GANGNEUNG, South Korea — It may not have been the most obvious choice for Yura Min and Alexander Gamelin, the American-born ice dancing pair representing South Korea at the Olympics, to skate on Tuesday to “Arirang,” a Korean folk song whose roots go back hundreds of years.

There was concern in their camp that the international judges at the Winter Games would not respond to a tune unfamiliar to them. But for Ms. Min — and for any Korean watching — the significance of the choice was clear.

“Even though it could be difficult to get high scores from foreign judges, I wanted to perform with ‘Arirang’ at the first Winter Olympics in Korea, and I did,” Ms. Min told Korean reporters on Tuesday. “I was born in the United States, but I am proud to be Korean.”

In an 1896 essay, Homer B. Hulbert, an American missionary in Korea, wrote: “To the average Korean, this one song holds the same place in music that rice does in his food — all else is mere appendage. You hear it everywhere and at all times.”