Is there a way to visualize a sphere instead of a circle ?
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There are many. The most popular one adds a third function to vary the size of circles along an axis (so you get a globe). In our world, most spheres describe the equidistant boundary of a region around a point (for instance, a shock wave).
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It is strange as way we were taught the relationship between points/lines/trig fns/circles was kinda like that. Put a pencil paper. A dot. Move it up/down, a line. Pul the paper left while doing that, sine. (also used to demonstrate vel/acc). Paper back/forward/up/down? Circle.
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When seen this way, we also understand that a wave function describes a rotating thing moving along a direction.
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Numbers (subsequent naming strategy for locations), addition = repeated incrementation = translation, multiplication = repeated addition = scaling, exponentiation = relation between addition and multiplication, 2d multiplication = rotation...
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This blows my mind. I'm a math tutor. Will you please teach math online! I will pay you money and it could influence teachers.
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P.s. you already do this for free on twitter. I'm just talking about something more structured for those of us who aren't exceptional at math.
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Light bulb!
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I was introduced to them like that. But not in school, but by my father when I asked him about it because of some programming stuff I wanted to do before those topics came up in school.
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