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Humans are known to regulate the timing of interceptive actions by modeling, in a simplified way, Newtonian mechanics. Specifically, when intercepting an approaching ball, humans trigger their movements a bit earlier when the target arrives from above than from below. This bias occurs regardless of the ball's true kinetics, and thus appears to reflect an a… (More)
We are interested in this paper in the family of curves M (p, k, r, n), solutions of equation z n = αz k + (1 − α), where z is a complex variable, n, k, p and r are nonzero integers and α is a real number greater than 1. Expressing each of these curves in polar coordinates (ρ, θ), we will prove that ρ (θ) is an increasing function.