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81-625: Orreries are typically driven by a clockwork mechanism with a globe representing the Sun at the centre, and with a planet at the end of each of a series of arms. The Antikythera mechanism , discovered in 1901 in a wreck off the Greek island of Antikythera in the Mediterranean Sea, exhibited the diurnal motions of the Sun , Moon , and the five planets known to the ancient Greeks . It has been dated between 205 to 87 BC. The mechanism

162-413: A liberal education , studying languages, music , history , geography , mathematics , logic , and rhetoric , alongside dancing , fencing and horse riding . In 1644, Huygens had as his mathematical tutor Jan Jansz Stampioen , who assigned the 15-year-old a demanding reading list on contemporary science. Descartes was later impressed by his skills in geometry, as was Mersenne, who christened him

243-594: A broad range of correspondents, though with some difficulty after 1648 due to the five-year Fronde in France. Visiting Paris in 1655, Huygens called on Ismael Boulliau to introduce himself, who took him to see Claude Mylon . The Parisian group of savants that had gathered around Mersenne held together into the 1650s, and Mylon, who had assumed the secretarial role, took some trouble to keep Huygens in touch. Through Pierre de Carcavi Huygens corresponded in 1656 with Pierre de Fermat, whom he admired greatly. The experience

324-534: A career. Huygens generally wrote in French or Latin. In 1646, while still a college student at Leiden, he began a correspondence with his father's friend, Marin Mersenne , who died soon afterwards in 1648. Mersenne wrote to Constantijn on his son's talent for mathematics, and flatteringly compared him to Archimedes on 3 January 1647. The letters show Huygens's early interest in mathematics. In October 1646 there

405-473: A certain amount of hiking in order to visit them. A census of all permanent human orreries has been initiated by the French group F-HOU with a new effort to study their impact for education in schools. A map of known human orreries is available. A normal mechanical clock could be used to produce an extremely simple orrery to demonstrate the principle, with the Sun in the centre, Earth on the minute hand and Jupiter on

486-402: A collection of solutions to classical problems at the end of the work under the title Illustrium Quorundam Problematum Constructiones ( Construction of some illustrious problems ). Huygens became interested in games of chance after he visited Paris in 1655 and encountered the work of Fermat, Blaise Pascal and Girard Desargues years earlier. He eventually published what was, at the time,

567-621: A complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle . Huygens invented the pendulum clock in 1657, which he patented the same year. His horological research resulted in an extensive analysis of the pendulum in Horologium Oscillatorium (1673), regarded as one of the most important 17th century works on mechanics. While it contains descriptions of clock designs, most of

648-559: A full cycle of rotation. His approach was thus equivalent to the principle of virtual work . Huygens was also the first to recognize that, for these homogeneous solids, their specific weight and their aspect ratio are the essentials parameters of hydrostatic stability . Huygens was the leading European natural philosopher between Descartes and Newton. However, unlike many of his contemporaries, Huygens had no taste for grand theoretical or philosophical systems and generally avoided dealing with metaphysical issues (if pressed, he adhered to

729-565: A larger audience until the publication of De Motu Corporum ex Percussione ( Concerning the motion of colliding bodies ) in 1703. In addition to his mathematical and mechanical works, Huygens made important scientific discoveries: he was the first to identify Titan as one of Saturn's moons in 1655, invented the pendulum clock in 1657, and explained Saturn's strange appearance as due to a ring in 1659; all these discoveries brought him fame across Europe. On 3 May 1661, Huygens, together with astronomer Thomas Streete and Richard Reeve, observed

810-530: A meeting at Gresham College . Shortly afterwards, he reevaluated Boyle's experimental design and developed a series of experiments meant to test a new hypothesis. It proved a yearslong process that brought to the surface a number of experimental and theoretical issues, and which ended around the time he became a Fellow of the Royal Society. Despite the replication of results of Boyle's experiments trailing off messily, Huygens came to accept Boyle's view of

891-564: A pendulum clock, which has 9 weights or ponds. The planets move around the model in real time. An innovative concept is to have people play the role of the moving planets and other Solar System objects. Such a model, called a human orrery, has been laid out at the Armagh Observatory. Clockwork Too Many Requests If you report this error to the Wikimedia System Administrators, please include

