doc_id int32 0 2.25M | text stringlengths 101 8.13k | source stringlengths 38 44 |
|---|---|---|
13,600 | For large values of , the value of = "e" may be so small that it is hard to represent. This can be solved by a change to the algorithm which uses an additional parameter STEP such that "e" does not underflow: | https://en.wikipedia.org/wiki?curid=23009144 |
13,601 | The choice of STEP depends on the threshold of overflow. For double precision floating point format the threshold is near "e", so 500 should be a safe "STEP". | https://en.wikipedia.org/wiki?curid=23009144 |
13,602 | Inverse transform sampling is simple and efficient for small values of , and requires only one uniform random number "u" per sample. Cumulative probabilities are examined in turn until one exceeds "u". | https://en.wikipedia.org/wiki?curid=23009144 |
13,603 | Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. A scientist who ... | https://en.wikipedia.org/wiki?curid=22939 |
13,604 | Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps "the" oldest. Over much of the past two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the Scientific Revolution in the 17th century these natural... | https://en.wikipedia.org/wiki?curid=22939 |
13,605 | Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism, solid-state physics, and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliance... | https://en.wikipedia.org/wiki?curid=22939 |
13,606 | Astronomy is one of the oldest natural sciences. Early civilizations dating back before 3000 BCE, such as the Sumerians, ancient Egyptians, and the Indus Valley Civilisation, had a predictive knowledge and a basic awareness of the motions of the Sun, Moon, and stars. The stars and planets, believed to represent gods, w... | https://en.wikipedia.org/wiki?curid=22939 |
13,607 | According to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. Egyptian astronomers left monuments showing knowledge of the constellations and the motions of the celestial bodies, while Greek poet Homer ... | https://en.wikipedia.org/wiki?curid=22939 |
13,608 | Natural philosophy has its origins in Greece during the Archaic period (650 BCE – 480 BCE), when pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause. They proposed ideas verified by reason and observation, and many of the... | https://en.wikipedia.org/wiki?curid=22939 |
13,609 | The Western Roman Empire fell in the fifth century, and this resulted in a decline in intellectual pursuits in the western part of Europe. By contrast, the Eastern Roman Empire (also known as the Byzantine Empire) resisted the attacks from the barbarians, and continued to advance various fields of learning, including p... | https://en.wikipedia.org/wiki?curid=22939 |
13,610 | In the sixth century, Isidore of Miletus created an important compilation of Archimedes' works that are copied in the Archimedes Palimpsest. | https://en.wikipedia.org/wiki?curid=22939 |
13,611 | In sixth-century Europe John Philoponus, a Byzantine scholar, questioned Aristotle's teaching of physics and noted its flaws. He introduced the theory of impetus. Aristotle's physics was not scrutinized until Philoponus appeared; unlike Aristotle, who based his physics on verbal argument, Philoponus relied on observati... | https://en.wikipedia.org/wiki?curid=22939 |
13,612 | Islamic scholarship inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further, especially placing emphasis on observation and "a priori" reasoning, developing early forms of the scientific method. | https://en.wikipedia.org/wiki?curid=22939 |
13,613 | Although Aristotle’s principles of physics was criticized, it is important to identify his the evidence he based his views off of. When thinking of the history of science and math, it is notable to acknowledge the contributions made by older scientists. Aristotle’s science was the backbone of the science we learn in s... | https://en.wikipedia.org/wiki?curid=22939 |
13,614 | He also devised his own laws of motion that include 1) heavier objects will fall faster, the speed being proportional to the weight and 2) the speed of the object that is falling depends inversely on the density object it is falling through (ex. density of air). He also stated that, when it comes to violent motion (mot... | https://en.wikipedia.org/wiki?curid=22939 |
13,615 | The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was "The Book of Optics" (also known as Kitāb al-Manāẓir), written by Ibn al-Haytham, in which he conclusively disprove... | https://en.wikipedia.org/wiki?curid=22939 |
13,616 | The seven-volume "Book of Optics" ("Kitab al-Manathir") hugely influenced thinking across disciplines from the theory of visual perception to the nature of perspective in medieval art, in both the East and the West, for more than 600 years. Many later European scholars and fellow polymaths, from Robert Grosseteste and ... | https://en.wikipedia.org/wiki?curid=22939 |
