A way of sawing lumber (diagonally, towards the center of a log, instead of just sawing flat) that crosses the grain in a way that gives you stronger, perhaps more dimensionally stable boards and often beautiful fleck and ray patterns. If you look closely at the Viking ships on display in Oslo at the Vikingskipshuset you can see patterns in the wood that are indicative of quarter-sawn lumber.

http://4.bp.blogspot.com/_9EPZm2S5P2I/Rvmm7AD8GJI/AAAAAAAAAAk/4avY9mpznK0/s1600/medullarylrg.jpg

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http://www.hardwooddistributors.org/postings/what-is-the-difference-between-quarter-sawn-rift-sawn-and-plain-sawn-lumber