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972-590: A planet, and with Mercury and Venus revolving around the Sun as its moons . At the court of William IV, Landgrave of Hesse-Kassel two complicated astronomic clocks were built in 1561 and 1563–1568. These use four sides to show the ecliptical positions of the Sun, Mercury, Venus, Mars, Jupiter, Saturn, the Moon, Sun and Dragon (Nodes of the Moon) according to Ptolemy , a calendar, the sunrise and sunset, and an automated celestial sphere with an animated Sun symbol which, for

1053-443: A segment of a circle, resulting in a faster and accurate approximation of the circle quadrature. From these theorems, Huygens obtained two set of values for π : the first between 3.1415926 and 3.1415927, and the second between 3.1415926533 and 3.1415926538. Huygens also showed that, in the case of the hyperbola , the same approximation with parabolic segments produces a quick and simple method to calculate logarithms . He appended

1134-645: A telescope with two lenses to diminish the amount of dispersion . As a mathematician, Huygens developed the theory of evolutes and wrote on games of chance and the problem of points in Van Rekeningh in Spelen van Gluck , which Frans van Schooten translated and published as De Ratiociniis in Ludo Aleae (1657). The use of expected values by Huygens and others would later inspire Jacob Bernoulli's work on probability theory . Christiaan Huygens

1215-719: A vain mission to meet the French Foreign Minister Arnauld de Pomponne . Leibniz was working on a calculating machine at the time and, after a short visit to London in early 1673, he was tutored in mathematics by Huygens until 1676. An extensive correspondence ensued over the years, in which Huygens showed at first reluctance to accept the advantages of Leibniz's infinitesimal calculus . Huygens moved back to The Hague in 1681 after suffering another bout of serious depressive illness. In 1684, he published Astroscopia Compendiaria on his new tubeless aerial telescope . He attempted to return to France in 1685 but

1296-473: Is considered one of the first orreries. It was geocentric and used as a mechanical calculator to calculate astronomical positions. Cicero , the Roman philosopher and politician writing in the first century BC, has references describing planetary mechanical models. According to him, the Greek polymaths Thales and Posidonius both constructed a device modeling celestial motion. In 1348, Giovanni Dondi built

1377-515: Is in Glasgow's Kelvingrove Art Gallery and Museum . The Eisinga Planetarium built by a wool carder named Eise Eisinga in his own living room, in the small city of Franeker in Friesland , is in fact an orrery. It was constructed between 1774 and 1781. The base of the model faces down from the ceiling of the room, with most of the mechanical works in the space above the ceiling. It is driven by

1458-480: Is the suspension bridge and the demonstration that a hanging chain is not a parabola , as Galileo thought. Huygens would later label that curve the catenaria ( catenary ) in 1690 while corresponding with Gottfried Leibniz . In the next two years (1647–48), Huygens's letters to Mersenne covered various topics, including a mathematical proof of the law of free fall , the claim by Grégoire de Saint-Vincent of circle quadrature , which Huygens showed to be wrong,

1539-659: The Cartesian philosophy of his time). Instead, Huygens excelled in extending the work of his predecessors, such as Galileo, to derive solutions to unsolved physical problems that were amenable to mathematical analysis. In particular, he sought explanations that relied on contact between bodies and avoided action at a distance . In common with Robert Boyle and Jacques Rohault , Huygens advocated an experimentally oriented, mechanical natural philosophy during his Paris years. Already in his first visit to England in 1661, Huygens had learnt about Boyle's air pump experiments during

1620-476: The Royal Society of London elected Huygens a Fellow in 1663, making him its first foreign member when he was just 34 years old. The Montmor Academy , started in the mid-1650s, was the form the old Mersenne circle took after his death. Huygens took part in its debates and supported those favouring experimental demonstration as a check on amateurish attitudes. He visited Paris a third time in 1663; when

1701-536: The Second Anglo-Dutch War , was guarded. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He later published them in the Journal des Sçavans in 1669. In 1659 Huygens found the constant of gravitational acceleration and stated what is now known as the second of Newton's laws of motion in quadratic form. He derived geometrically the now standard formula for

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1782-405: The a priori attitude of Descartes, but neither would he accept aspects of gravitational attractions that were not attributable in principle to contact between particles. The approach used by Huygens also missed some central notions of mathematical physics, which were not lost on others. In his work on pendulums Huygens came very close to the theory of simple harmonic motion ; the topic, however,

