IC 418 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 3600 light-years away and
Cone of curves "cone of curves" of formula_1 to be where the formula_6 are irreducible, reduced, proper curves on formula_1, and formula_18 their classes in formula_13. It is not difficult to see that formula_20 is indeed a convex cone in the sense of convex geometry. One useful application of the notion of the cone of curves is the Kleiman condition, which says that a (Cartier) divisor formula_11 on a complete variety formula_1 is ample if and only if formula_23 for any nonzero element formula_24 in formula_25, the closure of the cone of curves in the usual real topology. (In general, formula_20 need not