Tuesday, September 27, 2011

Early attempts to measure the earth's circumference

Abu Rayhan Muhammad ibn Ahmad Biruni, often referred to as al-Biruni( 973-1048 ), was the first scientist to provide a mathematical solution for determining the circumference of the earth.

Prior to al-Biruni, the first successful attempt to determine the circumference of earth was carried out in the early 9th century on the desire of Khalifah al-Makmun,. In 820 A.D., al-Makmun sent a team of astronomers in the desert of Sinjar ( in Iraq ) that performed the survey and estimated that one degree of earth was equivalent to 56 2/3 Arab miles. Conversion of this value gives the circumference of earth as 39,986 km ... quite close to the modern value of 40,075 (circumference if measured around the equator).

Al-Biruni described the above incident in his astronomical encyclopaedia 'al-Qanuni al-Masudi'. He devised a new method to determine circumference which he described in his work 'Kitab Tahdid al-Amakin' ( Book of Determining the Locations) in which he described :

"Here is another method to determine the circumference of the earth. It does not require walking in deserts."

Al-Biruni's method used the following trigonometric equation to determine the radius of the earth and required observing the distant horizon from a mountain peak.

R = h cos d / (1-cos d)

R : Radius of the earth
h : Height of the mountain
d : Angle of the dip

The details of this method are present in his book 'Kitab Tahdid al-Amakin'. He had constructed his own astrolabe to measure the heights of mountains. Al-Biruni found the radius of the earth to be 6,339.9 km. The circumference, according to his method, is 39,835 km quite close to the present accepted value.

Al-Biruni's method can be considered as one of the earliest examples of application of trigonometry to real-world problems. He is, therefore, regarded as the 'Father of Geodesy'.

Professor John J. O'connor and Edmund F. Robertson in 'The MacTutor Histoy of Mathematics Archive':

"Important contributions to geodesy and geography were also made by al-Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6, a value cannot obtained in the West until the 16th century. His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge."


http://www.shininghistory.com/2009/10/determination-of-earths-circumference.html

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