1863-479: The centre of gravity of the system remains the same in velocity and direction, which Huygens called the conservation of "quantity of movement" . While others at the time were studying impact, Huygens's theory of collisions was more general. These results became the main reference point and the focus for further debates through correspondence and in a short article in Journal des Sçavans but would remain unknown to

1944-402: The centrifugal force , exerted on an object when viewed in a rotating frame of reference , for instance when driving around a curve. In modern notation: with m the mass of the object, ω the angular velocity , and r the radius . Huygens collected his results in a treatise under the title De vi Centrifuga , unpublished until 1703, where the kinematics of free fall were used to produce

2025-523: The pendulum clock , the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters , and the first mathematical and mechanistic explanation of an unobservable physical phenomenon. Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione , completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically

2106-453: The revocation of the Edict of Nantes precluded this move. His father died in 1687, and he inherited Hofwijck, which he made his home the following year. On his third visit to England, Huygens met Isaac Newton in person on 12 June 1689. They spoke about Iceland spar , and subsequently corresponded about resisted motion. Huygens returned to mathematical topics in his last years and observed

2187-540: The Øresund to visit Descartes in Stockholm . This did not happen as Descartes had died in the interim. Although his father Constantijn had wished his son Christiaan to be a diplomat, circumstances kept him from becoming so. The First Stadtholderless Period that began in 1650 meant that the House of Orange was no longer in power, removing Constantijn's influence. Further, he realized that his son had no interest in such

2268-449: The "new Archimedes ." At sixteen years of age, Constantijn sent Huygens to study law and mathematics at Leiden University , where he studied from May 1645 to March 1647. Frans van Schooten was an academic at Leiden from 1646, and became a private tutor to Huygens and his elder brother, Constantijn Jr., replacing Stampioen on the advice of Descartes. Van Schooten brought Huygens's mathematical education up to date, introducing him to

2349-795: The 1930s. The pendulum clock was much more accurate than the existing verge and foliot clocks and was immediately popular, quickly spreading over Europe. Clocks prior to this would lose about 15 minutes per day, whereas Huygens's clock would lose about 15 seconds per day. Although Huygens patented and contracted the construction of his clock designs to Salomon Coster in The Hague, he did not make much money from his invention. Pierre Séguier refused him any French rights, while Simon Douw in Rotterdam and Ahasuerus Fromanteel in London copied his design in 1658. The oldest known Huygens-style pendulum clock

2430-512: The Circle , showing that the ratio of the circumference to its diameter or pi ( π ) must lie in the first third of that interval. Using a technique equivalent to Richardson extrapolation , Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of

2511-588: The English lecturer John Pell . His time in Breda ended around the time when his brother Lodewijk, who was enrolled at the school, duelled with another student. Huygens left Breda after completing his studies in August 1649 and had a stint as a diplomat on a mission with Henry, Duke of Nassau . It took him to Bentheim , then Flensburg . He took off for Denmark, visited Copenhagen and Helsingør , and hoped to cross

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2592-538: The French Académie was not always easy, and in 1670 Huygens, seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die. However, the aftermath of the Franco-Dutch War (1672–78), and particularly England's role in it, may have damaged his later relationship with the Royal Society. Robert Hooke , as a Royal Society representative, lacked

2673-674: The Montmor Academy closed down the next year, Huygens advocated for a more Baconian program in science. Two years later, in 1666, he moved to Paris on an invitation to fill a leadership position at King Louis XIV 's new French Académie des sciences . While at the Académie in Paris, Huygens had an important patron and correspondent in Jean-Baptiste Colbert , First Minister to Louis XIV. However, his relationship with

2754-495: The Moon around the Earth. In one orrery, these three motions could be mounted on a common table, separately using the central spindle as a prime mover. All orreries are planetariums . The term orrery has only existed since 1714. A grand orrery is one that includes the outer planets known at the time of its construction. The word planetarium has shifted meaning, and now usually refers to hemispherical theatres in which images of

2835-459: The Moon, and the Sun is called a tellurion or tellurium, and one which only includes the Earth and the Moon is a lunarium . A jovilabe is a model of Jupiter and its moons. A planetarium will show the orbital period of each planet and the rotation rate , as shown in the table above. A tellurion will show the Earth with the Moon revolving around the Sun. It will use the angle of inclination of

