I got a nice note from Vlorbik on my last post about the influence of political correctness (not his term) and its influence on math in the past. I don't know if that is a first name or a last name, and I actually tried a little to find out, but I do know he has an unusual collection of blogs, including one on Community College Calculus which is always a good read.

Vlorbik wrote, in part, "i've heard, though never verified, that victorian prudery also caused certain teachers to begin referring to the "arms" rather than the "legs" of a right triangle.."

I have a pretty extensive collection of old textbooks, including many British texts, and I don't remember ever seeing anyone use "arms" in that fashion, so my first thought was that, if it were true, it was only a very minor usage. Since the good lady ruled from 1819 to 1901, I thought I would search before and after her reign.

I pulled out my 1804 edition of Playfair's "Elements of Geometry", published in Edinburgh. He referred to the right triangles sides as..."sides"... His Book VI, prop. XXXI reads exactly like the Thomas Heath Translation. No help there, so I skipped forward 99 years to the other end of the Victorian period, 1903 and looked in "A Junior Geometry" by Noel S Lyndon, published in London, only to find he also used only the terms hypotenuse and "other two sides" in his statement of the Pythagorean Thm.

Perhaps neither term was common in the Victorian peridod, and these stories were a bit of urban legend. I went on to Google Books to see if I could find any examples of geometric usage such as Vlorbik had described..... I entered a search for "arms 'right triangle' geometry"

....Yikes", there they were. The first listing was "Plane Geometry" by Arthur Schultze, Frank Louis Sevenoak, Limond C. Stone, from 1901. It contained, "The sum of the squares of the arms of a right triangle is equal to ..." along with 388 other listings, some dated as late as 2008. "In a right triangle whose arms have lengths a and 6, find the length of the .." appears on page 451 of the fourth edition of Schaum's Outline of Geometry from that year. Ok, but that still did not mean it was the influence of the dreaded Victorian stuffed-shirts... I switched the cut-off to 1850... and there were NO results prior to that year... only one last check. Would there be examples with the use of "legs" prior to that year? There were indeed, including several by the famous American Mathematician, Benjamin Pierce. Another from 1734 was from the British Benjamin Martin.

So it appears that there was some pressure to use "arms of a right triangle" suggested by these dates; but there is still no smoking gun. Does anyone out there know of a document or statement of any kind in the math education literature that makes a clear suggestion to teachers? If you know of such a document, please share whatever level of information you have and I will pursue it.

And thanks again to Vlorbik for sharing this tidbit of math language history. I also followed up a second part of his comment, and learned a little more about the evolution of "parent functions".... but that will have to be another day.

## 3 comments:

Doesn't help, but I have a few old texts on my shelf:

Solid Geometry, by Wentworth, Ginn and Co, Boston, 1899 refers to the legs of a right triangle. Exercises are miscellaneous, not promiscuous.

A Short Course in Higher Algebra, Wells, Leach, Shewell, and Sanborn, Boston, 1889 does not use "promiscuous."

But I have a winner. Believe it or not: Modern School Geometry, John R Clark, World Book, Yonkers-on-Hudson, 1938, uses only "arm" and never "leg" for both right and isosceles triangles.

Thanks, and if anyone else has examples of these, please let me know.. I can compile a few.

nice little piece of research there.

looking forward to the results

of your investigations into parents.

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