Talk:Theorema Egregium

In joke?
I've discovered the following text removed from an earlier version of the article:


 * A somewhat whimsical application of the Theorema Egregium is seen in a common pizza-eating strategy: A slice of pizza can be seen as a surface with constant Gaussian curvature 0. Gently bending a slice must then roughly maintain this curvature (assuming the bend is roughly a local isometry). If one bends a slice horizontally across a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero. This creates rigidity in the direction perpendicular to the fold, an attribute desirable when eating pizza (since it prevents stuff from falling off and making a mess).

The removed wrote:


 * remove mathematical injoke, might be funny to mathematicians but should not be in an encyclopedia

The "application" itself is far from being formally encyclopaedic, but I disagree with its classification as the "injoke" and rather think that it is a good informal illustration of the meaning of the theorem. Arcfrk (talk) 03:24, 11 March 2008 (UTC)


 * I can assess that the removed explanation is perfectly clear, correct and appropriate as a real-world application of the Theorem. The only plausible reason to remove it seems to be that not every reader may know what pizza is, since wikipedia readers come from different cultures.  Otherwise, it is serious and clarifying.  Most certainly, it is not a joke.


 * If there remains no argument against the explanation, I will restore it shortly in the following form:


 * An application of the Theorema Egregium is seen in a common pizza-eating strategy: A slice of pizza can be seen as a surface with constant Gaussian curvature 0. Gently bending a slice must then roughly maintain this curvature (assuming the bend is roughly a local isometry). If one bends a slice horizontally across a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero. This creates rigidity in the direction perpendicular to the fold, an attribute desirable when eating pizza (since it prevents the pizza toppings from falling off).


 * coco (talk) 14:28, 15 July 2009 (UTC)

While it is clearly an actual application, is it really necessary to have it in the article? As a current student of mathematics, I found that the description of the pizza slice example was actually less clear than the previous one, firstly because bending a slice of pizza as instructed clearly leads to the pizza toppings falling off of where they are and then into the center fold, still ruining the pizza; secondly because, at least to me, the reference to when "one bends a slice horizontally across a radius" is not very specific; and thirdly, because it seems to make the SIGNIFICANCE of the theorem appear to be primarily related to the curving of objects, when, as I understand it from earlier in the article and a brief familiarity with several related articles, the primary significance of the theorem is the fact that when one has a surface/manifold, one does not necessarily have to take into consideration the surrounding space and can in fact act as if there is no surrounding space, as in relativity. I don't want to edit it away, but it just seems rather out of place, especially considering the overall length of the article and I figure it doesn't hurt to add my own 2 cents in. Zanotam - Google me (talk) 06:55, 9 June 2011 (UTC) (I was accidentally logged in anonymously on my laptop, the proceeding comment was indeed mine.)

Question
I am Jimmy Snyder. I looked up the word egregium and found many English equivalent words such as remarkable, extraordinary, and distinguished among others. The wiki article uses remarkable. Is this just a random choice among the various possibilities or is there a particular reason for choosing this one over the others? — Preceding unsigned comment added by 173.61.117.8 (talk) 13:32, 13 September 2011 (UTC)

What it says under the map, is not correct: the surface of a spheroid cannot be completely mapped in plane, whatever distorsion is applied. — Preceding unsigned comment added by Theodore Yoda (talk • contribs) 15:49, 9 February 2013 (UTC)

Missing details
The page is missing many basic details, including the equation associated with the theorem or even a sketch of its proof. Therefore, I am adding a Missing information tag. -V madhu (talk) 16:16, 9 January 2020 (UTC)


 * What do you mean by "the equation associated with the theorem"? Dfuz (talk) 12:24, 16 February 2021 (UTC)

Original wording
The Italian version of this article includes the latin wording "Si superficies curva in quamcumque aliam superficiem explicatur, mensura curvaturae in singulis punctis invariata manet" left out from this page that only quotes the English translation of the theorem. Should the translation not come in italics after the direct original latin quote, as is often the case for other languages such as German? 91.106.19.3 (talk) 14:59, 30 March 2020 (UTC)