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

The concept of a spherical Earth was espoused by Pythagoras apparently on aesthetic grounds, as he also held all other celestial bodies to be spherical. It replaced earlier beliefs in a flat Earth: In early Mesopotamian thought, the world was portrayed as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of Anaximander and Hecataeus. Other speculations as to the shape of Earth include a seven-layered ziggurat or cosmic mountain, alluded to in the Avesta and ancient Persian writings (see seven climes). In fact, the Earth is reasonably well-approximated by an oblate spheroid. Image File history File links John_Gower_world_Vox_Clamantis_detail. ... Image File history File links John_Gower_world_Vox_Clamantis_detail. ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times. ... This article is about Earth as a planet. ... Look up air in Wiktionary, the free dictionary. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... For other uses, see sphere (disambiguation). ... This article is about Earth as a planet. ... Pythagoras of Samos (Greek: ; between 580 and 572 BC–between 500 and 490 BC) was an Ionian (Greek) philosopher[1] and founder of the religious movement called Pythagoreanism. ... 15th century adaptation of a T-O map. ... Anaximander Possibly what Anaximanders map looked like Anaximander (Greek: Αναξίμανδρος)(c. ... Hecataeus (c. ... Dur-Untash, or Choqa Zanbil, built in 13th century BC by Untash Napirisha and located near Susa, Iran is one of the worlds best-preserved ziggurats. ... Sumeru Mount Meru (Mythology) Karshvar Purgatorio Axis mundi Category: ... See Avesta Municipality for the Swedish town Yasna 28. ... The Persian Empire was a series of historical empires that ruled over the Iranian plateau, the old Persian homeland, and beyond in Western Asia, Central Asia and the Caucasus. ... The seven climes (klima, plural klimata, meaning inclination, referring to the angle between the axis of the celestial sphere and the horizon) was a notion of dividing the Earth into zones in Classical Antiquity. ... An oblate spheroid is ellipsoid having a shorter axis and two equal longer axes. ...

Early development

Yajnavalkya

Yajnavalkya (c. 9th–8th century BCE) recognized that the Earth is spherical in his astronomical text Shatapatha Brahmana. This is also recognized in another Vedic Sanskrit text Aitareya Brahmana composed around the same time, and in a later Sanskrit commentary Vishnu Purana.^{[1][2][3][4][5]} Sage Yajnavalkya (याज्ञवल्क्य) of Mithila advanced a 95-year cycle to synchronize the motions of the sun and the moon. ... (10th century BC - 9th century BC - 8th century BC - other centuries) (900s BC - 890s BC - 880s BC - 870s BC - 860s BC - 850s BC - 840s BC - 830s BC - 820s BC - 810s BC - 800s BC - other decades) (2nd millennium BC - 1st millennium BC - 1st millennium AD) Events Kingdom of Kush (900 BC... (9th century BC - 8th century BC - 7th century BC - other centuries) (800s BC - 790s BC - 780s BC - 770s BC - 760s BC - 750s BC - 740s BC - 730s BC - 720s BC - 710s BC - 700s BC - other decades) (2nd millennium BC - 1st millennium BC - 1st millennium AD) Events Golden age in Armenia Assyria... Shatapatha Brahmana (Brahmana of one-hundred paths) is one of the prose texts describing the Vedic ritual. ... Vedic Sanskrit is the language of the Vedas, which are the earliest sacred texts of India,. The Vedas were first passed down orally and therefore have no known date. ... The Aitareya Brahmana is the Brahmana associated with the Rigveda in the Shakala school. ... The Sanskrit language ( , for short ) is a classical language of India, a liturgical language of Hinduism, Buddhism, Sikhism, and Jainism, and one of the 23 official languages of India. ... The Vishnu Purana is one of the oldest of the Puranas (dating to maybe the 5th century), containing some 23,000 shlokas, presented as a dialogue between Parasara with his disciple Maitreya. ...

Pythagoras

Pythagoras (b. 570 BCE) found harmony in the universe and sought to explain it. He reasoned that Earth and the other planets must be spheres, since the most harmonious geometric form was a circle. Pythagoras of Samos (Greek: ; between 580 and 572 BC–between 500 and 490 BC) was an Ionian (Greek) philosopher[1] and founder of the religious movement called Pythagoreanism. ... Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Theaetetus dealing with spatial relationships. ... Circle illustration This article is about the shape and mathematical concept of circle. ...

