In October 1957, the Soviet Union kicked off the Space Race with the launch of Sputnik.  In the United States, instant humiliation was immediately followed by a wave of national panic, and then a wide range of federal initiatives, ranging from investments in defense to investments in science, technology, and mathematics education.

One new piece of legislation, The National Defense Education Act, provided (among other things) a windfall for producers of educational films.  And according to historian Martin F. Norden, no company was better prepared to benefit from that windfall than Disney Studios, which had “already positioned itself as a significant educational force in the fields of education, science, nature and technology years before the Sputnik launch.”^[1]  Less than two years later, Disney Studios, with support from the US government, released its 27-minute educational featurette Donald in Mathmagic Land.  This film, subsequently nominated for an Academy Award (Best Documentary – Short Subjects), was widely made available to schools and became one of the most popular educational films ever made.  It can be watched here.

As Walt Disney once explained, Donald in Mathmagic Land was created to “excite public interest in this very important subject [of mathematics].” The film features Donald Duck roaming a Wonderland-esque world of mathematics.  During his journey, in which he follows the voice of the faceless Spirit, he is told that he’ll find “mathematics in the darnedest places.”  This peregrination takes Donald from ancient Greece and a meeting with Pythagoras to the Notre Dame Cathedral, where he learns about the golden rectangle.

But, it is when the Spirit tells him that “practically all games are played on geometric areas,” that Donald sees the application of mathematics to baseball, basketball, hopscotch, and ultimately, to a game that involves “two perfect squares, three perfect spheres, and a lot of diamonds…in other words, billiards” — three-cushion billiards, to be precise. (The billiards sequence runs from 16:49 – 22:15 in the clip above.)

Though Donald initially believe billiards to be a game of luck, he learns quickly from the Spirit that it is a game of skill in which “you have to know all the angles…it’s a game that takes precise calculation.” As the Spirit talks, a real (as opposed to animated), unidentified billiards player makes one gorgeous three-cushion shot after another.  (The unidentified player, in fact, is Roman Yanez, the owner of a Los Angeles billiards hall in the 1950s and a periodic tournament player, who got 10th place in the 1964 U.S. National 3-Cushion Championship.)

The Spirit explains that the player is using “the diamond system as a mathematical guide.”  He then elaborates on the “simple” math used in which the player subtracts the “cue position” from the “natural angle for the hit” to determine the appropriate numbered diamond at which to aim.  It’s interesting to hear the Spirit attempt to simplify the diamond system, and wildly humorous to watch Donald Duck attempt to internalize it.

The particular version he is describing – the five-corner system – is far less common now, except perhaps in three-cushion billiards.  Ironically, the diamonds have become an ongoing source of debate.  Some world-class players don’t use the diamonds at all, some use them to check their instinct and some swear by the diamonds for special situations.  For example, WPBA professional (and star of the movie 9-Ball) Jennifer Baretta says, “For people who play three-cushion billiards these systems are absolutely essential, but they also apply on any table where the width (short rail) is half the length (long rail).”^[2]

While Donald in Mathmagic Land may not have had a lasting impact on the adoption of the diamond system in billiards, it clearly has had a lasting impact on billiards players, many of whom remember it fondly from growing up.  There are an endless number of tender-hearted comments about the film online, but I particularly love the tribute below from John Sciatta’s blog:

The part that I loved, the part I looked forward to each year was when Donald would use math to explain three-cushion billiards. This part was brilliant. This part was fascinating. This part made total and absolute and perfect sense. I would watch this scene each year and be like, “Yes! You’re right, Donald! The diamond system…But then a strange phenomenon would happen; the movie would end, and with the diamond system dancing in your head, it would all start to get jumbled. And no matter HOW MANY times I watched it, I could never keep the diamond system straight. I felt like the guy from Memento… I rented it prior to going out and actually playing pool and it still didn’t stick. I swear, watching the DD in MM Land billiards scenes is like trying to solve one of the great mysteries of our day.