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HKO (@HKObservatory) - Posts - | X (formerly Twitter)
Understanding the Context
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๐ฐ This is the equation of a **circle** in the \( (r,z) \)-plane, rotated about the \(z\)-axis, forming a **torus**? No รขยย actually, since \(r\) is radial, this describes a **sphere** of radius \(c/2\) centered at \((x, y, z) = (0, 0, 0, c/2)\) in cylindrical coordinates.
๐ฐ Wait: \(\left(r - rac{c}{2}
๐ฐ ight)^2\) is a circle in the \(r\)-axis plane, centered at \(r = c/2, z = 0\), radius \(c/2\). Rotated about the \(z\)-axis, this forms a **torus**? No รขยย it forms a **sphere**.
