Shape of the tower
At the time the tower was built many people were shocked by its daring shape. Gustave Eiffel was criticised for the design and accused of trying to create something artistic, or inartistic according to the viewer, without regard to engineering. Eiffel and his engineers, as renowned bridge builders however, understood the importance of wind forces and knew that if they were going to build the tallest structure in the world they had to be certain it would withstand the wind. In an interview reported in the newspaper Le Temps, Eiffel said:
“ Now to what phenomenon did I give primary concern in designing the Tower? It was wind resistance. Well then! I hold that the curvature of the monument's four outer edges, which is as mathematical calculation dictated it should be (...) will give a great impression of strength and beauty, for it will reveal to the eyes of the observer the boldness of the design as a whole. ”
—translated from the French newspaper Le Temps of 14 February 1887
The shape of the tower was therefore determined by mathematical calculation involving wind resistance. Several theories of this mathematical calculation have been proposed over the years, the most recent is a nonlinear integral differential equation based on counterbalancing the wind pressure on any point on the tower with the tension between the construction elements at that point. That shape is exponential.
Since the beginning of the 20th century, the tower has been used for radio transmission. Until the 1950s, an occasionally modified set of antenna wires ran from the summit to anchors on the Avenue de Suffren and Champ de Mars. They were connected to long-wave transmitters in small bunkers; in 1909, a permanent underground radio centre was built near the south pillar and still exists today. On 20 November 1913 the Paris Observatory, using the Eiffel Tower as an antenna, exchanged sustained wireless signals with the United States Naval Observatory which used an antenna in Arlington, Virginia.
The object of the transmissions was to measure the difference in longitude between Paris and Washington, DC.
The tower has two restaurants: Altitude 95, on the first floor (95 m, 311 ft, above sea level); and the Jules Verne, an expensive gastronomical restaurant on the second floor, with a private lift. This restaurant has one star in the Michelin Red Guide. In January 2007 a new multi-Michelin star chef Alain Ducasse was brought in to run Jules Verne.
The uppermost observation deck, with a height of 275 metres, is the highest area of an architectural structure in the European Union open for the public.
The passenger lifts from ground level to the first level are operated by cables and pulleys driven by massive water-powered pistons. As they ascend the inclined arc of the legs, the elevator cabins tilt slightly, but with a slight jolt, every few seconds in order to keep the floor nearly level. The elevator works are on display and open to the public in a small museum located in one of the four tower bases, and waiting queues are much shorter than those for the tower ascent.
Lightning strikes the Eiffel Tower on 3 June 1902, at 9:20 P.M
On 10 September 1889 Thomas Edison visited the tower. He signed the guestbook with the following message—
“ To M Eiffel the Engineer the brave builder of so gigantic and original specimen of modern Engineering from one who has the greatest respect and admiration for all Engineers including the Great Engineer the Bon Dieu, Thomas Edison. ”
In 1902, the tower was struck by lightning (see photo below). 100 m (330 ft) of the top had to be reconstructed and the damaged lights illuminating the tower had to be replaced.
Father Theodor Wulf in 1910 took observations of radiant energy radiating at the top and bottom of the tower, discovering at the top more than was expected, and thereby detecting what are today known as cosmic rays. 
In 1925, the con artist Victor Lustig twice "sold" the tower for scrap metal.
In 1930, the tower lost the title of the world's tallest structure when the Chrysler Building was completed in New York City.
From 1925 to 1934, illuminated signs for Citroën adorned three of the tower's four sides, making it the tallest advertising space in the world at the time.
Upon the Nazi occupation of Paris in 1940, the lift cables were cut by the French so that Adolf Hitler would have to climb the steps to the summit. The parts to repair them were allegedly impossible to obtain because of the war, though they were working again within hours of the departure of the Nazis. In 1940 Nazi soldiers had to climb to the top to hoist the swastika, but the flag was so large it blew away just a few hours later, and it was replaced by a smaller one. Hitler chose to stay on the ground. A Frenchman scaled the tower during the German occupation to hang the French flag. In August 1944, when the Allies were nearing Paris, Hitler ordered General Dietrich von Choltitz, the military governor of Paris, to demolish the tower along with the rest of the city. Von Choltitz disobeyed the order.
On 3 January 1956, a fire damaged the top of the tower.
In 1957 the present radio antenna was added to the top.
In the 1980s an old restaurant and its supporting iron scaffolding midway up the tower was dismantled; it was purchased and reconstructed on St. Charles Avenue in New Orleans, Louisiana by entrepreneurs John Onorio and Daniel Bonnot, originally as the Tour Eiffel Restaurant, known more recently as the Red Room. The restaurant was re-assembled from 11,000 pieces that crossed the Atlantic in a 40-feet cargo container.
In 1985's James Bond action/adventure film A View to a Kill, Sir Roger Moore as James Bond chases May Day played by actress Grace Jones at the Eiffel Tower. She parachuted from the tower. The video of the film's theme, performed by the group Duran Duran, also included several scenes of the band staged on the tower.
On New Year's Eve 2000, the Eiffel Tower played host to Paris' Millennium Celebration. Fireworks exploded from the whole length of the tower in a spectacular display.
In 2000, flashing lights and four high-power searchlights were installed on the tower. Since then the light show has become a nightly event. The searchlights on top of the tower make it a beacon in Paris' night sky.
The tower received its 200,000,000th guest of all-time in 2002.
At 19:20 on 22 July 2003, a fire occurred at the top of the tower in the broadcasting equipment room. The entire tower was evacuated; the fire was extinguished after 40 minutes, and there were no reports of injuries.
Since 2004, the Eiffel Tower has hosted an ice skating rink on the first floor during the winter period. Skating is free in Paris.