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this post was submitted on 13 Sep 2026
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TechTakes
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Big brain tech dude got yet another clueless take over at HackerNews etc? Here's the place to vent. Orange site, VC foolishness, all welcome.
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The OpenStax textbook covers the development of the general equations of the various conic sections. If the Stewart book covers that in such detail, it must be jammed into the appendices or exercises someplace. I'll have to find the time to go over that, at least; I still don't have a great intuition for hyperbolas.
Yes, this looks like what I need to understand the negative j term in the cross product formula. Cambridge looks to have the 3rd edition of Boas' book up for download, so I have a copy now. We'll see how well I comprehend it, I feel like I'm missing the concept of index permutation to really understand the Wikipedia article.
I don't know how much traffic we'd get if we tried to cultivate a math discussion here. I did make an account on Mathstodon too and perhaps I should spend more time there. Tutoring at this level is sparse, at least at a community college. There's one tutor for my class available via Zoom, and the instructor himself is apparently teaching 5 classes when he's only under contract for three. If I signed up for 5 classes as a student, I'm sure I'd be setting off all sorts of alarm bells in the registration department, if they even let me go through with it.
The Levi-Civita symbol is, in programming lingo, a function that takes three arguments:
epsilon(i,j,k)wherei,jandkare integers that label the coordinate axes. Let 0 stand for the x axis, 1 for the y and 2 for the z. Thenepsilon(0,1,2)equals 1. If we swap the values of any two arguments, we flip the sign: e.g.,epsilon(1,0,2)evaluates to -1. Now, swap again:epsilon(1,2,0)must change sign again, so it evaluates to 1. But the sequence 1,2,0 is just the original sequence 0,1,2 read cyclically from a different starting point. In this way, we can work out what the value of theepsilonfunction is for any input. When the inputs are all different, the output is either 1 or -1, depending on whether the input sequence is "in order" or "in reverse order". Write the numbers 0, 1 and 2 around a circle. Read clockwise, and you get one output; read counterclockwise, and you get the other. If two inputs are the same, thenepsilonmust evaluate to zero, because, for example,epsilon(0,0,1)with the first two inputs swapped isepsilon(0,0,1)again, meaning that the output must be minus itself.