4 ms·

I wonder if instead of V-E+R it would be more intuitive to use V+R-E so there are no intermediate negative numbers in the calculation.

• j2kun 12y ago
  So it turns out that this formula generalizes to an alternating sum over many dimensions [1] (although it can be stated more simply than Wikipedia does). From that perspective, it makes more sense to put the minus sign in the middle. In either case, I don't think it is that big of a conceptual stumbling block to have a minus sign in the middle... [1]: http://en.wikipedia.org/wiki/Euler_characteristic#Generalizations http://en.wikipedia.org/wiki/Euler_characteristic#Generaliza...
  • jonsen 12y ago
    But it is an operational stumbling block when subtraction gives negative results. It may lead to calculation errors otherwise avoided. In a pedagogical setting like this one error sources should be minimized.
    • learnstats2 12y ago
      But the students are at exactly the stage where calculating with negative numbers has been introduced and needs practice and precision, so this works out very nicely with the curriculum.
• AllTalk 12y ago
  The V-E+R follows the pattern of zero-dimensional, one-dimensional, two-dimensional, and this alternating sum formulation continues for the Euler characteristic in higher dimensions. So that is one reason to keep V-E+R. Another reason, however, is that although some negative numbers show up, the numbers are all very small, and this could be a good opportunity to introduce some exposure to negative numbers.