2916-473: The Sun in ellipses . In 1687 Isaac Newton explained the cause of elliptic motion in his theory of gravitation . There is an orrery built by clock makers George Graham and Thomas Tompion dated c.  1710 in the History of Science Museum, Oxford . Graham gave the first model, or its design, to the celebrated instrument maker John Rowley of London to make a copy for Prince Eugene of Savoy . Rowley

2997-423: The Sun in 0.24 of an Earth year, while Phobos and Deimos orbit Mars in a similar 4:1 time ratio. Planetarium operators wishing to show this have placed a red cap on the Sun (to make it resemble Mars) and turned off all the planets but Mercury and Earth. Similar approximations can be used to show Pluto and its five moons. Shoemaker John Fulton of Fenwick, Ayrshire , built three between 1823 and 1833. The last

3078-488: The Sun revolved daily around the Earth . He observed that some Greek philosophers such as Aristarchus of Samos had proposed a heliocentric universe. This simplified the apparent epicyclic motions of the planets, making it feasible to represent the planets' paths as simple circles. This could be modeled by the use of gears. Tycho Brahe 's improved instruments made precise observations of the skies (1576–1601), and from these Johannes Kepler (1621) deduced that planets orbited

3159-507: The acoustical phenomenon now known as flanging in 1693. Two years later, on 8 July 1695, Huygens died in The Hague and was buried, like his father before him, in an unmarked grave at the Grote Kerk . Huygens never married. Huygens first became internationally known for his work in mathematics, publishing a number of important results that drew the attention of many European geometers. Huygens's preferred method in his published works

3240-454: The areas of hyperbolas, ellipses, and circles that paralleled Archimedes's work on conic sections, particularly his Quadrature of the Parabola . The second part included a refutation to Grégoire de Saint-Vincent's claims on circle quadrature, which he had discussed with Mersenne earlier. Huygens demonstrated that the centre of gravity of a segment of any hyperbola , ellipse , or circle

3321-531: The book is an analysis of pendular motion and a theory of curves . In 1655, Huygens began grinding lenses with his brother Constantijn to build refracting telescopes . He discovered Saturn's biggest moon, Titan, and was the first to explain Saturn's strange appearance as due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic." In 1662 Huygens developed what is now called the Huygenian eyepiece ,

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3402-475: The concepts of a "fair game" and equitable contract (i.e., equal division when the chances are equal), and extended the argument to set up a non-standard theory of expected values. His success in applying algebra to the realm of chance, which hitherto seemed inaccessible to mathematicians, demonstrated the power of combining Euclidean synthetic proofs with the symbolic reasoning found in the works of Viète and Descartes. Huygens included five challenging problems at

3483-669: The correct laws, including the conservation of the product of mass times the square of the speed for hard bodies, and the conservation of quantity of motion in one direction for all bodies. An important step was his recognition of the Galilean invariance of the problems. Huygens had worked out the laws of collision from 1652 to 1656 in a manuscript entitled De Motu Corporum ex Percussione , though his results took many years to be circulated. In 1661, he passed them on in person to William Brouncker and Christopher Wren in London. What Spinoza wrote to Henry Oldenburg about them in 1666, during

3564-511: The details below. Request from 172.68.168.226 via cp1108 cp1108, Varnish XID 217643891 Upstream caches: cp1108 int Error: 429, Too Many Requests at Thu, 28 Nov 2024 07:52:14 GMT Christiaan Huygens Christiaan Huygens , Lord of Zeelhem , FRS ( / ˈ h aɪ ɡ ən z / HY -gənz , US also / ˈ h ɔɪ ɡ ən z / HOY -gənz ; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens ; Latin : Hugenius ; 14 April 1629 – 8 July 1695)

3645-466: The end of the book that became the standard test for anyone wishing to display their mathematical skill in games of chance for the next sixty years. People who worked on these problems included Abraham de Moivre , Jacob Bernoulli, Johannes Hudde , Baruch Spinoza , and Leibniz. Huygens had earlier completed a manuscript in the manner of Archimedes's On Floating Bodies entitled De Iis quae Liquido Supernatant ( About parts floating above liquids ). It

