Eratosthenes in the context of Kingdom of Ma'in

The earliest known world maps date to classical antiquity, the oldest examples of the 6th to 5th centuries BCE still based on the flat Earth paradigm. World maps assuming a spherical Earth first appear in the Hellenistic period. The developments of Greek geography during this time, notably by Eratosthenes and Posidonius culminated in the Roman era, with Ptolemy's world map (2nd century CE), which would remain authoritative throughout the Middle Ages. Since Ptolemy, knowledge of the approximate size of the Earth allowed cartographers to estimate the extent of their geographical knowledge, and to indicate parts of the planet known to exist but not yet explored as terra incognita.

With the Age of Discovery, during the 15th to 18th centuries, world maps became increasingly accurate; exploration of Antarctica, Australia, and the interior of Africa by western mapmakers was left to the 19th and early 20th century.

Hipparchus (/hɪˈpɑːrkəs/; Greek: Ἵππαρχος, Hípparkhos; c. 190 – c. 120 BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.

Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (fifth century BC), Timocharis, Aristyllus, Aristarchus of Samos, and Eratosthenes, among others.

The Library of Alexandria in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world. The library was part of a larger research institution called the Mouseion, which was dedicated to the Muses, the nine goddesses of the arts. The idea of a universal library in Alexandria may have been proposed by Demetrius of Phalerum, an exiled Athenian statesman living in Alexandria, to Ptolemy I Soter, who may have established plans for the library, but the library itself was probably not built until the reign of his son Ptolemy II Philadelphus. The library quickly acquired many papyrus scrolls, owing largely to the Ptolemaic kings' aggressive and well-funded policies for procuring texts. It is unknown precisely how many scrolls were housed at any given time, but estimates range from 40,000 to 400,000 at its height.

Alexandria came to be regarded as the capital of knowledge and learning, in part because of the Great Library. Many important and influential scholars worked at the Library during the third and second centuries BC, including: Zenodotus of Ephesus, who worked towards standardizing the works of Homer; Callimachus, who wrote the Pinakes, sometimes considered the world's first library catalog; Apollonius of Rhodes, who composed the epic poem the Argonautica; Eratosthenes of Cyrene, who calculated the circumference of the earth within a few hundred kilometers of accuracy; Hero of Alexandria, who invented the first recorded steam engine; Aristophanes of Byzantium, who invented the system of Greek diacritics and was the first to divide poetic texts into lines; and Aristarchus of Samothrace, who produced the definitive texts of the Homeric poems as well as extensive commentaries on them. During the reign of Ptolemy III Euergetes, a daughter library was established in the Serapeum, a temple to the Greco-Egyptian god Serapis.

Geography (from Ancient Greek γεωγραφία geōgraphía; combining gê 'Earth' and gráphō 'write', literally 'Earth writing') is the study of the lands, features, inhabitants, and phenomena of Earth. Geography is an all-encompassing discipline that seeks an understanding of Earth and its human and natural complexities—not merely where objects are, but also how they have changed and come to be. While geography is specific to Earth, many concepts can be applied more broadly to other celestial bodies in the field of planetary science. Geography has been called "a bridge between natural science and social science disciplines."

The history of geography as a discipline spans cultures and millennia, being independently developed by multiple groups, and cross-pollinated by trade between these groups. Geography as a discipline dates back to the earliest attempts to understand the world spatially, with the earliest example of an attempted world map dating to the 9th century BCE in ancient Babylon. Origins of many of the concepts in geography can be traced to Greek Eratosthenes of Cyrene, who may have coined the term "geographia" (c. 276 BC – c. 195/194 BC). The first recorded use of the word γεωγραφία was as the title of a book by Greek scholar Claudius Ptolemy (100 – 170 AD). During the Middle Ages, geography was influenced by Islamic scholars, like Muhammad al-Idrisi, producing detailed maps of the world. The Age of Discovery was influential in the development of geography, as European explorers mapped the New World. Modern developments include the development of geomatics and geographic information science.

Earth's circumference is the distance around Earth. Measured around the equator, it is 40,075.017 km (24,901.461 mi). Measured passing through the poles, the circumference is 40,007.863 km (24,859.734 mi).

Treating the Earth as a sphere, its circumference would be its single most important measurement. The first known scientific measurement and calculation was done by Eratosthenes, by comparing altitudes of the mid-day sun at two places a known north–south distance apart. He achieved a great degree of precision in his computation. The Earth's shape deviates from spherical by flattening, but by only about 0.3%.

