9
$\begingroup$

So I heard that if one inscribes the largest circle that can fit into a equilateral triangle, then divides the perimeter of the triangle by the diameter of the inscribed circle, it gives a value which can be called "triangle $\pi$", and that value ($\sqrt{27}$) can be used in the place of regular $\pi$ to derive volumes of the other platonic solids. Is that true? Is there a different $\pi$ for triangles? What is that value? Is it close to $\sqrt{27}$? Can it be used to find volumes of platonic solids, especially the icosahedron and the one that looks like a pyramid flipped and stacked on its twin? 4 part question. Thanks we have been arguing about it at work for weeks

  • 5
    So, what is the question?2012-06-14
  • 2
    $\pi$ is a constant, it has only one value...2012-06-15
  • 0
    The word you are looking for is *octahedron*.2012-06-15
  • 1
    If you want to know the volumes of the Platonic solids, try http://en.wikipedia.org/wiki/Platonic_solid#Radii.2C_area.2C_and_volume.2012-06-15
  • 1
    The relationship of that number to triangles is somewhat analogous to the relationship of $\pi$ to circles, but calling it "triangle pi" is problematic in two respects: (1) It is not standard terminology, and (2) There are all sorts of special properties of the number $\pi$ that would not apply to that number. $\pi$, for example is a transcendental number. I can imagine it being called "triangle pi$ within the context of a particular article about it, but I'd be a bit surprised if the author proposed adopting that language as standard terminology.2012-06-15
  • 0
    I'm not sure if you get notified by edits to answers, so I'm leaving you a comment to say that I've added a little bit to my answer that you might find interesting.2012-06-15
  • 0
    It's actually very interesting. I've been working on just these sorts of questions to create some new geometry. Thanks!2015-09-28

1 Answers 1