13,617 | The translation of "The Book of Optics" had a huge impact on Europe. From it, later European scholars were able to build devices that replicated those Ibn al-Haytham had built and understand the way light works. From this, important inventions such as eyeglasses, magnifying glasses, telescopes, and cameras were develop... | https://en.wikipedia.org/wiki?curid=22939 |
13,618 | Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. | https://en.wikipedia.org/wiki?curid=22939 |
13,619 | Major developments in this period include the replacement of the geocentric model of the Solar System with the heliocentric Copernican model, the laws governing the motion of planetary bodies (determined by Kepler between 1609 and 1619), Galileo's pioneering work on telescopes and observational astronomy in the 16th an... | https://en.wikipedia.org/wiki?curid=22939 |
13,620 | The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from research efforts during the Industrial Revolution as energy needs increased. The laws comprising classical physics remain very widely used for objects on everyday scales travelling at non-relativistic speeds, since they provide a... | https://en.wikipedia.org/wiki?curid=22939 |
13,621 | Modern physics began in the early 20th century with the work of Max Planck in quantum theory and Albert Einstein's theory of relativity. Both of these theories came about due to inaccuracies in classical mechanics in certain situations. Classical mechanics predicted that the speed of light depends on the motion of the ... | https://en.wikipedia.org/wiki?curid=22939 |
13,622 | Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger and Paul Dirac. From this early work, and work in related fields, the Standard Model of particle physics was derived. Following the discovery of a particle with properties consistent with the Higgs boson at CERN in 2012, all fundamenta... | https://en.wikipedia.org/wiki?curid=22939 |
13,623 | In many ways, physics stems from ancient Greek philosophy. From Thales' first attempt to characterize matter, to Democritus' deduction that matter ought to reduce to an invariant state the Ptolemaic astronomy of a crystalline firmament, and Aristotle's book "Physics" (an early book on physics, which attempted to analyz... | https://en.wikipedia.org/wiki?curid=22939 |
13,624 | By the 19th century, physics was realized as a discipline distinct from philosophy and the other sciences. Physics, as with the rest of science, relies on philosophy of science and its "scientific method" to advance our knowledge of the physical world. The scientific method employs "a priori reasoning" as well as "a po... | https://en.wikipedia.org/wiki?curid=22939 |
13,625 | The development of physics has answered many questions of early philosophers but has also raised new questions. Study of the philosophical issues surrounding physics, the philosophy of physics, involves issues such as the nature of space and time, determinism, and metaphysical outlooks such as empiricism, naturalism an... | https://en.wikipedia.org/wiki?curid=22939 |
13,626 | Many physicists have written about the philosophical implications of their work, for instance Laplace, who championed causal determinism, and Erwin Schrödinger, who wrote on quantum mechanics. The mathematical physicist Roger Penrose has been called a Platonist by Stephen Hawking, a view Penrose discusses in his book, ... | https://en.wikipedia.org/wiki?curid=22939 |
13,627 | Though physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories was experimentally tested numerous times and found to be an adequate approximation of nature. For instance, the theory of classical mechanics accurately describes the motion of objects, provided they... | https://en.wikipedia.org/wiki?curid=22939 |
13,628 | These central theories are important tools for research into more specialized topics, and any physicist, regardless of their specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity. | https://en.wikipedia.org/wiki?curid=22939 |
13,629 | Classical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism. Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be di... | https://en.wikipedia.org/wiki?curid=22939 |
13,630 | Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light. Heat is a form of energy, the inte... | https://en.wikipedia.org/wiki?curid=22939 |
13,631 | Classical physics is generally concerned with matter and energy on the normal scale of observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on a very large or very small scale. For example, atomic and nuclear physics study matter on the smallest scale... | https://en.wikipedia.org/wiki?curid=22939 |
13,632 | The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics. Classical mechanics approximates nature as continuous, while quantum theory is concerned with the discrete nature of many phenomena at the atomic and subatomic level ... | https://en.wikipedia.org/wiki?curid=22939 |
13,633 | While physics aims to discover universal laws, its theories lie in explicit domains of applicability. | https://en.wikipedia.org/wiki?curid=22939 |
