[1] In 1791, the French Academy of Sciences chose to define the metre as one ten-millionth of the distance from the equator to the North or South Pole.
The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque.
The irregular and particular shape of the Earth smoothed to sea level is represented by a mathematical model called a geoid, which literally means "Earth-shaped".
Despite these issues, in 1793 France adopted this definition of the metre as its official unit of length based on provisional results from this expedition.
[2] When Carlos Ibáñez e Ibáñez de Ibero first president of both the International Geodetic Association and the International Committee for Weigths and Measures took part to the measurement of the West Europe-Africa Meridian-arc, mathematicians like Legendre and Gauss had developed new methods for processing data, including the "least squares method" which allowed to compare experimental data tainted with observational errors to a mathematical model.