Plato

Plato (427 BCE - 347 BCE) 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. If man could soar high above the clouds, Earth would resemble "a ball made of twelve pieces of leather, variegated, a patchwork of colours." PLATO was one of the first generalized Computer assisted instruction systems, originally built by the University of Illinois (U of I) and later taken over by Control Data Corporation (CDC), who provided the machines it ran on. ... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 470s BC 460s BC 450s BC 440s BC 430s BC - 420s BC - 410s BC 400s BC 390s BC 380s BC 370s BC Years: 432 BC 431 BC 430 BC 429 BC 428 BC - 427 BC - 426 BC 425 BC... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 390s BC 380s BC 370s BC 360s BC 350s BC - 340s BC - 330s BC 320s BC 310s BC 300s BC 290s BC 352 BC 351 BC 350 BC 349 BC 348 BC 347 BC 346 BC 345 BC 344... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Athens (Ancient Greek: αἱ Ἀθῆναι (plural), evolving into the modern Αθήναι in Greek until recently, and Αθήνα nowadays (IPA ); is both the largest and the capital city of Greece, located in the Attica periphery. ...

Aristotle

When a ship is at the horizon its lower part is invisible due to Earth's curvature. This was one of the first arguments favoring a round-earth model.

Aristotle (384 BCE - 322 BCE) was Plato's prize student and "the mind of the school." Aristotle observed "there are stars seen in Egypt and [...] Cyprus which are not seen in the northerly regions." Since this could only happen on a curved surface, he too believed Earth was a sphere "of no great size, for otherwise the effect of so slight a change of place would not be quickly apparent." (De caelo, 298a2-10) Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Aristotle (Greek: Aristotélēs) (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 430s BC 420s BC 410s BC 400s BC 390s BC - 380s BC - 370s BC 360s BC 350s BC 340s BC 330s BC Years: 389 BC 388 BC 387 BC 386 BC 385 BC - 384 BC - 383 BC 382 BC... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 370s BC 360s BC 350s BC 340s BC 330s BC - 320s BC - 310s BC 300s BC 290s BC 280s BC 270s BC 327 BC 326 BC 325 BC 324 BC 323 BC - 322 BC - 321 BC 320 BC 319... STARS can mean: Shock Trauma Air Rescue Society Special Tactics And Rescue Service, a fictional task force that appears in Capcoms Resident Evil video game franchise. ...

Aristotle provided physical and observational arguments supporting the idea of a spherical Earth:

• Every portion of the earth tends toward the center until by compression and convergence they form a sphere. (De caelo, 297a9-21)
• Travelers going south see southern constellations rise higher above the horizon; and
• The shadow of Earth on the Moon during a lunar eclipse is round.(De caelo, 297b31-298a10)

The concepts of symmetry, equilibrium and cyclic repetition permeated Aristotle's work. In his Meteorology he divided the world into five climatic zones: Two temperate areas were separated by a torrid zone near the equator, as well as two cold inhospitable regions, "one near our upper or northern pole and the other near the ... southern pole," both impenetrable and girdled with ice (Meteorologica, 362a31-35). Although no humans could survive in the frigid zones, inhabitants in the southern temperate regions could exist. Time lapse movie of the 3 March 2007 lunar eclipse A lunar eclipse occurs whenever the Moon passes through some portion of the Earths shadow. ... Meteorology (or Meteorologica) is a text by Aristotle which contains his theories about the earth sciences. ... World map showing the equator in red In tourist areas, the equator is often marked on the sides of roads The equator marked as it crosses Ilhéu das Rolas, in São Tomé and Príncipe. ... For the Figure of speech, see Ellipsis (figure of speech). ...

