Yes ,it is a curve that is just around a circle
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Technically, yes.
A small circle is a simple circle on a two dimensional plane. The great circle is the circle around a sphere that is on the plane that intersects with the center of the sphere. It is the reason that on a flat map the paths of planes seem to curve to go to and from Europe and the North American continent.
circle, compound curve, elipse . . . .
No, a circle can't be a parallelogram. A circle is a curve. A parallelogram is a quadrilateral with two pairs of parallel sides constructed with four line segments. The line segments are straight, and the circle is a continuous curve.
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