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Posts tagged with :desmos-threat:

I was wondering why electrical systems have 3 sinusoidal phases and why generators are typically built with 3:4 coils:magnets. So, I graphed the magnetic field strength at various phases to find out:
When you transform f(x)=e^x 1 unit to the left, you’re left with g(x)=e^(x+1) (Fig. A). This transformation is pretty simple; the new line is 1 unit away. However, it’s only 1 unit away horizontally. Vertically, it varies depending on the x value. The vertical difference at x=-1 is a lot smaller than the vertical difference at x=1. On this recent #hack-night, @carrot and I set out to transform f(x) so that at any point along f(x), the distance to the closest point on g(x) is equal to 1. Essentially, g(x) is 1 unit away throughout, not horizontally (Fig. B). This proved to be quite difficult. There were a lot of quadratics that needed solving, and we also had to use the pythagorean theorem to get some distances. He can probably explain the math behind it a lot better than I can. Anyways, here are a few links if you want to try it out: • Exponential Functions - • Quadratic Functions - • Linear Functions - • Circles - (I think)
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