Eratosthenes

Eratosthenes (276 BCE - 194 BCE) estimated Earth's circumference around 240 BCE. He had heard about a place in Egypt where the Sun was directly overhead at the summer solstice and used geometry to come up with a circumference of 250,000 stades. This estimate astonishes some modern writers, as it is within 2% of the modern value of the equatorial circumference, 40,075 kilometres. However, the length of a 'stade' is not precisely known; Eratosthenes' figure falls short if we do not use a fairly generous estimate for this length. Eratosthenes (Greek ; 276 BC - 194 BC) was a Greek mathematician, geographer and astronomer. ... (Redirected from 276 BCE) Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 320s BC 310s BC 300s BC 290s BC 280s BC 270s BC 260s BC 250s BC 240s BC 230s BC 220s BC Years: 281 BC 280 BC 279 BC 278 BC 277 BC - 276 BC... (Redirected from 194 BCE) Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 240s BC 230s BC 220s BC 210s BC 200s BC - 190s BC - 180s BC 170s BC 160s BC 150s BC 140s BC Years: 199 BC 198 BC 197 BC 196 BC 195 BC - 194 BC... This article is about Earth as a planet. ... (Redirected from 240 BCE) Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 290s BC 280s BC 270s BC 260s BC 250s BC - 240s BC - 230s BC 220s BC 210s BC 200s BC 190s BC Years: 245 BC 244 BC 243 BC 242 BC 241 BC - 240 BC... The Sun (Latin: Sol) is the star at the center of the Solar System. ... The Greek system of weights and measures was built mainly upon the Egyptian, and formed the basis of the later Roman system. ...

Claudius Ptolemy

Claudius Ptolemy (CE 90 - 168) lived in Alexandria, the centre of scholarship in the second century. Around 150, he produced his eight-volume Geographia. This article is about the geographer and astronomer Ptolemy. ... Dionysius Exiguus invented Anno Domini years to date Easter. ... This article is about the year 90. ... // Events Change of Han Huandi to Han Lingdi of Han Dynasty; first year of Jianning era. ... Nickname: Alexandria on the map of Egypt Map of Alexandria Coordinates: , Country Egypt Founded 334 BC Government  - Governor Adel Labib Population (2001)  - City 3,500,000 Time zone EET (UTC+2)  - Summer (DST) EEST (UTC+3) Twin Cities  - Baltimore  United States  - Cleveland  United States  - ConstanÅ£a  Romania  - Durban  South Africa... ( 1st century - 2nd century - 3rd century - other centuries) Events Roman Empire governed by the Five Good Emperors ( 96– 180) – Nerva, Trajan, Hadrian, Antoninus Pius, Marcus Aurelius. ... The Geographia is Ptolemys main work besides the Almagest. ...

The first part of the Geographia is a discussion of the data and of the methods he used. As with the model of the solar system in the Almagest, Ptolemy put all this information into a grand scheme. He assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe. Latitude was measured from the equator, as it is today, but Ptolemy preferred to express it as the length of the longest day rather than degrees of arc (the length of the midsummer day increases from 12h to 24h as you go from the equator to the polar circle). He put the meridian of 0 longitude at the most western land he knew, the Canary Islands. See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ... Look up grid in Wiktionary, the free dictionary. ... Latitude,usually denoted symbolically by the Greek letter phi, , gives the location of a place on Earth north or south of the equator. ... World map showing the equator in red In tourist areas, the equator is often marked on the sides of roads The equator marked as it crosses Ilhéu das Rolas, in São Tomé and Príncipe. ... This article describes the unit of angle. ... Midsummer may refer to the period of time centered upon the summer solstice and the diverse celebrations of it around the world, but more often refers to European celebrations that accompany the summer solstice, or to Western festivals that take place in June and are usually related to Saint John... The polar circle in Finland, 1975. ... On the earth, a meridian is a north-south line between the North Pole and the South Pole. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... Anthem: Arrorró Capital Las Palmas de Gran Canaria and Santa Cruz de Tenerife Official language(s) Spanish Area  â€“ Total  â€“ % of Spain Ranked 13th  7,447 km²  1. ...

Geographia indicated the countries of "Serica" and "Sinae" (China) at the extreme right, beyond the island of "Taprobane" (Sri Lanka, oversized) and the "Aurea Chersonesus" (Southeast Asian peninsula). Seres (Σηρες) was the ancient Greek and Roman name for the northwestern part of China and its inhabitants. ... Location of Southeast Asia Southeast Asia is a subregion of Asia. ...

