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Hippocrates Of Chios
Hippocrates of Chios ( grc-gre, Ἱπποκράτης ὁ Χῖος; c. 470 – c. 410 BC) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios, where he was originally a merchant. After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens, possibly for litigation, where he became a leading mathematician. On Chios, Hippocrates may have been a pupil of the mathematician and astronomer Oenopides of Chios. In his mathematical work there probably was some Pythagorean influence too, perhaps via contacts between Chios and the neighboring island of Samos, a center of Pythagorean thinking: Hippocrates has been described as a 'para-Pythagorean', a philosophical 'fellow traveler'. "Reduction" arguments such as ''reductio ad absurdum'' argument (or proof by contradiction) have been traced to him, as has the use of power to denote the square of a line. W. W. Rouse Ball, A Short Account of the H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of culturally and linguistically related city-states and other territories. Most of these regions were officially unified only once, for 13 years, under Alexander the Great's empire from 336 to 323 BC (though this excludes a number of Greek city-states free from Alexander's jurisdiction in the western Mediterranean, around the Black Sea, Cyprus, and Cyrenaica). In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Roughly three centuries after the Late Bronze Age collapse of Mycenaean Greece, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and the colonization of the Mediterranean Basin. This was followed by the age of Cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square The Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (\pi) is a transcendental number. That is, \pi is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if \pi were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been found. Despite the proof that it is impossible, attempts to square the circle have been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Chians
Ancient history is a time period from the beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian cuneiform script. Ancient history covers all continents inhabited by humans in the period 3000 BCAD 500. The three-age system periodizes ancient history into the Stone Age, the Bronze Age, and the Iron Age, with recorded history generally considered to begin with the Bronze Age. The start and end of the three ages varies between world regions. In many regions the Bronze Age is generally considered to begin a few centuries prior to 3000 BC, while the end of the Iron Age varies from the early first millennium BC in some regions to the late first millennium AD in others. During the time period of ancient history, the world population was already exponentially increasing due to the Neolithic Revolution, which was in full progress. While in 10,000 BC, the world population ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek Geometers
Ancient history is a time period from the beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian cuneiform script. Ancient history covers all continents inhabited by humans in the period 3000 BCAD 500. The three-age system periodizes ancient history into the Stone Age, the Bronze Age, and the Iron Age, with recorded history generally considered to begin with the Bronze Age. The start and end of the three ages varies between world regions. In many regions the Bronze Age is generally considered to begin a few centuries prior to 3000 BC, while the end of the Iron Age varies from the early first millennium BC in some regions to the late first millennium AD in others. During the time period of ancient history, the world population was already exponentially increasing due to the Neolithic Revolution, which was in full progress. While in 10,000 BC, the world population sto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
5th-century BC Greek People
The 5th century is the time period from 401 ( CDI) through 500 ( D) ''Anno Domini'' (AD) or Common Era (CE) in the Julian calendar. The 5th century is noted for being a period of migration and political instability throughout Eurasia. It saw the collapse of the Western Roman Empire, which came to an end in 476 AD. This empire had been ruled by a succession of weak emperors, with the real political might being increasingly concentrated among military leaders. Internal instability allowed a Visigoth army to reach and ransack Rome in 410. Some recovery took place during the following decades, but the Western Empire received another serious blow when a second foreign group, the Vandals, occupied Carthage, capital of an extremely important province in Africa. Attempts to retake the province were interrupted by the invasion of the Huns under Attila. After Attila's defeat, both Eastern and Western empires joined forces for a final assault on Vandal North Africa, but this campaign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numberphile
