Spherical Earth

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Medieval artistic representation of a spherical Earth – with compartments representing earth, air, and water (c. 1400).

The earliest reliably documented mention of the spherical Earth concept dates from around the 6th century BC when it appeared in ancient Greek philosophy[1][2] but remained a matter of speculation until the 3rd century BC, when Hellenistic astronomy established the spherical shape of the Earth as a physical given. The paradigm was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages.[3][4][5][6] A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's expedition's circumnavigation (1519–1522).[7]


The realization that the figure of the Earth is more accurately described as an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia. In the early 19th century, the flattening of the earth ellipsoid was determined to be of the order of 1/300 (Delambre, Everest), the modern value as determined by the US DoD World Geodetic System since the 1960s is close to 1/298.25.[9]



Though the earliest written mention of a spherical Earth comes from ancient Greek sources, there is no account of how the sphericity of the Earth was discovered.[10] A plausible explanation is that it was "the experience of travellers that suggested such an explanation for the variation in the observable altitude and the change in the area of circumpolar stars, a change that was quite drastic between Greek settlements"[attribution needed] around the eastern Mediterranean Sea, particularly those between the Nile Delta and Crimea.[11]

In The Histories, written 431–425 BC, Herodotus cast doubt on a report of the Sun observed shining from the north. He stated that the phenomenon was observed during a circumnavigation of Africa undertaken by Phoenician explorers employed by Egyptian pharaoh Necho II c. 610–595 BC (The Histories, 4.42) who claimed to have had the Sun on their right when circumnavigating in a clockwise direction. To modern historians, these details confirm the truth of the Phoenicians' report and even open the possibility that the Phoenicians knew about the spherical model. However, nothing certain about their knowledge of geography and navigation has survived.[12]

The Hebrew Bible imagined a three-part world, with the heavens (shamayim) above, earth (eres) in the middle, and the underworld (sheol) below.[13] After the 4th century BCE this was gradually replaced by a Greek scientific cosmology of a spherical earth surrounded by multiple concentric heavens.[14]


Early Greek philosophers alluded to a spherical Earth, though with some ambiguity.[15] Pythagoras (6th century BC) was among those said to have originated the idea, but this might reflect the ancient Greek practice of ascribing every discovery to one or another of their ancient wise men.[10] Some idea of the sphericity of the Earth seems to have been known to both Parmenides and Empedocles in the 5th century BC,[16] and although the idea cannot reliably be ascribed to Pythagoras,[17] it might nevertheless have been formulated in the Pythagorean school in the 5th century BC[10][16] although some disagree.[18] After the 5th century BC, no Greek writer of repute thought the world was anything but round.[15]


Plato (427–347 BC) travelled to southern Italy to study Pythagorean mathematics. When he returned to Athens and established his school, Plato also taught his students that Earth was a sphere, though he offered no justifications. "My conviction is that the Earth is a round body in the centre of the heavens, and therefore has no need of air or of any similar force to be a support".[19] If man could soar high above the clouds, Earth would resemble "one of those balls which have leather coverings in twelve pieces, and is decked with various colours, of which the colours used by painters on Earth are in a manner samples."[20] In Timaeus, his one work that was available throughout the Middle Ages in Latin, we read that the Creator "made the world in the form of a globe, round as from a lathe, having its extremes in every direction equidistant from the centre, the most perfect and the most like itself of all figures",[21] though the word "world" here refers to the heavens.

Round Earth umbra during the August 2008 lunar eclipse





Hellenistic astronomy[edit]


In proposition 2 of the First Book of his treatise "On floating bodies," Archimedes demonstrates that "The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the earth,".[23] Subsequently, in propositions 8 and 9 of the same work, he assumes the result of proposition 2 that the Earth is a sphere and that the surface of a fluid on it is a sphere centered on the center of the Earth.[24]


