Monetae cudendae ratio is a paper on coinage by which Renaissance- and Reformation-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe?
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Monetae cudendae ratio Monetae cudendae ratio (also spelled Monetæ cudendæ ratio; English: On the Minting of Coin or On the Striking of Coin; sometimes, Treatise on Money) is a paper on coinage by Nicolaus Copernicus (Polish: Mikołaj Kopernik). It was written in 1526 at the request of Sigismund I the Old, King of Poland, and presented to the Prussian Diet.
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Nicolaus Copernicus Nicolaus Copernicus ( ; Polish: "Mikołaj Kopernik" ; German: "Nikolaus Kopernikus; Niklas Koppernigk" ; 19 February 1473 – 24 May 1543) was a Renaissance- and Reformation-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe, likely independently of Aristarchus of Samos, who had formulated such a model some eighteen centuries earlier.
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Astronomer An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside the scope of Earth. They look at stars, planets, moons, comets and galaxies, as well as many other celestial objects — either in observational astronomy, in analyzing the data or in theoretical astronomy. Examples of topics or fields astronomers work on include: planetary science, solar astronomy, the origin or evolution of stars, or the formation of galaxies. There are also related but distinct subjects like physical cosmology which studies the Universe as a whole.
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Newton's law of universal gravitation Newton's law of universal gravitation states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work "Philosophiæ Naturalis Principia Mathematica" ("the "Principia""), first published on 5 July 1687. (When Newton's book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him; see the History section below.)
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Francesco Barozzi Francesco Barozzi (in Latin, "Franciscus Barocius") (9 August 1537 – 23 November 1604) was an Italian mathematician, astronomer and humanist.
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Vera Rubin Vera Cooper Rubin (July 23, 1928 – December 25, 2016) was an American astronomer who pioneered work on galaxy rotation rates. She uncovered the discrepancy between the predicted angular motion of galaxies and the observed motion, by studying galactic rotation curves. This phenomenon became known as the galaxy rotation problem, and was evidence of the existence of dark matter. Although initially met with skepticism, Rubin's results were confirmed over subsequent decades. Her legacy was described by "The New York Times" as "ushering in a Copernican-scale change" in cosmological theory.
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Faber–Jackson relation The Faber–Jackson relation is an early empirical power-law relation between the luminosity formula_1 and the central stellar velocity dispersion formula_2 of elliptical galaxies, first noted by the astronomers Sandra M. Faber and Robert Earl Jackson in 1976. The original relation can be expressed mathematically as:
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Helioseismology Helioseismology is the process of inferring the internal structure and kinematics of the Sun from the propagation of seismic waves, particularly acoustic waves (p waves) and surface gravity waves (f waves). It was developed by analogy to geoseismology (originally called simply seismology), and subsequently there emerged asteroseismology, in which seismic waves are analysed to constrain the internal structures of other stars. Because the Sun is fluid, to a first approximation it cannot support shear waves (s-waves), unlike the seismic waves on Earth. An exception is the magneto-acoustic waves which appear to be important only in the atmosphere. The helioseismic waves are generated by the turbulence in the convection zone immediately beneath the Sun's surface. Certain frequencies are amplified by constructive interference, leading to resonance. In other words, the turbulence "rings" the sun like a bell. The resonant waves are reflected near the photosphere, the visible surface of the sun, where they can be observed. The oscillations are detectable in almost any time series of solar images, but are best observed by measuring the Doppler shift of atmospheric absorption lines. Details of the propagation of the seismic waves through the Sun, inferred from the resonant frequencies, reveal the Sun's inner structure, allowing astrophysicists to develop an extremely detailed representation of the hydrostatic stratification and the internal angular velocity. That has permitted the evaluation of the quadrupole moment, formula_1, and higher-order moments of the Sun's external gravitational potential. It is a more accurate and more robust procedure than trying to infer it from the oblateness of the visible disc. Together with measurements of the orbits of Mercury and of spacecraft, the result is consistent with General Relativity.
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Cyclic model A cyclic model (or oscillating model) is any of several cosmological models in which the universe follows infinite, or indefinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a big bang and ending with a big crunch; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce.
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Letters on Sunspots " Letters on Sunspots " ("Istoria e Dimostrazioni intorno alle Macchie Solari") was a pamphlet written by Galileo Galilei in 1612 and published in Rome by the Accademia dei Lincei in 1613. In it Galileo outlined his recent observation of dark spots on the face of the sun. His claims were significant in undermining the traditional Aristotelian view that the sun was both unflawed and unmoving. The third letter contains his first clear public statement of support for Copernicus.
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Johannes Fabricius Johann Goldsmid, better known by his Latinized name Johann(es) Fabricius (8 January 1587 – 19 March 1616), eldest son of David Fabricius (1564–1617), was a Frisian/German astronomer and a discoverer of sunspots (in 1610), independently of Galileo Galilei.
