Calculating Area and Perimeter of Geometric Figures with pi^2 and (pi^2-1)

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Discussion Overview

The discussion revolves around the calculation of area and perimeter of geometric figures, specifically exploring whether terms like pi^2 or (pi^2-1) are involved in these calculations. The scope includes theoretical aspects of geometry and references to specific geometric shapes.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions whether any geometric figure's calculations involve the terms pi^2 or (pi^2-1).
  • Another participant asserts that the area of a circle is well-known to be \pi r^2, implying that pi^2 is not directly relevant to this calculation.
  • A different participant suggests that the surface area of a torus, given by the formula A=4\pi^{2}Rr, does involve pi^2, indicating that such figures do exist.
  • One participant provides a link to higher-dimensional expressions, potentially related to the discussion, but does not elaborate on their relevance.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are competing views regarding the relevance of pi^2 in geometric calculations. Some participants suggest specific figures while others question the applicability of pi^2.

Contextual Notes

The discussion does not clarify the definitions or contexts in which pi^2 or (pi^2-1) might be relevant, nor does it resolve the mathematical implications of the claims made.

arivero
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Is there any geometric figure whose calculation (area, perimeter, ...) involves the terms pi^2 or (pi^2-1) ?
 
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I thought it was pretty well known that the area of a circle of radius r is
[tex]\pi r^2[/tex]?
 
arivero said:
Is there any geometric figure whose calculation (area, perimeter, ...) involves the terms pi^2 or (pi^2-1) ?
Sure, check up the torus..
The surface area of a torus with big radius R and small radius r has surface area:
[tex]A=4\pi^{2}Rr (r<R)[/tex]
 

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