Eratosthenes, a Greek astronomer from Hellenistic Libya (276–194 BC), estimated Earth's circumference around 240 BC. He had heard that in Syene the Sun was directly overhead at the summer solstice whereas in Alexandria it still cast a shadow. Using the differing angles the shadows made as the basis of his trigonometric calculations he estimated a circumference of around 250,000 stades, the length of a 'stade' is not precisely known, but Eratosthenes's figure only has an error of around five to fifteen percent.[25][26][27] Eratosthenes used rough estimates and round numbers, but depending on the length of the stadion, his result is within a margin of between 2% and 20% of the actual meridional circumference, 40,008 kilometres (24,860 mi). Note that Eratosthenes could only measure the circumference of the Earth by assuming that the distance to the Sun is so great that the rays of sunlight are practically parallel.[28]

Seventeen hundred years after Eratosthenes, Christopher Columbus studied Eratosthenes's findings before sailing west for the Indies. However, ultimately he rejected Eratosthenes in favour of other maps and arguments that interpreted Earth's circumference to be a third smaller than reality. If, instead, Columbus had accepted Eratosthenes findings, then he may have never gone west, since he didn't have the supplies or funding needed for the much longer voyage.[29]

Seleucus of Seleucia




Roman Empire[edit]

From its Greek origins, the idea of a spherical earth, along with much of Greek astronomical thought, slowly spread across the globe and ultimately became the adopted view in all major astronomical traditions.[3][4][5][6]


When a ship is at the horizon, its lower part is obscured by the Earth's curvature. This was one of the first arguments favouring a round-Earth model.

It has been suggested that seafarers probably provided the first observational evidence that the Earth was not flat, based on observations of the horizon, this argument was put forward by the geographer Strabo (c. 64 BC – 24 AD), who suggested that the spherical shape of the Earth was probably known to seafarers around the Mediterranean Sea since at least the time of Homer,[31] citing a line from the Odyssey[32] as indicating that the poet Homer knew of this as early as the 7th or 8th century BC. Strabo cited various phenomena observed at sea as suggesting that the Earth was spherical. He observed that elevated lights or areas of land were visible to sailors at greater distances than those less elevated, and stated that the curvature of the sea was obviously responsible for this.[33]

Claudius Ptolemy





Late Antiquity




Greek ethnographer Megasthenes, c. 300 BC, has been interpreted as stating that the contemporary Brahmans believed in a spherical earth as the center of the universe.[38] With the spread of Greek culture in the east, Hellenistic astronomy filtered eastwards to ancient India where its profound influence became apparent in the early centuries AD.[39] The Greek concept of an Earth surrounded by the spheres of the planets and that of the fixed stars, vehemently supported by astronomers like Varahamihir and Brahmagupta, strengthened the astronomical principles, some ideas were found possible to preserve, although in altered form.[39][40]


Middle Ages[edit]

Knowledge of the sphericity of the Earth survived into the medieval corpus of knowledge by direct transmission of the texts of Greek antiquity (Aristotle), and via authors such as Isidore of Seville and Beda Venerabilis. It became increasingly traceable with the rise of scholasticism and medieval learning.[30] Spread of this knowledge beyond the immediate sphere of Greco-Roman scholarship was necessarily gradual, associated with the pace of Christianisation of Europe, for example, the first evidence of knowledge of the spherical shape of the Earth in Scandinavia is a 12th-century Old Icelandic translation of Elucidarius.[43]

A non-exhaustive list of more than a hundred Latin and vernacular writers from Late Antiquity and the Middle Ages who were aware that the earth was spherical has been compiled by Reinhard Krüger, professor for Romance literature at the University of Stuttgart.[30]

Early Medieval world[edit]

Isidore of Seville

Bishop Isidore of Seville (560–636) taught in his widely read encyclopedia, The Etymologies, that the Earth was "round".[44] The bishop's confusing exposition and choice of imprecise Latin terms have divided scholarly opinion on whether he meant a sphere or a disk or even whether he meant anything specific.[45] Notable recent scholars claim that he taught a spherical earth.[46] Isidore did not admit the possibility of people dwelling at the antipodes, considering them as legendary[47] and noting that there was no evidence for their existence.[48]

Bede the Venerable



Anania Shirakatsi


Islamic astronomy[edit]

Islamic astronomy was developed on the basis of a spherical earth inherited from Hellenistic astronomy.[53] The Islamic theoretical framework largely relied on the fundamental contributions of Aristotle (De caelo) and Ptolemy (Almagest), both of whom worked from the premise that the earth was spherical and at the centre of the universe (geocentric model).[53]

Early Islamic scholars recognized earth's sphericity,[54] leading Muslim mathematicians to develop spherical trigonometry[55] in order to further mensuration and to calculate the distance and direction from any given point on the Earth to Mecca. This determined the Qibla, or Muslim direction of prayer.


