In 1983, a wealthy American wandered into the Royal Shakespeare Company in Stratford-upon-Avon in England. He saw a scale model of a new theater that the company hoped to build, if only it had the money. The American said he would underwrite the project, but wanted to remain anonymous.

Three years later, Queen Elizabeth II presided at the opening of the new Swan Theater. The American, Frederick R. Koch, who had built the theater for $2.8 million, stood by her side. But she respected his wish for privacy: She thanked “our generous benefactor” — but did not name him.

Mr. Koch (pronounced coke) kept a low profile for most of his life. When the news media mentioned him at all, it was usually in passing in reports about his three hard-charging billionaire younger brothers: Charles and David, who ran Koch Industries, the industrial behemoth founded by their father, and bankrolled libertarian causes; and William, David’s twin, an eclectic entrepreneur, collector and yachtsman who won the 1992 America’s Cup. (David died in August at 79.)

Frederick, who bore the aspect of an Edwardian gentleman, had little in common with his brothers. He devoted himself not to oil, the bedrock of Koch Industries, or to politics, but to the arts and historic preservation.