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Archimedes's Spiral and Its Tangents

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simple view
constructive view
t
15
This Demonstration uses parametric equations and radius vectors to plot Archimedes's spiral (blue) and the curve of its tangents (orange), which represent the derivative. The function is
ϕ(t)=at
in polar coordinates or in this implementation,
ϕ(t)=ax/(4π)(sinx,-cosx)
in rectangular coordinates.
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