Around 830 AD, Caliph Al-Ma'mun commissioned a group of Muslim astronomers and geographers to measure the distance from Tadmur (Palmyra) to Raqqa in modern Syria. They found the cities to be separated by one degree of latitude and the meridian arc distance between them to be 66​23 miles and thus calculated the Earth's circumference to be 24,000 miles.[56]

Another estimate given by his astronomers was 56​23 Arabic miles (111.8 km) per degree, which corresponds to a circumference of 40,248 km, very close to the currently modern values of 111.3 km per degree and 40,068 km circumference, respectively.[57]

Ibn Hazm

Andalusian polymath Ibn Hazm stated that the proof of the Earth's sphericity "is that the Sun is always vertical to a particular spot on Earth".[58]


Al-Farghānī (Latinized as Alfraganus) was a Persian astronomer of the 9th century involved in measuring the diameter of the Earth, and commissioned by Al-Ma'mun. His estimate given above for a degree (56​23 Arabic miles) was much more accurate than the 60​23 Roman miles (89.7 km) given by Ptolemy. Christopher Columbus uncritically used Alfraganus's figure as if it were in Roman miles instead of in Arabic miles, in order to prove a smaller size of the Earth than that propounded by Ptolemy.[59]

Biruni's Method for calculation of Earth's radius

Abu Rayhan Biruni (973–1048) used a new method to accurately compute the Earth's circumference, by which he arrived at a value that was close to modern values for the Earth's circumference.[60] His estimate of 6,339.6 km for the Earth radius was only 31.4 km less than the modern mean value of 6,371.0 km.[61] In contrast to his predecessors, who measured the Earth's circumference by sighting the Sun simultaneously from two different locations, Biruni developed a new method of using trigonometric calculations based on the angle between a plain and mountain top. This yielded more accurate measurements of the Earth's circumference and made it possible for a single person to measure it from a single location.[62][63] Biruni's method was intended to avoid "walking across hot, dusty deserts," and the idea came to him when he was on top of a tall mountain in India, from the top of the mountain, he sighted the angle to the horizon which, along with the mountain's height (which he calculated beforehand), allowed him to calculate the curvature of the Earth.[64][65] He also made use of algebra to formulate trigonometric equations and used the astrolabe to measure angles.[66]


"Important contributions to geodesy and geography were also made by 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."[67]


Muslim scholars who held to the round Earth theory used it for a quintessentially Islamic purpose: to calculate the distance and direction from any given point on the Earth to Mecca,[68] this determined the Qibla, or Muslim direction of prayer.

A terrestrial globe (Kura-i-ard) was among the presents sent by the Persian Muslim astronomer Jamal-al-Din to Kublai Khan's Chinese court in 1267. It was made of wood on which "seven parts of water are represented in green, three parts of land in white, with rivers, lakes etc."[69] Ho Peng Yoke remarks that "it did not seem to have any general appeal to the Chinese in those days".[70]

High and late medieval Europe[edit]





Many scholastic commentators on Aristotle's On the Heavens and Sacrobosco's Treatise on the Sphere unanimously agreed that the earth is spherical or round.[74] Grant observes that no author who had studied at a medieval university thought that the earth was flat.[75]




Early Modern period[edit]

Circumnavigation of the globe[edit]