Ptolemy also devised and provided instructions on how to create maps both of the whole inhabited world (oikoumenè) and of the Roman provinces. In the second part of the Geographia he provided the necessary topographic lists, and captions for the maps. His oikoumenè spanned 180 degrees of longitude from the Canary islands in the Atlantic Ocean to China, and about 81 degrees of latitude from the Arctic to the East Indies and deep into Africa; Ptolemy was well aware that he knew about only a quarter of the globe. Topography, a term in geography, has come to refer to the lay of the land, or the physiogeographic characteristics of land in terms of elevation, slope, and orientation. ... The Indies, on the display globe of the Field Museum, Chicago The Indies or East Indies (or East India) is a term used to describe lands of South and South-East Asia, occupying all of the former British India, the present Indian Union, Pakistan, Bangladesh, Myanmar, Sri Lanka, Maldives, and... A world map showing the continent of Africa Africa is the worlds second-largest and second most-populous continent, after Asia. ...

Aryabhata

The works of the classical Indian astronomer and mathematician Aryabhata (476 - 550 CE) deal with the sphericity of the Earth and the motion of the planets. The final two parts of his Sanskrit magnum opus the Aryabhatiya, which were named the Kalakriya ("reckoning of time") and the Gola ("sphere"), state that the earth is spherical and that its circumference is 4,967 yojanas, which in modern units is 39,968 km, very close to the current value of 40,030 km.^[6][7] He also stated that the apparent rotation of the celestial objects was due to the actual rotation of the earth, calculating the length of the sidereal day to be 23 hours, 56 minutes and 4.1 seconds, which is also surprisingly accurate. It is likely that Aryabhata's results influenced European astronomy, because the 8th century Arabic version of the Aryabhatiya was translated into Latin in the 13th century. Statue of Aryabhata on the grounds of IUCAA, Pune. ... Events August - The usurper Basiliscus is deposed and Zeno is restored as Eastern Roman Emperor. ... Events By Place Byzantine Empire Silk reaches Constantinople (approximate date). ... The Sanskrit language ( , for short ) is a classical language of India, a liturgical language of Hinduism, Buddhism, Sikhism, and Jainism, and one of the 23 official languages of India. ... Āryabhatīya, an astronomical treastise, is the Magnum Opus and only extant work of the 5th century Indian Mathematician, Aryabhatta. ... On a prograde planet like the Earth, the sidereal day is shorter than the solar day. ... Arabic can mean: From or related to Arabia From or related to the Arabs The Arabic language; see also Arabic grammar The Arabic alphabet, used for expressing the languages of Arabic, Persian, Malay ( Jawi), Kurdish, Panjabi, Pashto, Sindhi and Urdu, among others. ...

Geodesy

Geodesy, also called geodetics, is the scientific discipline that deals with the measurement and representation of the Earth, its gravitational field and geodynamic phenomena (polar motion, earth tides, and crustal motion) in three-dimensional time-varying space. It has been suggested that geodetic system be merged into this article or section. ... “Gravity” redirects here. ... This article needs to be wikified. ... “Ebb tide” redirects here. ...

Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of Earth's magnetic field. Especially in the German speaking world, geodesy is divided in geomensuration ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring the earth on a global scale, and surveying ("Ingenieurgeodäsie"), which is concerned with measuring parts of the surface. Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges and magnetic dipoles, such as those in electric currents and magnets. ... Geophysical survey refers to the systematic collection of geophysical data for spatial studies. ...

Earth's shape can be thought of in at least two ways;

• as the shape of the geoid, the mean sea level of the world ocean; or
• as the shape of Earth's land surface as it rises above and falls below the sea.

As the science of geodesy measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an oblate spheroid, a specific type of ellipsoid. More recent measurements have measured the geoid to unprecedented accuracy, revealing mass concentrations beneath Earth's surface. The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ... It has been suggested that geodetic system be merged into this article or section. ... In mathematics, a spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ... A mass concentration or mascon is a region of a planet or moons crust that contains a large amount of material that is denser than average for that body. ...

Spherical models

The Earth as seen from the Apollo 17 mission.

