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    The Art of Computer Programming: Fundamental Algorithms, Volume 1 – Fundamental Algorithms, was published in 1968, and had a section 2 about trees. Can someone owning this book verify that diagrams show trees growing down? If so, the history points us to a convention started even earlier. Also, I wonder if computer science picked up from mathematics this convention from even earlier than 1960. Wolfram shows trees were studied in 1857. Commented May 17, 2012 at 12:28
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    @maxpolk Knuth draws his trees in the root-at-top way in, and discusses his decision (sec. 2.3, pp. 311 in the 3rd edition) to convert form root-at-bottom form prior to publication of the first edition. It boils down to "most of the existing literature goes top-down, and we need a consistent model for discussion purposes" (80% according to Knuth's survey). Commented May 20, 2012 at 15:57