The first direct demonstration of Earth's sphericity came in the form of the first circumnavigation in history, an expedition captained by Portuguese explorer Ferdinand Magellan,[76] the expedition was financed by the Spanish Crown. On August 10, 1519, the five ships under Magellan's command departed from Seville, they crossed the Atlantic Ocean, passed through what is now called the Strait of Magellan, crossed the Pacific, and arrived in Cebu, where Magellan was killed by Philippine natives in a battle. His second in command, the Spaniard Juan Sebastián Elcano, continued the expedition and, on September 6, 1522, arrived at Seville, completing the circumnavigation. Charles I of Spain, in recognition of his feat, gave Elcano a coat of arms with the motto Primus circumdedisti me (in Latin, "You went around me first").[77]

A circumnavigation alone does not prove that the earth is spherical, it could be cylindric or irregularly globular or one of many other shapes. Still, combined with trigonometric evidence of the form used by Eratosthenes 1,700 years prior, the Magellan expedition removed any reasonable doubt in educated circles in Europe,[78] the Transglobe Expedition (1979–1982) was the first expedition to make a circumpolar circumnavigation, traveling the world "vertically" traversing both of the poles of rotation using only surface transport.

Ming China[edit]

In the 17th century, the idea of a spherical Earth, now considerably advanced by Western astronomy, ultimately spread to Ming China, when Jesuit missionaries, who held high positions as astronomers at the imperial court, successfully challenged the Chinese belief that the Earth was flat and square.[79][80][81]

The Ge zhi cao (格致草) treatise of Xiong Mingyu (熊明遇) published in 1648 showed a printed picture of the Earth as a spherical globe, with the text stating that "the round Earth certainly has no square corners",[82] the text also pointed out that sailing ships could return to their port of origin after circumnavigating the waters of the Earth.[82]



Although mainstream Chinese science until the 17th century held the view that the earth was flat, square, and enveloped by the celestial sphere, this idea was criticized by the Jin-dynasty scholar Yu Xi (fl. 307–345), who suggested that the Earth could be either square or round, in accordance with the shape of the heavens.[83] The Yuan-dynasty mathematician Li Ye (c. 1192–1279) firmly argued that the Earth was spherical, just like the shape of the heavens only smaller, since a square Earth would hinder the movement of the heavens and celestial bodies in his estimation.[84] The 17th-century Ge zhi cao treatise also used the same terminology to describe the shape of the Earth that the Eastern-Han scholar Zhang Heng (78–139 AD) had used to describe the shape of the sun and moon (i.e. that the former was as round as a crossbow bullet, and the latter was the shape of a ball).[85]







See also[edit]


