Arch is related to Gentoo in that both offer rolling updates and try to keep you on the bleeding edge. They differ in that Gentoo is a primarily source-based system with binary packages bolted on and Arch is a primarily binary-based system with source bolted on (admittedly, Arch has better source support than Gentoo has binary).
Arch also compiles it's packages for i686, to appease the gentoo-ricers.
Their goals are similar, so you could argue that Gentoo inspired arch, but they are unrelated.
It's really not even inspired by Gentoo. Judd was always quite clear that Arch started it's life as Crux with a more automated package manager. The ancestry still shows in the BSD style init, the use of tar.gz as the package format, and the almost identical package build syntax.
The only reason people keep mentioning Gentoo around Arch is because Arch is occasionally concerned with speed and they're both seen as nerd distros.
well said, im disappointed by the misconceptions posted here about arch.
rolling release does not mean you have to upgrade to python 3 if you still want to use python 2.6. it is very trivial to configure pacman to ignore certain packages.
Arch also compiles it's packages for i686, to appease the gentoo-ricers.
Their goals are similar, so you could argue that Gentoo inspired arch, but they are unrelated.