13,634 | Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match predictions provided by classical mechanics. Einstein contributed the f... | https://en.wikipedia.org/wiki?curid=22939 |
13,635 | Mathematics provides a compact and exact language used to describe the order in nature. This was noted and advocated by Pythagoras, Plato, Galileo, and Newton. | https://en.wikipedia.org/wiki?curid=22939 |
13,636 | Physics uses mathematics to organise and formulate experimental results. From those results, precise or estimated solutions are obtained, or quantitative results, from which new predictions can be made and experimentally confirmed or negated. The results from physics experiments are numerical data, with their units of ... | https://en.wikipedia.org/wiki?curid=22939 |
13,637 | Ontology is a prerequisite for physics, but not for mathematics. It means physics is ultimately concerned with descriptions of the real world, while mathematics is concerned with abstract patterns, even beyond the real world. Thus physics statements are synthetic, while mathematical statements are analytic. Mathematics... | https://en.wikipedia.org/wiki?curid=22939 |
13,638 | The distinction is clear-cut, but not always obvious. For example, mathematical physics is the application of mathematics in physics. Its methods are mathematical, but its subject is physical. The problems in this field start with a "mathematical model of a physical situation" (system) and a "mathematical description o... | https://en.wikipedia.org/wiki?curid=22939 |
13,639 | Pure physics is a branch of fundamental science (also called basic science). Physics is also called ""the" fundamental science" because all branches of natural science like chemistry, astronomy, geology, and biology are constrained by laws of physics. Similarly, chemistry is often called the central science because of ... | https://en.wikipedia.org/wiki?curid=22939 |
13,640 | Applied physics is a general term for physics research, which is intended for a particular use. An applied physics curriculum usually contains a few classes in an applied discipline, like geology or electrical engineering. It usually differs from engineering in that an applied physicist may not be designing something i... | https://en.wikipedia.org/wiki?curid=22939 |
13,641 | The approach is similar to that of applied mathematics. Applied physicists use physics in scientific research. For instance, people working on accelerator physics might seek to build better particle detectors for research in theoretical physics. | https://en.wikipedia.org/wiki?curid=22939 |
13,642 | Physics is used heavily in engineering. For example, statics, a subfield of mechanics, is used in the building of bridges and other static structures. The understanding and use of acoustics results in sound control and better concert halls; similarly, the use of optics creates better optical devices. An understanding o... | https://en.wikipedia.org/wiki?curid=22939 |
13,643 | With the standard consensus that the laws of physics are universal and do not change with time, physics can be used to study things that would ordinarily be mired in uncertainty. For example, in the study of the origin of the earth, one can reasonably model earth's mass, temperature, and rate of rotation, as a function... | https://en.wikipedia.org/wiki?curid=22939 |
13,644 | But there is also considerable interdisciplinarity, so many other important fields are influenced by physics (e.g., the fields of econophysics and sociophysics). | https://en.wikipedia.org/wiki?curid=22939 |
13,645 | Physicists use the scientific method to test the validity of a physical theory. By using a methodical approach to compare the implications of a theory with the conclusions drawn from its related experiments and observations, physicists are better able to test the validity of a theory in a logical, unbiased, and repeata... | https://en.wikipedia.org/wiki?curid=22939 |
13,646 | A scientific law is a concise verbal or mathematical statement of a relation that expresses a fundamental principle of some theory, such as Newton's law of universal gravitation. | https://en.wikipedia.org/wiki?curid=22939 |
13,647 | Theorists seek to develop mathematical models that both agree with existing experiments and successfully predict future experimental results, while experimentalists devise and perform experiments to test theoretical predictions and explore new phenomena. Although theory and experiment are developed separately, they str... | https://en.wikipedia.org/wiki?curid=22939 |
13,648 | Physicists who work at the interplay of theory and experiment are called phenomenologists, who study complex phenomena observed in experiment and work to relate them to a fundamental theory. | https://en.wikipedia.org/wiki?curid=22939 |
13,649 | Theoretical physics has historically taken inspiration from philosophy; electromagnetism was unified this way. Beyond the known universe, the field of theoretical physics also deals with hypothetical issues, such as parallel universes, a multiverse, and higher dimensions. Theorists invoke these ideas in hopes of solvin... | https://en.wikipedia.org/wiki?curid=22939 |
