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Nehad Ahmed fields the question day in and day out: What is that little tiled triangle carved into the sidewalk outside the smoke shop he manages in Greenwich Village?

The answer: It was once considered the smallest piece of private property in Manhattan.

The triangle is roughly 25 by 27 inches — smaller than a yield sign on a highway, or about 0.0000797113 of an acre. Not quite eight hundred-thousandths.

Mr. Ahmed said the triangle is one of those things that tour guides mention, along with what has long been known as the narrowest house in the Village, a nine-and-a-half-foot-wide structure at 75½ Bedford Street that has been home to famous residents, including Cary Grant, John Barrymore and the poet and playwright Edna St. Vincent Millay.

The triangle outside Mr. Ahmed’s smoke shop is completely covered by a plaque. People walk right over it. They stomp on it. They hopscotch around it. Or they do not notice it as they trudge toward the corner of Seventh Avenue South and Christopher Street — itself a triangle, Olympic-size by comparison and bracketed by sidewalks and two subway staircases less than 30 feet apart.

New York has many lots that were too narrow to build on or, like the triangle, were left over after construction was finished. But Andrew Berman, the executive director of the Greenwich Village Society for Historic Preservation, had a lot to say about the little triangle.

“Literally and figuratively, it’s emblematic of the Village,” Mr. Berman said. “It goes against the grain — it’s about a resistance to having the order imposed that is commonplace in the rest of the city — and it’s about the little guy taking on City Hall.”

He could have said the Village went against the grid. Its patchwork of streets was laid out when the city pushed northward on a rectangular plan. That was fine until the city decided to connect the subway to Pennsylvania Station after it opened in 1910 — and extended the subway line farther south.

Until then, the city’s one subway line had run down the West Side to 42nd Street, where it turned east and went to Grand Central Terminal. Then it headed south, with stations all the way to City Hall.

For the extension below Penn Station, the city planned a long, straight avenue — Seventh Avenue South — atop the newly dug subway. The project forced massive demolition of buildings that were in the way. The New York Times said an 11-block stretch was to be “ruthlessly cut through, destroying many curious old residences and businesses.” More than 250 buildings faced demolition, most by condemnation by the city, amid some concerns that the project would “cut the heart out of old Greenwich Village.”

One of the condemned buildings was an apartment house known as the Voorhis, owned by the estate of David M. Hess, a Philadelphia entrepreneur and real estate investor who had died in 1907.

Mr. Berman of the historical society said that Mr. Hess’s heirs put up a fight to save the Voorhis. They went to court. They lost.

And then a surveyor made a mistake. Somehow, after the distances and angles were calculated and recorded on the tax roll, the Voorhis lot did not disappear completely, as the city expected it to. The tiny triangle survived.

“Some versions of the story say it was overlooked by the city,” Mr. Berman said. “Others say the Hess estate refused to give up the property from the beginning. From most of the writing I’ve seen about it, it seems that it was a mistake on the city’s part that the city tried to correct” by asking the Hesses simply to donate the triangle.

Apparently still angry about the razing of the Voorhis, they refused, he said.

So the triangle stayed. And the city moved on.

“My assumption is, the city decided it wasn’t worth it or didn’t think there was a case for eminent domain here,” Mr. Berman said.

Some accounts suggest that no one realized the triangle existed until well after the subway had been finished, and Seventh Avenue South paved over. The Philadelphia Evening Public Ledger ran an article about the little lot in 1922. It said the city had demanded payment of property taxes in 1921 and that Frank Hess, the son of David M. Hess, said he had not been aware of the existence of “any such ‘lot.’”

“He went to New York,” The Evening Public Ledger reported, “and saw it — a piece scarcely large enough for the erection of a slot machine.”

The building that the smoke shop occupies had been built by then. It was a cigar store, and Frank Hess arranged for the owners to lease the triangle. The deal called for it to be marked so “the city might know it had not been dedicated to public purposes,” The Evening Public Ledger explained. “Had the piece been allowed to remain unmarked and unfenced, the city might have claimed it.”

So the plaque was laid, saying the triangle belonged to the Hess estate. The last six words mattered the most, at least to the Hesses: “Never been dedicated for public purposes.”

The Hess estate finally sold the triangle to the cigar store’s owners in the 1930s, for $100, about $1,781 in today’s dollars. At the time, the Hesses had been charging the store rent of “a couple of hundred dollars a year,” according to The New York Herald Tribune. The triangle has been a part of the cigar store’s lot ever since.

For all the times that the Hess triangle was in the newspapers (and, more recently, online) it did not get the spotlight the way a slightly larger but still small slice of the city did.

That sliver belonged to Brian G. Hughes, a “famous joker,” as the headline on his obituary described him when he died in 1924. He had also been the president of the Dollar Savings Bank in the Bronx and owner of a company that made paper boxes.

He said he would give the city the little piece of land he owned for use as a park.

He arranged for a ceremony to hand over the deed. He hired a band to entertain the crowd that showed up — all without saying exactly where the property was or how large it was. Meaning, how small.

“He solemnly turned over the deed to a two-by-four bit of property to a popeyed city official,” according to Ross Duff Whytock, who wrote about New York for a number of newspapers, including The Hartford Courant. He did not say where the plot was.

“No attempt has been made, so far as I can discover, to carry out Mr. Hughes’s injunctions that it be set out with trees, shrubs, flower beds, a bandstand and benches,” Mr. Whytock wrote. “In Manhattan it would hardly serve as a breathing space for a subway sardine.”

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