I was kindly granted permission by the Mathematical Association of America and Orlando Neto to post here the publisher's final version of the article.

I was asked to include a full bibliographic reference: Jaime Gaspar and Orlando Neto, All Triangles at Once, The American Mathematical Monthly, volume 122, number 10, page 982, December 2015.

I was asked to include this text: Copyright 2015 Mathematical Association of America.  All Rights Reserved.