13,650 | Experimental physics expands, and is expanded by, engineering and technology. Experimental physicists who are involved in basic research design and perform experiments with equipment such as particle accelerators and lasers, whereas those involved in applied research often work in industry, developing technologies such... | https://en.wikipedia.org/wiki?curid=22939 |
13,651 | Physics covers a wide range of phenomena, from elementary particles (such as quarks, neutrinos, and electrons) to the largest superclusters of galaxies. Included in these phenomena are the most basic objects composing all other things. Therefore, physics is sometimes called the "fundamental science". Physics aims to de... | https://en.wikipedia.org/wiki?curid=22939 |
13,652 | For example, the ancient Chinese observed that certain rocks (lodestone and magnetite) were attracted to one another by an invisible force. This effect was later called magnetism, which was first rigorously studied in the 17th century. But even before the Chinese discovered magnetism, the ancient Greeks knew of other o... | https://en.wikipedia.org/wiki?curid=22939 |
13,653 | Contemporary research in physics can be broadly divided into nuclear and particle physics; condensed matter physics; atomic, molecular, and optical physics; astrophysics; and applied physics. Some physics departments also support physics education research and physics outreach. | https://en.wikipedia.org/wiki?curid=22939 |
13,654 | Since the 20th century, the individual fields of physics have become increasingly specialised, and today most physicists work in a single field for their entire careers. "Universalists" such as Einstein (1879–1955) and Lev Landau (1908–1968), who worked in multiple fields of physics, are now very rare. | https://en.wikipedia.org/wiki?curid=22939 |
13,655 | The major fields of physics, along with their subfields and the theories and concepts they employ, are shown in the following table. | https://en.wikipedia.org/wiki?curid=22939 |
13,656 | Particle physics is the study of the elementary constituents of matter and energy and the interactions between them. In addition, particle physicists design and develop the high-energy accelerators, detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many... | https://en.wikipedia.org/wiki?curid=22939 |
13,657 | Currently, the interactions of elementary particles and fields are described by the Standard Model. The model accounts for the 12 known particles of matter (quarks and leptons) that interact via the strong, weak, and electromagnetic fundamental forces. Dynamics are described in terms of matter particles exchanging gaug... | https://en.wikipedia.org/wiki?curid=22939 |
13,658 | Nuclear physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and ... | https://en.wikipedia.org/wiki?curid=22939 |
13,659 | Atomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules. The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of their relevant energy scales. All three ar... | https://en.wikipedia.org/wiki?curid=22939 |
13,660 | Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions, low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see hyperfine splitti... | https://en.wikipedia.org/wiki?curid=22939 |
13,661 | Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light. Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects but on the fundamental properties of optical fields and their int... | https://en.wikipedia.org/wiki?curid=22939 |
13,662 | Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong. | https://en.wikipedia.org/wiki?curid=22939 |
13,663 | The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed phases include the superfluid and the Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase e... | https://en.wikipedia.org/wiki?curid=22939 |
13,664 | Condensed matter physics is the largest field of contemporary physics. Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term "condensed matter physics" was apparently coined by Philip Anderson when he renamed his research group—previously "so... | https://en.wikipedia.org/wiki?curid=22939 |
13,665 | Astrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the Solar System, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including m... | https://en.wikipedia.org/wiki?curid=22939 |
13,666 | The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere make space-based observations necessary for inf... | https://en.wikipedia.org/wiki?curid=22939 |
13,667 | Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe is expanding, as shown by the Hubble diagram, prompted ri... | https://en.wikipedia.org/wiki?curid=22939 |
13,668 | The Big Bang was confirmed by the success of Big Bang nucleosynthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle. Cosmologists have recently established the ΛCDM model of the evolu... | https://en.wikipedia.org/wiki?curid=22939 |
