Post by @brad@social.chinwag.org

OK, say you wanted to define expressions for the length of the line a, and the length of the arc b, given you only know the length r and the angle theta. How might you do that? I do have two expressions but they’re pretty wild, I’m wondering if I’m missing a trick.

A hand drawn diagram. It’s an x-y coordinate plane, with a semicircle drawn on it. The arc of the semicircle begins at the origin. The radius of the semi circle is marked on the x-axis, labelled ‘r’. The diameter is also marked, labelled ‘2r’. There is a line labelled ‘a’ which traces from the origin to a point labelled (x, y). The arc from point (x, y) to point 2r is labelled ‘b’.

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Deborah Pickett

@futzle@old.mermaid.town 12 min. ago

@brad There’s an isosceles triangle formed by the two radii and a. So you can compute the third angle, and from there, pi - that angle, and so b. Divide the isosceles triangle in two, a/2 should be r*cos(theta).