3726-543: The equator from the table above to show how it rotates around its own axis. It will show the Earth's Moon, rotating around the Earth. A lunarium is designed to show the complex motions of the Moon as it revolves around the Earth. Orreries are usually not built to scale . Human orreries, where humans move about as the planets, have also been constructed, but most are temporary. There is a permanent human orrery at Armagh Observatory in Northern Ireland , which has

3807-525: The finesse to handle the situation in 1673. The physicist and inventor Denis Papin was an assistant to Huygens from 1671. One of their projects, which did not bear fruit directly, was the gunpowder engine . Huygens made further astronomical observations at the Académie using the observatory recently completed in 1672. He introduced Nicolaas Hartsoeker to French scientists such as Nicolas Malebranche and Giovanni Cassini in 1678. The young diplomat Leibniz met Huygens while visiting Paris in 1672 on

3888-460: The first generalized conception of force prior to Newton. The general idea for the centrifugal force, however, was published in 1673 and was a significant step in studying orbits in astronomy. It enabled the transition from Kepler's third law of planetary motion to the inverse square law of gravitation. Yet, the interpretation of Newton's work on gravitation by Huygens differed from that of Newtonians such as Roger Cotes : he did not insist on

3969-483: The first graph of a continuous distribution function under the assumption of a uniform death rate , and used it to solve problems in joint annuities . Contemporaneously, Huygens, who played the harpsichord , took an interest in Simon Stevin's theories on music; however, he showed very little concern to publish his theories on consonance , some of which were lost for centuries. For his contributions to science,

4050-408: The first known clock driven mechanism of the system. It displays the ecliptic position of the Moon, Sun, Mercury , Venus , Mars , Jupiter and Saturn according to the complicated geocentric Ptolemaic planetary theories. The clock itself is lost, but Dondi left a complete description of its astronomic gear trains . As late as 1650, P. Schirleus built a geocentric planetarium with the Sun as

4131-818: The first time on a celestial globe, shows the real position of the Sun, including the equation of time . The clocks are now on display in Kassel at the Astronomisch-Physikalisches Kabinett and in Dresden at the Mathematisch-Physikalischer Salon . In De revolutionibus orbium coelestium , published in Nuremberg in 1543, Nicolaus Copernicus challenged the Western teaching of a geocentric universe in which

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4212-458: The following progression: 4 + 0 10 , 4 + 3 10 , 4 + 6 10 , 4 + 12 10 , 4 + 24 10 , . . . {\displaystyle {\frac {4+0}{10}},{\frac {4+3}{10}},{\frac {4+6}{10}},{\frac {4+12}{10}},{\frac {4+24}{10}},...} That is, 0.4, 0.7, 1.0, 1.6, 2.8, ... The numbers refer to astronomical units ,

4293-404: The formula in classical mechanics for the centrifugal force in his work De vi Centrifuga , a decade before Newton . In optics, he is best known for his wave theory of light , which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light , until Augustin-Jean Fresnel adapted Huygens's principle to give

4374-539: The gear trains needed to represent a year of 365.242 days, and used that to produce the cycles of the principal planets. Joseph Wright 's painting A Philosopher giving a Lecture on the Orrery ( c.  1766 ), which hangs in the Derby Museum and Art Gallery , depicts a group listening to a lecture by a natural philosopher . The Sun in a brass orrery provides the only light in the room. The orrery depicted in

4455-457: The hour hand; Earth would make 12 revolutions around the Sun for every 1 revolution of Jupiter. As Jupiter's actual year is 11.86 Earth years long, the model would lose accuracy rapidly. Many planetariums have a projection orrery , which projects onto the dome of the planetarium a Sun with either dots or small images of the planets. These usually are limited to the planets from Mercury to Saturn, although some include Uranus. The light sources for

4536-413: The mathematics of Thomas Hobbes . Persisting in trying to explain the errors Hobbes had fallen into, he made an international reputation. Huygens's next publication was De Circuli Magnitudine Inventa ( New findings in the measurement of the circle ), published in 1654. In this work, Huygens was able to narrow the gap between the circumscribed and inscribed polygons found in Archimedes's Measurement of

4617-529: The mean distance between Sun and Earth, which is 1.496 × 10 km (93 × 10 miles). The Derby Orrery does not show mean distance, but demonstrated the relative planetary movements. The Eisinga Planetarium was built from 1774 to 1781 by Eise Eisinga in his home in Franeker , in the Netherlands. It displays the planets across the width of a room's ceiling, and has been in operation almost continually since it