  2. ^ Cormack, Lesley B. (2015), "That before Columbus, geographers and other educated people thought the Earth was flat", in Numbers, Ronald L.; Kampourakis, Kostas, Newton's Apple and Other Myths about Science, Harvard University Press, pp. 16–22, ISBN 9780674915473 
  8. ^ Otto E. Neugebauer (1975). "A History of Ancient Mathematical Astronomy". Birkhäuser: 577. ISBN 3-540-06995-X. 
  11. ^ Otto E. Neugebauer (1975). "A History of Ancient Mathematical Astronomy". Birkhäuser: 575–6. ISBN 3-540-06995-X. 
  12. ^ Friis, Herman Ralph (1967). The Pacific Basin: A History of Its Geographical Exploration. American Geographical Society. p. 19. 
  13. ^ Wright, J. Edward (2002). The Early History of Heaven. Oxford University Press. p. 54. ISBN 9780195348491. 
  14. ^ Aune, David E. (2003). "Cosmology". Westminster Dictionary of the New Testament and Early Christian Literature. Westminster John Knox Press. p. 119. ISBN 9780664219178. 
  17. ^ Huffman, Carl. "Pythagoras". In Zalta, Edward N. Stanford Encyclopedia of Philosophy. 
  18. ^ Burch, George Bosworth (1954). "The Counter-Earth". Osiris. 11: 267–294. doi:10.1086/368583. JSTOR 301675. 
  19. ^ Plato. Phaedo. p. 108. 
  20. ^ Plato. Phaedo. p. 110b. 
  21. ^ Plato. Timaeus. p. 33. 
  23. ^ "The works of Archimedes". Translated by Heath, T. L. Cambridge: Cambridge University Press. 1897. p. 254. Retrieved 13 November 2017. 
  24. ^ Rorres, Chris (2016), "Archimedes' floating bodies on a spherical Earth", American Journal of Physics, 84 (61): 61–70, doi:10.1119/1.4934660 
  28. ^ Lloyd, G. E. R. (1996), Adversaries and Authorities: Investigations into ancient Greek and Chinese science, Cambridge: Cambridge University Press, p. 60, ISBN 0-521-55695-3 
  29. ^ "When Our Round Earth Was First Measured". The Science Teacher. National Science Teachers Association. 83 (6): 10. 
  36. ^ Calcidius (1962), Klibansky, Raymond, ed., Timaeus a Calcidio translatus commentarioque instructus, Corpus Platonicum Medii Aevi, Plato Latinus, 4, Leiden / London: Brill / Warburg Institute, pp. 141–144, ISBN 9780854810529 
  37. ^ Klaus Anselm Vogel, "Sphaera terrae – das mittelalterliche Bild der Erde und die kosmographische Revolution," PhD dissertation Georg-August-Universität Göttingen, 1995, p. 19.
  38. ^ E. At. Schwanbeck (1877). Ancient India as described by Megasthenês and Arrian; being a translation of the fragments of the Indika of Megasthenês collected by Dr. Schwanbeck, and of the first part of the Indika of Arrian. p. 101. 
  43. ^ Rudolf Simek, Altnordische Kosmographie, Berlin, 1990, p. 102.
  44. ^ Isidore, Etymologiae, XIV.ii.1 [3].
  46. ^ Wesley M. Stevens, "The Figure of the Earth in Isidore's 'De natura rerum," Isis, 71(1980): 268–277.
  47. ^ Isidore, Etymologiae, XIV.v.17 [4].
  48. ^ Isidore, Etymologiae, IX.ii.133 [5].
  58. ^ "How Islamic inventors changed the world". The Independent. March 11, 2006.
  63. ^ Behnaz Savizi (2007). "Applicable Problems in History of Mathematics: Practical Examples for the Classroom". Teaching Mathematics and Its Applications. Oxford University Press. 26 (1): 45–50. doi:10.1093/teamat/hrl009. Retrieved 2010-02-21. 
  64. ^ Mercier, Raymond P. (1992). "Geodesy". In J. B. Harley; David Woodward. The History of Cartography: Vol. 2.1, Cartography in the traditional Islamic and South Asian societies. Chicago & London: University of Chicago Press. pp. 182–184. ISBN 978-0-226-31635-2. 
  65. ^ Beatrice Lumpkin (1997). "Geometry Activities from Many Cultures". Walch Publishing: 60 & 112–3. ISBN 0-8251-3285-1.  [3]
  66. ^ Jim Al-Khalili, The Empire of Reason 2/6 (Science and Islam – Episode 2 of 3) on YouTube, BBC
  69. ^ Needham 1959, p. 374
  71. ^ Hildegard of Bingen, Liber divinorum operum
  73. ^ The Sphere of Sacrobosco. trans. Lynn Thorndike. 1949. 
  74. ^ Grant, Edward (1996), Planets, Stars, & Orbs: The Medieval Cosmos, 1200–1687, Cambridge: Cambridge University Press, pp. 620–622, 737–738, ISBN 0-521-56509-X 
  78. ^ RK Jain. ICSE Geography IX. Ratna Sagar. p. 7. 
  79. ^ a b "Jean-Claude Martzloff, "Space and Time in Chinese Texts of Astronomy and of Mathematical Astronomy in the Seventeenth and Eighteenth Centuries", Chinese Science 11 (1993–94): 66–92 (69)" (PDF). Archived from the original (PDF) on 2009-03-05. 
  83. ^ Needham, Joseph; Wang, Ling. (1995) [1959]. Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth, vol. 3, reprint edition. Cambridge: Cambridge University Press. ISBN 0-521-05801-5, pp. 220, 498–499.

Further reading[edit]

External links[edit]

Media related to Spherical Earth at Wikimedia Commons