area they are laid on, whereas non-overlapping circles don't, see for example link.
answered Apr 8 at 8:01
DirkDirk
4,658219
$endgroup$
add a comment |
$begingroup$
I don't see how this could be any better than the current method. Yes, you can approach any area with extremely small circles, but the same is true for extremely small rectangles, or extremely small triangles, or extremely small almost anything. The reason rectangles are usually used is that they make computation easier than other geometric forms would. Not because they approach good or less good, in the limit they approach the area perfectly, so there is no chance that circles will be better in this sense. If you want to have better approximation already before taking the limit, I don't think that will happen:
Rectangles cover the whole area they are laid on, whereas non-overlapping circles don't, see for example link.
answered Apr 8 at 8:01
DirkDirk
4,658219
$endgroup$
add a comment |
$begingroup$
I don't see how this could be any better than the current method. Yes, you can approach any area with extremely small circles, but the same is true for extremely small rectangles, or extremely small triangles, or extremely small almost anything. The reason rectangles are usually used is that they make computation easier than other geometric forms would. Not because they approach good or less good, in the limit they approach the area perfectly, so there is no chance that circles will be better in this sense. If you want to have better approximation already before taking the limit, I don't think that will happen:
Rectangles cover the whole area they are laid on, whereas non-overlapping circles don't, see for example link.
answered Apr 8 at 8:01
DirkDirk
4,658219
$endgroup$
I don't see how this could be any better than the current method. Yes, you can approach any area with extremely small circles, but the same is true for extremely small rectangles, or extremely small triangles, or extremely small almost anything. The reason rectangles are usually used is that they make computation easier than other geometric forms would. Not because they approach good or less good, in the limit they approach the area perfectly, so there is no chance that circles will be better in this sense. If you want to have better approximation already before taking the limit, I don't think that will happen:
Rectangles cover the whole area they are laid on, whereas non-overlapping circles don't, see for example link.
answered Apr 8 at 8:01
DirkDirk
4,658219
answered Apr 8 at 8:01
DirkDirk
4,658219
answered Apr 8 at 8:01
DirkDirk
4,658219
answered Apr 8 at 8:01
DirkDirk
4,658219
4,658219
add a comment |
add a comment |
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