# 1 from old math terms notes Obtuse, Amblygon (with explementary)

  Recovering some old notes I wrote for students over time and adding them as I go:

Obtuse is from the Latin formation ob (against) + tundere (to beat) and literally means to beat against. An object thus beaten becomes blunt, dull, or rounded, as in the application to an obtuse angle, one having more than 90 degrees but less than 180 degrees. A triangle with an obtuse angle is called an obtuse triangle.

You may (very rarely) encounter the name amblygon used for an obtuse triangle. It is also sometimes spelled ambligon. Amblygon is drawn from the Greek roots for blunt amblu preceding the root gon for angle (from knee). The use in English probably first occurred in Billingsley's translation of Euclid in 1570, although he wrote "amblygonum". Billingsley's translation was the first translation of Euclid's "Elements" in English. It was published at London in 1570 with the title The Elements of Geometric of the most auncient Philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, Citizen of London

And a bonus

Explementary I first heard of the word explementary in July of 1999. It was "re-created" by Steve Wells of a company called Think3 while working on a new CAD program, thinkdesign. The word was needed to represent the angle required to complete a 360o angle. They wanted a word that would be a natural sounding extension of complement and supplement. The Latin explementum means "filling" or "stuffing" and it is in the OED as "that which fills up". This is actually very similar to the meanings of complement and supplement. After a couple of days, he found hte word was not as new to mathematics as we had thought. Several days later he wrote to tell me that the word already appeared on the "Dictionary of Technical Terms for Aerospace Use (Web Edition by Daniel R. Glover, Jr at the NASA Lewis Research Center, Cleveland, Ohio. Here is there definition, as sent to me by Mr. Wells: Explement -- An angle equal to 360 degrees minus a given angle. Thus, 150o is the explement of 210o and the two angles are called explementary angle--Two angles whose sum is 360o. My thanks to Mr. Wells for his advice and corrections as much of this content came directly from his emails. Later I found earlier citations of the mathematical term in the Oxford English Dictionary, which lists an 1830 book of Geometry by a Pierce Morton who published other editions in 1838. Morton also shared credits with Augustus De Morgan for a book title Mathematics II, from the Society for the Diffusion of Useful Knowledge. I have little information about has life and would seek input from anyone with additional information about his life.