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Determination of the Earth's Circumference through Mathematics
by Meam Wye
During the medieval Islamic Civilization , 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 Caliph Al-mamun. In 820 AD, Al-mamun 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 km (circumference if measured around the equator).
Al-biruni descibed the above incident in his astronomical encyclopaedia 'Al-Qanun Al-Musudi'. He devised a new method to detrmine circumference which he described in his work 'Kitab Tahdid al-Amakin' i.e.Book of Determination of the Location (thanks to Hicham Maged [http://blog.hichamaged.net] for providing the translation in the comment below) as:
"Here is another method for the determination of the circumference of the earth. It does not require walking in deserts."
Al-biruni's method used the following trignometric equation to determine the radius of the earth that required observing the distant horizon from a mountain peak.
R= h cos d /(1-cos d)
h: Height of the mountain
d: Angle of dip
The details of this method are present in his book 'Kitab Tahdid al-Amakin'. He had constructed his own astrolobe to measure the height 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-Birunis' method can be considered as one of the earliest examples of application of trignometry to real-world problems. He is, therefore, regarded as the 'Father of Geodesy' (Geodesy ~ Mathematical Geography).
Professor John J. O'Connor and Edmund F. Robertson in 'The MacTutor History 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 km, a value not 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."
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October 18, 2009 3:48 PM
Another fine, informative post, Meam. And I love this quote, showing al-Biruni's sense of humor:
"Here is another method for the determination of the circumference of the earth. It does not require walking in deserts."
It made me chuckle.
October 19, 2009 10:49 PM
I wonder, how's today? If not for the great minds of these geniuses...
Thanks for sharing this.
BTW, I have a blog award for you, please pick it up!
XO
October 20, 2009 6:22 AM
The circumference of the Earth...I wonder if this came before the knowledge of the circumference of a circle? Still it's rather interesting how these things come about. It's more of a curiosity of the person designing the formula to complete the calculation. It seems like everything in history that was discovered is all based on someone's curiosity!
October 20, 2009 1:40 PM
This is such a fascinating blog. Thank you so much for undertaking the assemblage, writing and sharing of this knowledge.
timethief
October 22, 2009 9:32 PM
Meam, it's very interesting how things ends when people implement the knowlegde they have. al-Biruni was using the advanced scientific methods that was later implemented by other european scientists.
As for his book "Kitab Tahdid al-Amakin" the title can be transtlated in English as "Book of Determination of the Location" if people want to know it's meaning!
October 23, 2009 4:18 AM
@George Polley: I also found it quite funny :) Thanks.
October 23, 2009 4:19 AM
@butterfly: I feel honored...thank you!
October 23, 2009 4:22 AM
@Frank: Interesting point. Circumference of circle was determined, centuries before al-biruni, by the greek mathematician Archimedes (born in 287 BC).
October 23, 2009 4:24 AM
@timethief: Thank you for stopping by and for your positive feedback.
October 23, 2009 4:28 AM
@Hicham Maged: I am so delighted to learn the English translation of the Arabic title of the book as I couldn't find it online. Thank you so much for this very valuable feedback. I'll update the post with the English title.
October 25, 2009 1:07 AM
wonderful post, also shows that their was a time when some brilliant brains of Muslims were curious about this universe and spend their lives to solve the puzzles of god,may be they were free of these fears we are facing today fears of unavailability of basic needs and security and may be they they were free of endless lust of material .
October 27, 2009 3:20 AM
Baili, I feel that the absence of love of gaining knowledge is the major reason for the problems that any individual (and in turn the society) faces. Nothing can be worse than citing other factors instead of taking responsibility for whatever problems one faces. I agree that this 'endless lust of material' affects the creativity of human mind. Thank you for sharing your views.
November 1, 2009 10:27 AM
Hi Meam it now appears however that the Ancient Egyptians and whoever built Stonehenge may also have known the circumference of the Earth.Recent studies by archeoastronomers suggest that the location and precise dimensions of these structures reflect a sophistication in mathematics not believed possible until Pythagoras and Euclid.A fascinating post.simon
November 1, 2009 10:56 AM
As mentioned in this post, the ancients Greeks and Indians did determine the circumference of earth. However, al-biruni's contribution is using trignometry, for the first time, to determine radius of the earth that did not require the ancient method of sighting of the sun from multiple directions. With regards to mathematics, ancient civilizations as well as the medieval Islamic civilization, each made their own great achievements in this area. More on the contributions in mathematics in subsequent posts. Thanks for your feedback.
November 4, 2009 5:37 AM
Like others, I'm fascinated by the desire and curiosity that drives people to make these kind of discoveries. It seems that everything new in the world derives from an obsession.
November 8, 2009 7:47 AM
Quite true. The question now arises whether necessity is the mother of invention or is it the curiosity/desire for new things.......