Have you heard of using wedges in calculus to approach integration differently?

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Discussion Overview

The discussion revolves around a proposed idea of using wedges in calculus as an alternative approach to integration, particularly in modeling the area under a curve. Participants explore the implications of this concept and its relation to traditional methods of integration, such as using rectangles and polar integrals.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests a unique idea involving wedges to model the area under a curve, questioning if anyone has encountered similar concepts.
  • Another participant asks for clarification on whether the original poster understands the traditional method of calculating area under a curve using rectangles, implying a need for foundational knowledge before exploring wedges.
  • Some participants mention counting pixels and looking for patterns in curves, though the relevance to integration is questioned.
  • Polar integrals are introduced as an alternative method of integration that uses different shapes, which some participants find promising.
  • One participant expresses a preference for letting their computer handle calculations rather than engaging deeply with the math themselves.

Areas of Agreement / Disagreement

The discussion contains multiple competing views, with no consensus reached on the validity or utility of using wedges in integration. Participants express differing levels of understanding and approaches to integration.

Contextual Notes

There are limitations in the discussion regarding the foundational understanding of integration techniques, as well as the assumptions made about the relevance of pixel counting to the topic at hand.

jerromyjon
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I can't seem to find anything about what I am thinking about but it has to do with a possibly unique idea I am just wondering if any has ever heard of any such "variation" of calculus. I'm certainly not fluent with even basic calculus, but I can model the "area under a curve" and the aspect that doesn't fit is the x/y grid. What I am considering is way to complex for me to grasp its implications, but the basic idea is to flip the problem around to a set of identical wedges which puts the chord of the curve as the "width" of the wedges. I haven't gotten any further than that and it is a very shaky hypothetical idea I'm just looking to see if anyone knows anything that sounds similar?
 
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jerromyjon said:
I can model the "area under a curve" and the aspect that doesn't fit is the x/y grid.
Are you saying that you don't understand how you can calculate the area under a curve using rectangles?

If that's what you meant, I would advise getting an understanding of that technique before attempting to find the area using wedge shapes. A rectangle has a very simple area: width x length. Do you know a corresponding formula for the area of a wedge?

Another form of integration (polar integrals) uses a different shape entirely.
 
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Mark44 said:
Are you saying that you don't understand how you can calculate the area under a curve using rectangles?
I've been sitting here counting pixels trying to find any patterns in progressively larger curves or figure out what to try next.
Mark44 said:
Another form of integration (polar integrals) uses a different shape entirely.
Ah, polar integrals sounds promising, I'll have to check that out when I have time. Thanks a lot!
 
Last edited:
Mark44 said:
Are you saying that you don't understand how you can calculate the area under a curve using rectangles?
jerromyjon said:
I've been sitting here counting pixels trying to find any patterns in progressively larger curves or figure out what to try next.
You quoted what I asked, but didn't answer my question. What does counting pixels have to do with integration?
 
Mark44 said:
What does counting pixels have to do with integration?
Different methods to get the same results. I've also been doing some origami of sorts...
 
Mark44 said:
Another form of integration (polar integrals) uses a different shape entirely.
This is exactly what I was trying to figure out in a bass ackwards kind of way. :mad: Thanks again! :cool:
 
Mark44 said:
What does counting pixels have to do with integration?
I don't do the math, I make my computer do it exactly how I think it, to accomplish the results I intend. I try, not to think, harder than I have to. :smile:
 
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