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I'm not a mathematician.

Merriam-Webster defines a spiral as "the path of a point in a plane moving around a central point while continuously receding from or approaching it." Other sources I checked don't mention the word "continuously". MathWorld doesn't give a generic definition.
Is the Fibonacci spiral a "proper" spiral, given that the radius of curvature changes stepwise, and the centers of curvature are a set of individual points?

Ѕᴀᴀᴅ
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stevenvh
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    This issue lies more with language than anything else. What Merriam-Webster is likely trying to imply is that the distance from points on the spiral (if thought of as a parameterized thought) to the origin increases or decreases over time, with respect to the parameterization's direction and assuming that the parameterization is "continuous" (no weird jumps). There isn't really a "formal" mathematical definition as far as I know, however, outside of certain specific classes of spirals, e.g. logarithmic/hyperbolic types. It's more just an adjective describing the shape more than anything. – PrincessEev Apr 25 '23 at 09:28
  • The Fibonacci spiral is actually "continuously receding" from the origin despite the fact that the segments have piecewise constant curvature. – Ethan Bolker Apr 25 '23 at 18:10

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"Continuous" doesn't imply "at a constant rate", so the Fibonacci spiral certainly satisfies the dictionary definition.

Karl
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