The History of geography includes many histories of geography which have differed over time and between different cultural and political groups. In more recent developments, geography has become a distinct academic discipline. 'Geography' derives from the Greek γεωγραφία – geographia, literally "Earth-writing", that is, description or writing about the Earth. The first person to use the word geography was Eratosthenes (276–194 BC). However, there is evidence for recognizable practices of geography, such as cartography, prior to the use of the term.

Alexander the Great (356 – 323 BC), a king of ancient Macedon, created one of the largest empires in history by waging an extensive military campaign throughout Asia. Alexander was groomed for rulership from an early age and acceded to the throne after the assassination of his father, Philip II. After subduing rebellious vassals, he invaded the Persian Achaemenid Empire in 334 BC. Alexander swiftly conquered large areas of Western Asia and Egypt before defeating the Persian king Darius III in battle at Issus and Gaugamela. Achieving complete domination over the former lands of the Achaemenids by 327 BC, Alexander attempted to conquer India but turned back after his weary troops mutinied. Following his death aged thirty-two in Babylon in 323 BC, his empire disintegrated in a series of civil wars fought between his followers.

Alexander founded numerous settlements during his campaigns, naming them after himself or close followers. These have been the subject of intense debate, as the accounts of ancient and medieval scholars differ wildly and are often contradictory. Plutarch provides the maximum estimate of seventy cities in his Life of Alexander, but most texts attest to between ten and twenty foundations. The Greek Alexander Romance lists between nine and thirteen cities, depending on the recension; the Syriac, Armenian, Hebrew, and Ethiopic versions of the Romance also record twelve or thirteen foundations. Persian sources such as al-Tabari, al-Dinawari, Hamza al-Isfahani, and Qudama ascribe between nine and twelve settlements to Alexander. Stephanus of Byzantium recorded around twenty settlements. Some authors additionally document the number of cities established in a specific area: for example, Strabo records that Alexander founded eight cities in Bactria. The accounts of Alexander's campaigns, primarily those of Arrian, Plutarch, Diodorus, Curtius Rufus, and Justin, provide supplementary evidence. Finally, the geographers Eratosthenes, Ptolemy, and Pliny draw upon the otherwise-lost evidence of Alexander's bematist distance-measurers.

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which are "pure" or perfect, with ratio ${\displaystyle 3:2}$. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio ${\displaystyle 2:1}$), and hence is the next most consonant "pure" interval, and the easiest to tune by ear. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈ 702 cents wide.

The system dates back to Ancient Mesopotamia;. (See Music of Mesopotamia § Music theory.) It is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (sixth century BC) by modern authors of music theory. Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium" and "tonus" in Latin (256:243 × 9:8 × 9:8), to Eratosthenes. The so-called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals, particularly the major third, to be so badly out of tune that major chords [may be considered] a dissonance."

Aristophanes of Byzantium (Ancient Greek: Ἀριστοφάνης ὁ Βυζάντιος Aristophánēs ho Buzántios; Byzantium c. 257 BC – Alexandria c. 185–180 BC) was a Hellenistic Greek scholar, critic and grammarian, particularly renowned for his work in Homeric scholarship, but also for work on other classical authors such as Pindar and Hesiod. He soon moved to Alexandria and studied under Zenodotus, Callimachus, and Dionysius Iambus. He succeeded Eratosthenes as head librarian of the Library of Alexandria at the age of sixty. His students included Callistratus, Aristarchus of Samothrace, and perhaps Agallis. He was succeeded by Apollonius "The Classifier" (not to be confused with Apollonius of Rhodes, a previous head librarian of Alexandria). Aristophanes' pupil, Aristarchus of Samothrace, would be the sixth head librarian at the Library of Alexandria.

Ma'in (Minaean: 𐩣𐩲𐩬; Arabic: معين, romanized: Maʿīn) was an ancient South Arabian kingdom in modern-day Yemen. It was located along the strip of desert called Ṣayhad by medieval Arab geographers, which is now known as Ramlat al-Sab'atayn. Wadd was the national god of Ma'in. The spoken language was Minaic. The kingdom appears in the historical record in the 8th century BCE, and transition from a city-state to kingdom in the last quarter of the 7th century BCE. The date of the end of Ma'in is heavily disputed, but the most popular hypothesis places its demise in the 1st century CE.

The Minaean people were one of four ancient Yemeni groups mentioned by Eratosthenes. The others were the Sabaeans, Ḥaḑramites and Qatabānians. Each of these had regional kingdoms in ancient Yemen, with the Minaeans in the north-west (in Wādī al-Jawf), the Sabaeans to the south-east of them, the Qatabānians to the south-east of the Sabaeans, and the Ḥaḑramites further east still.