Dividing curve area in to equal parts?

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Discussion Overview

The discussion revolves around the challenge of dividing the area under a given curve into 'n' equal parts after calculating the area using Simpson's 1/3 rule. Participants explore methods and considerations related to this problem, touching on numerical integration techniques.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that while the area under a curve can be found using Simpson's 1/3 rule, dividing this area into 'n' equal parts poses significant challenges.
  • Another participant suggests that achieving exactly equal areas is difficult and typically involves computing the area first, then checking subdivisions iteratively.
  • It is mentioned that in numerical integration, a common approach is to divide the x-axis into 'n' equal parts and apply Simpson's rule, recommending that 'n' be a multiple of 3 for simplicity.
  • A participant expresses their intention to potentially write a paper on the topic, indicating ongoing interest in the problem.

Areas of Agreement / Disagreement

Participants generally agree on the difficulty of dividing the area into exactly equal parts, with multiple viewpoints on the methods and implications of numerical integration techniques. The discussion remains unresolved regarding the best approach to achieve equal area divisions.

Contextual Notes

Participants acknowledge the complexity of the problem, particularly the dependence on the unknown area and the iterative nature of checking subdivisions. There are no specific assumptions or definitions clarified in the discussion.

pjunky
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For any given curve,we can find out the area bounded by the curve.
Using 'Simpson's 1/3 rule' I found out the area of the curve.
Now how to divide the area into 'n' equal parts, so that

total Area=sum of n areas.

Thanks.:approve:
 
Last edited:
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If you want to divide the area into n EXACTLY equal parts, it will be very hard, since you need (in general) to compute the area first and then subdivide and check each subdivision before proceeding to the next. However when doing numerical integration, the usual procedure is divide the x-axis domain into n equal parts, and use Simpson's rule. To keep things simple, choose n to be a multiple of 3.
 
Yes. I puzzled over this for a while myself. In using Simpson's rule, you divide the x-axis into equal parts, which is very easy, not the (unknown) area, which is very hard!
 
Ok
so may be I'll try to write a paper on this topic.
Thanks
 

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