For a period of time during the 1880's, a scientist named Giovanni Schiaparelli observed and recorded visible features of Mercury and propounded that the planet must be tidally locked to the Sun, meaning that the planet never rotates on its axis. However, in 1962, radio astronomers observed that the dark side of Mercury was unusually warm. This meant that had the planet been tidally locked, the dark side that always faces away from the Sun would exhibit much colder temperatures. But since the dark side was too warm, it meant that Mercury is not tidally locked like Schiaparelli had once said.
With this knowledge, scientists began to investigate Mercury's rotational period. At first, Mercury was thought to have an orbital/rotational resonance with a ratio of 1:1, but in 1965, Pettengill and Dyce showed this to be false in 1965 by Doppler radar observations. It was determined that Mercury's period of rotation based on radar to be 59 plus or minus 5 days. In 1971, Goldstein performed a more careful experiment and refined the value to be 58.65 plus or minus 0.25 days using radar observations. And finally, the Mariner 10 spacecraft provided the most accurate measurement of Mercury's rotational period: 58.646 plus or minus 0.005 days.
Surprisingly, Mercury rotates three times in two of its years. It is the only planet in our solar system having an orbital/rotational resonance ratio of 1:1. Because of this 3:2 ratio resonance, a day on Mercury is 176 Earth days long.