IC 418 spans 0.3 light-years across. IC 418 IC 418, also known as Spirograph Nebula, is a planetary nebula in the Milky Way Galaxy. The name derives from the intricate pattern of the nebula, which resembles a pattern which can be created using the Spirograph, a toy that produces geometric patterns (specifically, hypotrochoids and epitrochoids) on paper. Only a few million years ago, IC 418 was probably a common red giant star. Since running out of nuclear fuel, though, the outer envelope has begun expanding outward leaving a hot remnant core destined to become a white dwarf star. IC 418 lies about
Affine geometry of curves arclength). Then, In concrete terms, the matrix "C" is the pullback of the Maurer–Cartan form of the special linear group along the frame given by the first "n" derivatives of x. Affine geometry of curves In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under the special affine group formula_1 In the classical Euclidean geometry of curves, the fundamental tool is the Frenet–Serret frame. In affine geometry, the Frenet–Serret frame is no longer well-defined, but it is possible