The Singer Building (at Liberty Street and Broadway in Manhattan) was the tallest building in the world when the 45-story structure opened in 1909. The building was named after the Singer Manufacturing Company, maker of the Singer sewing machine. The building was demolished in 1967, the tallest building to be peacefully demolished. (The World Trade Center towers were destroyed by terrorism in 2001 and are the tallest buildings ever to be destroyed.)
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As early as 1907 (before the building was completed), the Singer Building was dubbed the “Singerhorn,” after the Matterhorn mountain in the Alps. An article in the December 23, 1907 New York (NY) Sun newspaper described how the ‘Singerhorn” would be climbed.
     
 
Wikipedia: Singer Building
The Singer Building at Liberty Street and Broadway in Manhattan, New York, was an office building completed in 1908 as the headquarters of the Singer Manufacturing Company.
 
The building’s architect, Ernest Flagg, was a supporter of height limitations and restrictive zoning, and showed his solution to tall-building crowding with the Singer’s set-back design. The 12-story base of the building filled an entire blockfront, while the tower above was relatively narrow. The tower floors were squares only 65 feet (20 m) on a side.
 
At 612 feet (187 m) above grade, the Singer Building was the tallest building in the world from its completion until the completion in 1909 of the Metropolitan Life Insurance Company Tower on Madison Avenue, again in Manhattan.
 
In 1968, the building, considered to be functionally obsolete, was demolished in order to make way for the U.S. Steel Building (currently known as One Liberty Plaza). At the time, it was the tallest building ever to be destroyed. This record has been surpassed twice since: once when the Avala TV Tower in Serbia was destroyed during a NATO bombing raid in 1999 and again by the September 11, 2001 collapse of the nearby World Trade Center. It is still the tallest building ever peacefully demolished.
 
Wikipedia: Matterhorn
The Matterhorn (German), Monte Cervino (Italian) or Mont Cervin (French), is a mountain in the Pennine Alps on the border between Switzerland and Italy. Its summit is 4,478 metres (14,692 ft) high, making it one of the highest peaks in the Alps. The four steep faces, rising above the surrounding glaciers, indicate the four compass points. The mountain overlooks the town of Zermatt in the canton of Valais to north-east and Breuil-Cervinia in the Aosta Valley to the south. The Theodul Pass, located at the eastern base of the peak, is the lowest passage between its north and south side.
 
Chronicling America
23 December 1907, New York (NY) Sun, pg. 5, col. 3:
SCALING THE SINGERHORN
SPORT IN THE HIGHLANDS FOR
THE ALPINE CLIMBERS.
Up Into the Clouds With Alpenstock and
So Forth—Hunting the Chamois on the
Eleventh Floor, With Good Results
—Popular Activity of Lower Broadway.
Plans are now being made by the sporting and athletic element in Wall Street for the opening of the mountain climbing season. The alpenstocks, the life lines and the Tyrolese hats are being refurbished up, and as soon as the Singer building opens up the climbing season will begin.
(...)
Climbing the Singerhorn is likely to be as popular a sport as ever the Alpine climber encountered.
 
Google Books
2 January 1909, The Living Age, “Towered Cities,” pg. 45, col. 2:
The great Singer building in New York—nicknamed the Singerhorn—was finished not long ago. It has forty-five stories. This is a notable increase of height on the Park Row Syndicate building, which a few years since astounded the world with its twenty-six stories.