13,669 | Numerous possibilities and discoveries are anticipated to emerge from new data from the Fermi Gamma-ray Space Telescope over the upcoming decade and vastly revise or clarify existing models of the universe. In particular, the potential for a tremendous discovery surrounding dark matter is possible over the next several... | https://en.wikipedia.org/wiki?curid=22939 |
13,670 | IBEX is already yielding new astrophysical discoveries: "No one knows what is creating the ENA (energetic neutral atoms) ribbon" along the termination shock of the solar wind, "but everyone agrees that it means the textbook picture of the heliosphere—in which the Solar System's enveloping pocket filled with the solar w... | https://en.wikipedia.org/wiki?curid=22939 |
13,671 | In condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers. | https://en.wikipedia.org/wiki?curid=22939 |
13,672 | In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrin... | https://en.wikipedia.org/wiki?curid=22939 |
13,673 | Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include... | https://en.wikipedia.org/wiki?curid=22939 |
13,674 | These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the... | https://en.wikipedia.org/wiki?curid=22939 |
13,675 | The Gregorian calendar is the calendar used in most parts of the world. It was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years differently so as to make the average calendar year 365.2425 days long, more closely... | https://en.wikipedia.org/wiki?curid=23306251 |
13,676 | There were two reasons to establish the Gregorian calendar. First, the Julian calendar assumed incorrectly that the average solar year is exactly 365.25 days long, an overestimate of a little under one day per century, and thus has a leap year every four years without exception. The Gregorian reform shortened the avera... | https://en.wikipedia.org/wiki?curid=23306251 |
13,677 | The reform was adopted initially by the Catholic countries of Europe and their overseas possessions. Over the next three centuries, the Protestant and Eastern Orthodox countries also moved to what they called the "Improved calendar", with Greece being the last European country to adopt the calendar (for civil use only)... | https://en.wikipedia.org/wiki?curid=23306251 |
13,678 | The Gregorian calendar, like the Julian calendar, is a solar calendar with 12 months of 28–31 days each. The year in both calendars consists of 365 days, with a leap day being added to February in the leap years. The months and length of months in the Gregorian calendar are the same as for the Julian calendar. The only... | https://en.wikipedia.org/wiki?curid=23306251 |
13,679 | A leap year normally occurs every four years: the leap day, historically, was inserted by doubling 24 February there were indeed two days dated 24 February. However, for many years it has been customary to put the extra day at the end of the month of February, adding a 29 February for the leap day. Before the 1969 revi... | https://en.wikipedia.org/wiki?curid=23306251 |
13,680 | Gregorian years are identified by consecutive year numbers. A calendar date is fully specified by the year (numbered according to a calendar era, in this case "Anno Domini" or Common Era), the month (identified by name or number), and the day of the month (numbered sequentially starting from 1). Although the calendar y... | https://en.wikipedia.org/wiki?curid=23306251 |
13,681 | Calendar cycles repeat completely every 400 years, which equals 146,097 days. Of these 400 years, 303 are regular years of 365 days and 97 are leap years of 366 days. A mean calendar year is days = 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds. During intervals that do not contain any century common ye... | https://en.wikipedia.org/wiki?curid=23306251 |
13,682 | The Gregorian calendar was a reform of the Julian calendar. It was instituted by papal bull "Inter gravissimas" dated 24 February 1582 by Pope Gregory XIII, after whom the calendar is named. The motivation for the adjustment was to bring the date for the celebration of Easter to the time of year in which it was celebra... | https://en.wikipedia.org/wiki?curid=23306251 |
13,683 | Because the date of Easter is a function the "computus" of the date of the (northern hemisphere) spring equinox, the Catholic Church considered unacceptable the increasing divergence between the canonical date of the equinox and observed reality. Easter is celebrated on the Sunday after the ecclesiastical full moon on ... | https://en.wikipedia.org/wiki?curid=23306251 |
13,684 | Bede, writing in the 8th century, showed that the accumulated error in his time was more than three days. Roger Bacon in c. 1200 estimated the error at seven or eight days. Dante, writing c. 1300, was aware of the need for calendar reform. An attempt to go forward with such a reform was undertaken by Pope Sixtus IV, wh... | https://en.wikipedia.org/wiki?curid=23306251 |
13,685 | In 1545, the Council of Trent authorised Pope Paul III to reform the calendar, requiring that the date of the vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for more consisten... | https://en.wikipedia.org/wiki?curid=23306251 |
