On Feb. 14, Ben Frisch, in his 34th year teaching at Friends Seminary, a private school in downtown Manhattan was seeking to demonstrate an obtuse angle in an 11th grade math class. Straightening his arm and pointing it outward, he mimicked the Nazi salute and said, “Heil Hitler.”

Mr. Frisch’s father was an Austrian Jew who suffered traumatic anti-Semitic attacks as a child in Poland before World War II and lost his grandparents in the Holocaust. Mr. Frisch, a devout Quaker, has been considered one of the most spiritually serious members of the faculty at the school, founded in 1786, by members of the Religious Society of Friends. No one believed he had suddenly become a Third Reich sympathizer, but at the same time not everyone found his professed effort at comedy particularly whimsical.

Not long after the incident, Mr. Frisch received a call from the administration telling him that there had been complaints about his analogy, that some students were offended and that he should not come to school the following morning. A period of limbo preceded a suspension, and on March 9, the day after the school’s gala and auction, he was fired.

Later that day, the school’s principal, Robert Lauder (Friends is the rare independent school that shuns the term headmaster), sent a letter to the community explaining the termination. “Our students know that words and signs of hate and fear have no place at Friends,’’ he wrote, adding that as news of Mr. Frisch’s gaffe had circulated, the administration started to receive calls and emails about “other equally inappropriate and troubling actions by Ben.”