''Numberphile'' is an educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, but the channel has since expanded its scope, featuring videos on more advanced mathematical concepts such as Fermat's Last Theorem, the Riemann hypothesis and Kruskal's tree theorem. The videos are produced by Brady Haran, a former BBC video journalist and creator of Periodic Videos, Sixty Symbols, and several other YouTube channels. Videos on the channel feature several university professors, maths communicators and famous mathematicians. In 2018, Haran released a spin-off audio podcast titled ''The Numberphile Podcast''. YouTube channel The ''Numberphile'' YouTube channel was started on 15 September 2011. Most videos consist of Haran interviewing an expert on a number, mathematical theorem or other mathematical concept. The expert usually draws out their explanation on a lar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ivor Bulmer-Thomas
Ivor Bulmer-Thomas CBE FSA (30 November 1905 – 7 October 1993), born Ivor Thomas, was a British journalist and scientific writer who served eight years as a Member of Parliament (MP). His career was much influenced by his conversion to the Church of England in his youth, and he became a pious believer on the Anglo-Catholic wing of the Church. A brilliant scholar and champion athlete while at university, Bulmer-Thomas wrote biographies and worked as a sub-editor on ''The Times'' during his early life. His experience in wartime Italian propaganda led him to doubt its value. Serving in the Attlee Labour Party government in junior roles made him resent the influence of the Labour left; he fell out with party policy on nationalisation and moved to the Conservative Party. He was a workaholic and after leaving politics he became a leading layman in the Church of England; an interest in historic buildings led him to set up the Friends of Friendless Churches group, which campaigns ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed. For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence ''θ1'' and angle of refraction ''θ2'' is equal to the ratio of phase velocities (''v''1 / ''v''2) in the two media, or equivalently, to the refractive indices (''n''2 / ''n''1) of the two media. :\frac =\frac=\frac Optical prisms and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. The term ''Milky Way'' is a translation of the Latin ', from the Ancient Greek, Greek ('), meaning "milky circle". From Earth, the Milky Way appears as a band because its disk-shaped structure is viewed from within. Galileo Galilei first resolved the band of light into individual stars with his telescope in 1610. Until the early 1920s, most astronomers thought that the Milky Way contained all the stars in the Universe. Following the 1920 Great Debate (astronomy), Great Debate between the astronomers Harlow Shapley and Heber Curtis, observations by Edwin Hubble showed that the Milky Way is just one of many galaxies. The Milky Way is a barred spiral galaxy with an estimated Galaxy#Isophotal diameter, D25 isophotal diameter of , but only ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comet
A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena are due to the effects of solar radiation and the solar wind acting upon the nucleus of the comet. Comet nuclei range from a few hundred meters to tens of kilometers across and are composed of loose collections of ice, dust, and small rocky particles. The coma may be up to 15 times Earth's diameter, while the tail may stretch beyond one astronomical unit. If sufficiently bright, a comet may be seen from Earth without the aid of a telescope and may subtend an arc of 30° (60 Moons) across the sky. Comets have been observed and recorded since ancient times by many cultures and religions. Comets usually have highly eccentric elliptical orbits, and they have a wide range of orbital periods, ranging from several years to potentially several ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube Root
In mathematics, a cube root of a number is a number such that . All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of , denoted \sqrt , is , because , while the other cube roots of are -1+i\sqrt 3 and -1-i\sqrt 3. The three cube roots of are :3i, \quad \frac-\fraci, \quad \text \quad -\frac-\fraci. In some contexts, particularly when the number whose cube root is to be taken is a real number, one of the cube roots (in this particular case the real one) is referred to as the ''principal cube root'', denoted with the radical sign \sqrt The cube root is the inverse function of the cube function if considering only real numbers, but not if considering also complex numbers: although one has always \left(\sqrt \right)^3 =x, the cube of a nonzero number has more than one complex cube root and its principal cube root ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duplication Of The Cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible to construct by using only a compass and straightedge, but even in ancient times solutions were known that employed other tools. The Egyptians, Indians, and particularly the Greeks were aware of the problem and made many futile attempts at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a compass-and-straightedge solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, , the cube root of two. This is because a cube of side length 1 has a volume of , and a cube of twice that volume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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