Computing the length of day anywhere, anytime

The amount of daylight varies with latitude and time of year. But how, exactly? I began thinking about this as an exercise in spherical coordinates for second-year multivariable calculus students. After all, how hard could it be? If you follow the solution to the end, you'll see why I doubt I would ever assign this to students. However, I was happy with my own approach to the problem, and needed some practice using the tikz graphics program, so I thought I would write it up.…

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