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Cake day: February 1st, 2024

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  • qjkxbmwvz@startrek.websiteto196@lemmy.blahaj.zonemrrp rule
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    1 month ago

    I have heard, but have trouble finding references to it, that you can build a simple arbitrary waveform generator circuit by using an analog scope, a photodiode, and a cardboard cutout.

    You make a photodiode circuit that rails high with no light, but light on the photodiode pushes the signal low. Then you aim this at the phosphor screen with a cardboard cutout of the desired waveform: signal goes up until the phosphor trace is above the screen, and then it gets pushed low (i.e., feedback keeps the trace right on the edge of the cardboard).

    Never seen it in action, but I choose to believe it works beautifully :)







  • 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.


  • 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


  • 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.)