GeometryGeometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Greek mathematicsGreek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly attested from the late 7th century BC to the 6th century AD, around the shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire region, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of proofs is an important difference between Greek mathematics and those of preceding civilizations.
Theon of SmyrnaTheon of Smyrna (Θέων ὁ Σμυρναῖος Theon ho Smyrnaios, gen. Θέωνος Theonos; fl. 100 CE) was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. His surviving On Mathematics Useful for the Understanding of Plato is an introductory survey of Greek mathematics. Little is known about the life of Theon of Smyrna. A bust created at his death, and dedicated by his son, was discovered at Smyrna, and art historians date it to around 135 CE.
NousNous, or Greek νοῦς (UKnaʊs, USnuːs), sometimes equated to intellect or intelligence, is a concept from classical philosophy for the faculty of the human mind necessary for understanding what is true or real. Alternative English terms used in philosophy include "understanding" and "mind"; or sometimes "thought" or "reason" (in the sense of that which reasons, not the activity of reasoning). It is also often described as something equivalent to perception except that it works within the mind ("the mind's eye").
Porphyry (philosopher)Porphyry of Tyre (ˈpɔrfɪri; Πορφύριος, Porphýrios; فُرْفُورِيُوس, Furfūriyūs; 234 – 305 AD) was a Neoplatonic philosopher born in Tyre, Roman Phoenicia during Roman rule. He edited and published The Enneads, the only collection of the work of Plotinus, his teacher. He wrote original works in the Greek language on a wide variety of topics, ranging from music theory to Homer to vegetarianism. His Isagoge or Introduction, an introduction to logic and philosophy, was the standard textbook on logic throughout the Middle Ages in its Latin and Arabic translations.
Musica universalisThe musica universalis (literally universal music), also called music of the spheres or harmony of the spheres, is a philosophical concept that regards proportions in the movements of celestial bodies – the Sun, Moon, and planets – as a form of music. The theory, originating in ancient Greece, was a tenet of Pythagoreanism, and was later developed by 16th-century astronomer Johannes Kepler. Kepler did not believe this "music" to be audible, but felt that it could nevertheless be heard by the soul.
Sieve of EratosthenesIn mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.
NeopythagoreanismNeopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic and Roman philosophy which revived Pythagorean doctrines. Neopythagoreanism was influenced by middle Platonism and in turn influenced Neoplatonism. It originated in the 1st century BC and flourished during the 1st and 2nd centuries AD. The Encyclopædia Britannica Eleventh Edition describes Neopythagoreanism as "a link in the chain between the old and the new" within Hellenistic philosophy.
ArchytasArchytas (ˈɑrkɪtəs; Ἀρχύτας; 435/410–360/350 BC) was an Ancient Greek philosopher, mathematician, music theorist, astronomer, statesman, and strategist. He was a scientist affiliated with the Pythagorean school and famous for being the reputed founder of mathematical mechanics and a friend of Plato. Archytas was born in the Greek city of Taras (Tarentum), Magna Graecia, and was the son of either Mnesagoras or Hadees. For a while, he was taught by Philolaus, and taught mathematics to Eudoxus of Cnidus and to Eudoxus' student, Menaechmus.
Perfect numberIn number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, where is the sum-of-divisors function.
