Proportionality of triangles problem

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Homework Help Overview

The discussion revolves around the concept of proportionality in triangles and its application to a given figure, specifically a parabola. The original poster seeks to understand if there are any formulas that relate the proportionality of triangles to the proportionality of the areas defined by the curve.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the definition of "proportionality" in the context of areas defined by a parabola. Questions arise regarding the relationship between magnifying areas and fitting them over one another, as well as the mathematical representation of this relationship.

Discussion Status

Some participants have provided clarifications and posed questions to further explore the original poster's inquiry. There is an ongoing examination of the definitions and relationships involved, with no clear consensus reached yet.

Contextual Notes

The discussion includes an assumption that the curve in question is a parabola, and there may be constraints related to the definitions of proportionality being used.

darkmagic
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Homework Statement



Is any formulas similar to that of proportionality of the triangles to proportionality of the given figure?

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The Attempt at a Solution

 

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Not in general, no. How is that curve defined?
 


the curve is a parabola
 


What do you mean by "proportionality"?
That if you magnify area I by some appropriate factor, that you can perfectly fit it over area II? Because that is not true.

Or do you mean: some formula for y2 / y1 given x2 / x1 (where yi is the function value on the right of area i with x-value xi)?
 


proportionality x1/x2=y1/y2
 


<br /> \frac{x_1}{x_2} = \frac{a x_1^2 + b x_2 + c}{a x_2^2 + b x_2 + c}<br />

where ax^2 + bx + c is the formula for the parabola?
 

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