4698-479: The most coherent presentation of a mathematical approach to games of chance in De Ratiociniis in Ludo Aleae ( On reasoning in games of chance ). Frans van Schooten translated the original Dutch manuscript into Latin and published it in his Exercitationum Mathematicarum (1657). The work contains early game-theoretic ideas and deals in particular with the problem of points . Huygens took from Pascal

4779-408: The night sky are projected onto an overhead surface. Orreries can range widely in size from hand-held to room-sized. An orrery is used to demonstrate the motion of the planets, while a mechanical device used to predict eclipses and transits is called an astrarium . An orrery should properly include the Sun, the Earth and the Moon (plus optionally other planets). A model that only includes the Earth,

4860-425: The painting has rings, which give it an appearance similar to that of an armillary sphere . The demonstration was thereby able to depict eclipses . To put this in chronological context, in 1762 John Harrison 's marine chronometer first enabled accurate measurement of longitude . In 1766, astronomer Johann Daniel Titius first demonstrated that the mean distance of each planet from the Sun could be represented by

4941-463: The paraboloid by a clever application of Torricelli's principle (i.e., that bodies in a system move only if their centre of gravity descends). He then proves the general theorem that, for a floating body in equilibrium, the distance between its centre of gravity and its submerged portion is at a minimum. Huygens uses this theorem to arrive at original solutions for the stability of floating cones , parallelepipeds , and cylinders , in some cases through

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5022-508: The planet Mercury transit over the Sun using Reeve's telescope in London. Streete then debated the published record of Hevelius , a controversy mediated by Henry Oldenburg . Huygens passed to Hevelius a manuscript of Jeremiah Horrocks on the transit of Venus in 1639 , printed for the first time in 1662. In that same year, Sir Robert Moray sent Huygens John Graunt 's life table , and shortly after Huygens and his brother Lodewijk dabbled on life expectancy . Huygens eventually created

5103-535: The planets are projected onto mirrors which are geared to a motor which drives the images on the dome. Typically the Earth will circle the Sun in one minute, while the other planets will complete an orbit in time periods proportional to their actual motion. Thus Venus, which takes 224.7 days to orbit the Sun, will take 37 seconds to complete an orbit on an orrery, and Jupiter will take 11 minutes, 52 seconds. Some planetariums have taken advantage of this to use orreries to simulate planets and their moons. Thus Mercury orbits

5184-459: The rectification of the ellipse, projectiles, and the vibrating string . Some of Mersenne's concerns at the time, such as the cycloid (he sent Huygens Torricelli 's treatise on the curve), the centre of oscillation , and the gravitational constant , were matters Huygens only took seriously later in the 17th century. Mersenne had also written on musical theory. Huygens preferred meantone temperament ; he innovated in 31 equal temperament (which

5265-549: The six ancient planets, Ceres , and comets Halley and Encke . Uranus and beyond are also shown, but in a fairly limited way. Another is at Sky's the Limit Observatory and Nature Center in Twentynine Palms, California ; it is a true to scale (20 billion to one), true to position (accurate to within four days) human orrery. The first four planets are relatively close to one another, but the next four require

5346-497: The universe this way made the theory of collisions central to physics, as only explanations that involved matter in motion could be truly intelligible. While Huygens was influenced by the Cartesian approach, he was less doctrinaire. He studied elastic collisions in the 1650s but delayed publication for over a decade. Huygens concluded quite early that Descartes's laws for elastic collisions were largely wrong, and he formulated

5427-492: The void against the Cartesian denial of it. Newton's influence on John Locke was mediated by Huygens, who assured Locke that Newton's mathematics was sound, leading to Locke's acceptance of a corpuscular-mechanical physics. The general approach of the mechanical philosophers was to postulate theories of the kind now called "contact action." Huygens adopted this method but not without seeing its limitations, while Leibniz, his student in Paris, later abandoned it. Understanding

5508-556: The work of Viète , Descartes, and Fermat . After two years, starting in March 1647, Huygens continued his studies at the newly founded Orange College , in Breda , where his father was a curator . Constantijn Huygens was closely involved in the new College, which lasted only to 1669; the rector was André Rivet . Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber while attending college, and had mathematics classes with

