# Etymology of "exterior" in "exterior calculus"

What is the origin of the term "exterior" in "exterior calculus"? How does this term relate to "interior products" and "inner products", if it does at all?

• Looks like an E&LU quesuion. Mar 8, 2017 at 15:24

• So, just to fill in a step you’ve omitted, that’s maybe not obvious to all readers: Grassmann’s original contrast is between the interior and exterior products of vectors in $\mathbb{R}^3$ — aka the dot-product and cross-product. The former of these was later generalised to “inner products”, etc; the later was generalised to “exterior algebra”, etc. Mar 8, 2017 at 10:16