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Joined 2 years ago
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Cake day: February 1st, 2024

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  • Yeah I’ve been very happy with them.

    No experience with their software, but the service is great — I have an ARM SBC with WireGuard handling my tunnels, and my router does the rest (so my TV/guest SSID/personal SSID/whatever can get routed over Mullvad with no client setup). My DNS forwarders are each routed through a different Mullvad interface too.












  • qjkxbmwvz@startrek.websiteto196Triangle rule
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    10 days ago

    That almost makes sense, but pi radians = 180°

    Right, a triangle “has 180deg,” like I said.

    in which case π÷n is infinitesimally small. In other words, substituting infinity for n would be incalculable

    That’s not how limits work. Substitution is not the same as taking the limit.

    infinite and infinitesimal numbers are impossible to express rationally.

    That’s not true at all. https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_⋯

    It’s not about colloquialism or language

    Having one word (or phrase) with two meanings is a property of language.


  • qjkxbmwvz@startrek.websiteto196Triangle rule
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    10 days ago

    That’s exactly my point, there are two different colloquial ways of talking about angles. I am not claiming there is a mathematical inconsistency.

    Colloquially, a “triangle has 180 degrees” and a “circle has 360 degrees.” Maybe that’s different in different education systems, but certainly in the US that’s how things are taught at the introductory level.

    The sum of internal angles for a regular polygon with n sides is (n-2pi. In the limit of n going to infinity, a regular polygon is a circle. From above it’s clear that the sum of the internal angles also goes to infinity (wheres for n=3 it’s pi radians, as expected for a triangle).

    There is no mystery here, I am just complaining about sloppy colloquial language that, in my opinion, doesn’t foster good geometric intuition, especially as one is learning geometry.


  • qjkxbmwvz@startrek.websiteto196Triangle rule
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    10 days ago

    I don’t think we’re talking about the same thing.

    If you take a circle to be the limit of a polygon as the number of sides goes to infinity, then you have infinite interior angles, with each angle approaching 180deg, as the edges become infinitely short and approach being parallel. The sum of the angles is infinite in this case.

    If you reduce this to three sides instead of infinite, then you get a triangle with a sum of interior angles of 180deg which we know and love.

    On the other hand, any closed shape (Euclidean, blah blah), from the inside, is 360deg basically by definition.

    It’s just a different meaning of angle.

    See, for example, the internal angle sum, which is unbounded: https://en.wikipedia.org/wiki/Regular_polygon


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    10 days ago

    Triangle, “has 180 degrees,” subtends 360 degrees.

    Circle, “has 360 degrees,” the sum of the interior angles is infinite.

    (I’m not actually confused, it’s just that “a circle has 360 degrees” and “a triangle has 180 degrees” is a little annoying in that they use different definitions.)