13,686 | In 1577, a was sent to expert mathematicians outside the reform commission for comments. Some of these experts, including Giambattista Benedetti and Giuseppe Moleto, believed Easter should be computed from the true motions of the Sun and Moon, rather than using a tabular method, but these recommendations were not adopt... | https://en.wikipedia.org/wiki?curid=23306251 |
13,687 | Lilius's proposal included reducing the number of leap years in four centuries from 100 to 97, by making three out of four centurial years common instead of leap years. He also produced an original and practical scheme for adjusting the epacts of the Moon when calculating the annual date of Easter, solving a long-stand... | https://en.wikipedia.org/wiki?curid=23306251 |
13,688 | Ancient tables provided the Sun's mean longitude. The German mathematician Christopher Clavius, the architect of the Gregorian calendar, noted that the tables agreed neither on the time when the Sun passed through the vernal equinox nor on the length of the mean tropical year. Tycho Brahe also noticed discrepancies. Th... | https://en.wikipedia.org/wiki?curid=23306251 |
13,689 | Lilius's proposals had two components. First, he proposed a correction to the length of the year. The mean tropical year is 365.24219 days long. A commonly used value in Lilius's time, from the Alfonsine tables, is 365.2425463 days. As the average length of a Julian year is 365.25 days, the Julian year is almost 11 min... | https://en.wikipedia.org/wiki?curid=23306251 |
13,690 | Lilius's work was expanded upon by Christopher Clavius in a closely argued, 800-page volume. He would later defend his and Lilius's work against detractors. Clavius's opinion was that the correction should take place in one move, and it was this advice that prevailed with Gregory. | https://en.wikipedia.org/wiki?curid=23306251 |
13,691 | The second component consisted of an approximation that would provide an accurate yet simple, rule-based calendar. Lilius's formula was a 10-day correction to revert the drift since the Council of Nicaea, and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. The proposed rule was that "ye... | https://en.wikipedia.org/wiki?curid=23306251 |
13,692 | The 19-year cycle used for the lunar calendar required revision because the astronomical new moon was, at the time of the reform, four days before the calculated new moon. It was to be corrected by one day every 300 or 400 years (8 times in 2500 years) along with corrections for the years that are no longer leap years ... | https://en.wikipedia.org/wiki?curid=23306251 |
13,693 | When the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of 10 days. The Julian calendar day Thursday, 4 October 1582 was followed by the first day of the Gregorian calendar, Friday, 15 October 1582 (the cycle of weekdays was not affected). | https://en.wikipedia.org/wiki?curid=23306251 |
13,694 | A month after having decreed the reform, the pope (with a brief of 3 April 1582) granted to one Antoni Lilio the exclusive right to publish the calendar for a period of ten years. The was printed by Vincenzo Accolti, one of the first calendars printed in Rome after the reform, notes at the bottom that it was signed wit... | https://en.wikipedia.org/wiki?curid=23306251 |
13,695 | Although Gregory's reform was enacted in the most solemn of forms available to the Church, the bull had no authority beyond the Catholic Church (of which he was the supreme religious authority) and the Papal States (which he personally ruled). The changes that he was proposing were changes to the civil calendar, over w... | https://en.wikipedia.org/wiki?curid=23306251 |
13,696 | The bull became the law of the Catholic Church in 1582, but it was not recognised by Protestant Churches, Eastern Orthodox Churches, Oriental Orthodox Churches, and a few others. Consequently, the days on which Easter and related holidays were celebrated by different Christian Churches again diverged. | https://en.wikipedia.org/wiki?curid=23306251 |
13,697 | On 29 September 1582, Philip II of Spain decreed the change from the Julian to the Gregorian calendar. This affected much of Roman Catholic Europe, as Philip was at the time ruler over Spain and Portugal as well as much of Italy. In these territories, as well as in the Polish–Lithuanian Commonwealth (ruled by Anna Jagi... | https://en.wikipedia.org/wiki?curid=23306251 |
13,698 | Many Protestant countries initially objected to adopting a Catholic innovation; some Protestants feared the new calendar was part of a plot to return them to the Catholic fold. For example, the British could not bring themselves to adopt the Catholic system explicitly: the Annexe to their Calendar (New Style) Act 1750 ... | https://en.wikipedia.org/wiki?curid=23306251 |
13,699 | Britain and the British Empire (including the eastern part of what is now the United States) adopted the Gregorian calendar in 1752. Sweden followed in 1753. | https://en.wikipedia.org/wiki?curid=23306251 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.