There are several reasonable ways to approximate Earth's shape as a sphere. Each preserves a different feature of the true Earth in order to compute the radius of the spherical model. All examples in this section assume the WGS 84 datum, with an equatorial radius "a" of 6,378.137 km and a polar radius "b" of 6,356.752 km. A sphere being a gross approximation of the spheroid, which itself is an approximation of the geoid, units are given here in kilometers rather than the millimeter resolution appropriate for geodesy. Image File history File linksMetadata Download high resolution version (3000x3002, 6358 KB) The Blue Marble: This photo is of Africa, Antarctica, and the Arabian Peninsula as taken en route to the Moon by Apollo 17s Harrison Schmitt on December 7, 1972. ... Image File history File linksMetadata Download high resolution version (3000x3002, 6358 KB) The Blue Marble: This photo is of Africa, Antarctica, and the Arabian Peninsula as taken en route to the Moon by Apollo 17s Harrison Schmitt on December 7, 1972. ... Apollo 17 was the eleventh manned space mission in the NASA Apollo program. ... Remote Authentication Dial In User Service (RADIUS) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... The World Geodetic System defines a reference frame for the earth, for use in geodesy and navigation. ...

• Preserve the equatorial circumference. This is simplest, being a sphere with circumference identical to the equatorial circumference of the real Earth. Since the circumference is the same, so is the radius, at 6,378.137 km.
• Preserve the lengths of meridians. This requires an elliptic integral to find, given the polar and equatorial radii: . A sphere preserving the lengths of meridians has a rectifying radius of 6,367.449 km. This can be approximated using the elliptical quadratic mean: , about 6,367.454 km.
• Preserve the average circumference. As there are different ways to define an ellipsoid's average circumference (radius vs. arcradius/radius of curvature; elliptically fixed vs. ellipsoidally "fluid"; different integration intervals for quadrant-based geodetic circumferences), there is no definitive, "absolute average circumference". The ellipsoidal quadratic mean is one simple model: , giving a spherical radius of 6,372.798 km.
• Preserve the surface area of the real Earth. This gives the authalic radius: , or 6,371.007 km.
• Preserve the volume of the real Earth. This volumetric radius is computed as: , or 6,371.001 km.

Note that the authalic and volumetric spheres have radii that differ by less than 7 meters, yet both preserve important properties. Hence both are common and occasionally an average of the two is used. The circumference is the distance around a closed curve. ...

References

1. ^ Haug, Martin and Basu, Major B. D. (1974). The Aitareya Brahmanam of the Rigveda, Containing the Earliest Speculations of the Brahmans on the Meaning of the Sacrifical Prayers. ISBN 0-404-57848-9.
2. ^ Joseph, George G. (2000). The Crest of the Peacock: Non-European Roots of Mathematics, 2nd edition. Penguin Books, London. ISBN 0691006598.
3. ^ Teresi, Dick (2002). Lost Discoveries: The Ancient Roots of Modern Science - from the Babylonians to the Maya. Simon & Schuster, New York. ISBN 0-684-83718-8.
4. ^ Kak, Subhash C. (2000). 'Birth and Early Development of Indian Astronomy'. In Selin, Helaine (2000). Astronomy Across Cultures: The History of Non-Western Astronomy (303-340). Kluwer, Boston. ISBN 0-7923-6363-9.
5. ^ * Blavatsky, H. P. (1877). 'Science. Chapter I'. Isis Unveiled.
6. ^ http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html
7. ^ http://www.gongol.com/research/math/aryabhatiya The Aryabhatiya: Foundations of Indian Mathematics

Jean-François Millet Le Semeur (The Sower) Simon & Schuster logo, circa 1961. ... Subhash Kak (सुभाष काक) (born March 26, 1947, Srinagar, Kashmir) is Delaune Distinguished Professor of Electrical Engineering and Professor in the Asian Studies and Cognitive Science Programs at Louisiana State University, Baton Rouge. ...

See also

• Earth radius
• Figure of the Earth
• Flat Earth
• Celestial sphere
• Physical geodesy
• Terra Australis
• WGS 84

Since the Earth, like all planets, is not a perfect sphere, the radius of Earth can refer to various values. ... The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earths size and shape is to be defined. ... 15th century adaptation of a T-O map. ... The celestial sphere is divided by the celestial equator. ... Definition Physical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy. ... Terra Australis is the large continent on the bottom of the map Terra Australis (also: Terra Australis Incognita, Latin for the unknown land of the South) was an imaginary continent, appearing on European maps from the 15th to the 18th century. ... WGS 84 is the 1984 revision of the World Geodetic System. ...

External links

• You say the earth is round? Prove it (from The Straight Dope)
• Oblate Spheroid
• NASA-Most Changes in Earth's Shape Are Due to Changes in Climate