An Archi gif, compliments to Lucas V. Barbosa

Given the last weblog on radians, I noticed that Wikipedia had a nice gif animation created by Lucas V. Barbosa. The article even mentions: “This is a featured picture on the English language Wikipedia and is considered one of the finest images.” Barbosa even made a version with tau = 2 pi. The latter is less appealing since it does not mention pi, while, of course, tau reads like radius r, and then can cause confusion (indeed, run that gif too).

It appears that Barbosa put his gif into the public domain. Thus I adapted it for Archi = Θ = 2 π, including a note of reference that he did most of the creative work.

1 Archi = 2 pi

A radian is an angle measured by an arc of a circle with the same length as the radius of that circle. A full circle corresponds to an angle of 1 Archi = 2π radians. Use 1 Turn ⇔ Θ radians, so 1 radian ⇔ 1 / Θ Turn ≈ 16% Turn.

Interestingly, Barbosa’s original gif has a small shaded disc in the center. If we take the radius of the larger circle as r = 1 then we get the smaller Angular Circle in the center with r = 1 / Θ and circumference 1. My proposal is to speak about “angles” on the Angular Circle (use α and β), and to use “arc” for the radians on the Unit Circle (use φ and ψ). Of course, angles as measured on the Angular Circle are arcs too, but it helps being able to say that angles add up to 1 Turn and Unit Circle arcs to 1 Archi rad.

PM. The Wikipedia article I referred to has a wrong statement on dimensions (today, July 2014). For a discussion of this, see the earlier weblog entry on radians.


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