5589-473: Was a Dutch mathematician , physicist , engineer , astronomer , and inventor who is regarded as a key figure in the Scientific Revolution . In physics, Huygens made seminal contributions to optics and mechanics , while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan . As an engineer and inventor, he improved the design of telescopes and invented

5670-455: Was a diplomat and advisor to the House of Orange , in addition to being a poet and a musician. He corresponded widely with intellectuals across Europe; his friends included Galileo Galilei , Marin Mersenne , and René Descartes . Christiaan was educated at home until the age of sixteen, and from a young age liked to play with miniatures of mills and other machines. From his father he received

5751-552: Was bittersweet and somewhat puzzling since it became clear that Fermat had dropped out of the research mainstream, and his priority claims could probably not be made good in some cases. Besides, Huygens was looking by then to apply mathematics to physics, while Fermat's concerns ran to purer topics. Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead. In his early days, his mentor Frans van Schooten provided technical feedback and

5832-474: Was born on 14 April 1629 in The Hague , into a rich and influential Dutch family, the second son of Constantijn Huygens . Christiaan was named after his paternal grandfather. His mother, Suzanna van Baerle , died shortly after giving birth to Huygens's sister. The couple had five children: Constantijn (1628), Christiaan (1629), Lodewijk (1631), Philips (1632) and Suzanna (1637). Constantijn Huygens

5913-482: Was cautious for the sake of his reputation. Between 1651 and 1657, Huygens published a number of works that showed his talent for mathematics and his mastery of classical and analytical geometry , increasing his reach and reputation among mathematicians. Around the same time, Huygens began to question Descartes's laws of collision , which were largely wrong, deriving the correct laws algebraically and later by way of geometry. He showed that, for any system of bodies,

5994-413: Was commissioned to make another copy for his patron Charles Boyle, 4th Earl of Orrery , from which the device took its name in English. This model was presented to Charles' son John, later the 5th Earl of Cork and 5th Earl of Orrery . Independently, Christiaan Huygens published in 1703 details of a heliocentric planetary machine which he had built while living in Paris between 1665 and 1681. He calculated

6075-573: Was covered fully for the first time by Newton in Book II of the Principia Mathematica (1687). In 1678 Leibniz picked out of Huygens's work on collisions the idea of conservation law that Huygens had left implicit. In 1657, inspired by earlier research into pendulums as regulating mechanisms, Huygens invented the pendulum clock, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years until

6156-546: Was created. This orrery is a planetarium in both senses of the word: a complex machine showing planetary orbits, and a theatre for depicting the planets' movement. Eisinga house was bought by the Dutch Royal family who gave him a pension. In 1764, Benjamin Martin devised a new type of planetary model, in which the planets were carried on brass arms leading from a series of concentric or coaxial tubes. With this construction it

6237-414: Was difficult to make the planets revolve, and to get the moons to turn around the planets. Martin suggested that the conventional orrery should consist of three parts: the planetarium where the planets revolved around the Sun, the tellurion (also tellurian or tellurium ) which showed the inclined axis of the Earth and how it revolved around the Sun, and the lunarium which showed the eccentric rotations of

6318-408: Was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to cover all conic sections, Huygens extended classical methods to generate new results. Quadrature was a live issue in the 1650s and, through Mylon, Huygens intervened in the discussion of

6399-507: Was not itself a new idea but known to Francisco de Salinas ), using logarithms to investigate it further and show its close relation to the meantone system. In 1654, Huygens returned to his father's house in The Hague and was able to devote himself entirely to research. The family had another house, not far away at Hofwijck , and he spent time there during the summer. Despite being very active, his scholarly life did not allow him to escape bouts of depression. Subsequently, Huygens developed

6480-542: Was that of Archimedes, though he made use of Descartes's analytic geometry and Fermat's infinitesimal techniques more extensively in his private notebooks. Huygens's first publication was Theoremata de Quadratura Hyperboles, Ellipsis et Circuli ( Theorems on the quadrature of the hyperbola, ellipse, and circle ), published by the Elzeviers in Leiden in 1651. The first part of the work contained theorems for computing

6561-401: Was written around 1650 and was made up of three books. Although he sent the completed work to Frans van Schooten for feedback, in the end Huygens chose not to publish it, and at one point suggested it be burned. Some of the results found here were not rediscovered until the eighteenth and nineteenth centuries. Huygens first re-derives Archimedes's solutions for the stability of the sphere and

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