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
Geometric calculus the correspondences of the differential form its derivative and its Hodge dual embed the theory of differential forms within geometric calculus. Following is a diagram summarizing the history of geometric calculus. Geometric calculus In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories including differential geometry and differential forms. With a geometric algebra given, let "a" and "b" be vectors and let "F(a)" be a multivector-valued function. The directional derivative of "F(a)" along "b" is defined as provided that the limit exists, where the