Dividing curve area in to equal parts?

In summary, for any given curve, the area bounded by the curve can be found using Simpson's 1/3 rule. To divide the area into n equal parts, one can divide the x-axis domain into n equal parts and use Simpson's rule. Choosing n to be a multiple of 3 can simplify the process. While it may be difficult to divide the area into exactly equal parts, this method is commonly used in numerical integration.
  • #1
pjunky
22
0
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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  • #2
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.
 
  • #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!
 
  • #4
Ok
so may be I'll try to write a paper on this topic.
Thanks
 

1. What is the purpose of dividing a curve area into equal parts?

The purpose of dividing a curve area into equal parts is to accurately calculate the area of a complex shape. By dividing the shape into smaller, equal parts, it becomes easier to calculate the total area using mathematical formulas.

2. How many equal parts should a curve area be divided into?

The number of equal parts to divide a curve area into depends on the complexity of the shape and the accuracy required for the calculation. In some cases, dividing the area into 4 or 8 equal parts may be sufficient, while in others, a higher number of parts may be necessary.

3. What tools or methods can be used to divide a curve area into equal parts?

There are various tools and methods that can be used to divide a curve area into equal parts, such as a compass, a protractor, or mathematical formulas. Some software programs also have built-in features for dividing shapes into equal parts.

4. Can any curve area be divided into equal parts?

Yes, any curve area can be divided into equal parts as long as the shape is well-defined and the methodology used is accurate. However, dividing very complex shapes into equal parts may require advanced mathematical techniques.

5. What are the potential challenges when dividing a curve area into equal parts?

One potential challenge is ensuring that the parts are truly equal in size, as even small variations can result in significant errors in the final area calculation. Another challenge is determining the appropriate number of parts to use, as too few parts may result in an inaccurate calculation, while too many parts may be time-consuming and unnecessary.

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