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What level of math does one need for some simple 2D physics?

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Specifically, I mean programming the physics for a side scrolling platformer, such as Super Mario World. Is something like Calculus required?

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This really depends on how "accurate" you make your simulation. A technically inaccurate collision model can be very convincing and simple to implement.

A good basic understanding of calculus will certainly help, but it isn't strictly necessary. You'll want to look up kinematic equations (I personally don't even know them myself - I always derive them whenever I need them).

I would definitely suggest brushing up on your trigonometry.

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Trig is the absolute minimum, but realistically you'll probably need 1st semester calculus.

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