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Mathematics in medieval Islam Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as the full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra (named for "The Compendious Book on Calculation by Completion and Balancing" by scholar Al-Khwarizmi), and advances in geometry and trigonometry.
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R. Catesby Taliaferro Robert Catesby Taliaferro (1907–1989) was an American mathematician, philosopher, and translator of ancient Greek and Latin works into English. An Episcopalian from an old Virginia family, he taught in the mathematics department of the University of Notre Dame. He translated Ptolemy's "Almagest", a 2nd-century book on astronomy, the 13 books of Euclid's "Elements", Apollonius' works on conic sections, and some works of Plato, and St. Augustine. He contributed a celebrated foreword to the Bollingen Series 1944 reprint of the Thomas Taylor translation of Plato's Timaeus and Critias. He also wrote a book titled "The concept of matter in Descartes and Leibniz" and one titled "Number systems, introduction to Euclid book V, and to the theory of limits".
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Paradox of value The paradox of value (also known as the diamond–water paradox) is the apparent contradiction that, although water is on the whole more useful, in terms of survival, than diamonds, diamonds command a higher price in the market. The philosopher Adam Smith is often considered to be the classic presenter of this paradox, although it had already appeared as early as Plato's "Euthydemus". Nicolaus Copernicus, John Locke, John Law and others had previously tried to explain the disparity.
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History of Mars observation The recorded history of Mars observation dates back to the era of the ancient Egyptian astronomers in the 2nd millennium BCE. Chinese records about the motions of Mars appeared before the founding of the Zhou Dynasty (1045 BCE). Detailed observations of the position of Mars were made by Babylonian astronomers who developed arithmetic techniques to predict the future position of the planet. The ancient Greek philosophers and Hellenistic astronomers developed a geocentric model to explain the planet's motions. Measurements of Mars' angular diameter can be found in ancient Greek and Indian texts. In the 16th century, Nicolaus Copernicus proposed a heliocentric model for the Solar System in which the planets follow circular orbits about the Sun. This was revised by Johannes Kepler, yielding an elliptic orbit for Mars that more accurately fitted the observational data.
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Thomas Cajetan Thomas Cajetan ( ; 20 February 1469 - 9 August 1534), ), also known as Gaetanus, commonly Tommaso de Vio or Thomas de Vio, was an Italian philosopher, theologian, cardinal (from 1517 until his death) and the Master of the Order of Preachers 1508-18. He was a leading theologian of his day who is now best known as the spokesman for Catholic opposition to the teachings of Martin Luther and the Protestant Reformation while he was the Pope's Legate in Wittenberg, and perhaps also among Catholics for his extensive commentary on the "Summa Theologica" of Thomas Aquinas.
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Abraham Zelmanov Abraham Zelmanov (May 15, 1913 – February 2, 1987), was a prominent scientist working in the General Theory of Relativity and cosmology. He first constructed, in 1944, the complete mathematical method to calculate physical observable quantities in the General Theory of Relativity (the theory of chronometric invariants). Applying the mathematical apparatus, in the 1940s, he established the basics of the theory of inhomogeneous anisotropic universe, where he determined specific kinds of all cosmological models — scenarios of evolution — which could be theoretically conceivable for a truly inhomogeneous and anisotropic Universe in the framework of Einstein's theory.
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Daniel Bernoulli Daniel Bernoulli FRS ( ; ] ; 8 February 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. His name is commemorated in the Bernoulli's principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing.
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Barycenter The barycenter (or barycentre; from the Ancient Greek βαρύς "heavy" + κέντρον "centre") is the center of mass of two or more bodies that are orbiting each other, which is the point around which they both orbit. It is an important concept in fields such as astronomy and astrophysics. The distance from a body's center of mass to the barycenter can be calculated as a simple two-body problem.
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On the Universe De mundo (Greek: Περὶ Κόσμου ), known in English as On the Universe, is the work of an unknown author who wrote under the name of Aristotle. Because of this, the author is referred to as a Pseudo-Aristotle. The date of the work is uncertain; it has been argued that it was composed before 250 BC or between 350 and 200 BC. It is found under the Bekker numbers 391–401. It should not be confused with "On the Heavens".
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Equant Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in planetary orbit during different stages of the orbit. This planetary concept allowed Ptolemy to keep the theory of uniform circular motion alive by stating that the path of heavenly bodies was uniform around one point and circular around another point.
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Galileo's paradox Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. The ideas were not new with him, but his name has come to be associated with them. In his final scientific work, "Two New Sciences", Galileo Galilei made apparently contradictory statements about the positive integers. First, some numbers are squares, while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares. And yet, for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other. This is an early use, though not the first, of the idea of one-to-one correspondence in the context of infinite sets.