An aircraft is a machine, able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. Common examples of aircraft include airplanes, airships and hot air balloons; the human activity that surrounds aircraft is called aviation. The science of aviation, including designing and building aircraft, is called aeronautics. Crewed aircraft are flown by an onboard pilot, but unmanned aerial vehicles may be remotely controlled or self-controlled by onboard computers. Aircraft may be classified by different criteria, such as lift type, aircraft propulsion and others. Flying model craft and stories of manned flight go back many centuries, however the first manned ascent – and safe descent – in modern times took place by larger hot-air balloons developed in the 18th century; each of the two World Wars led to great technical advances. The history of aircraft can be divided into five eras: Pioneers of flight, from the earliest experiments to 1914.
First World War, 1914 to 1918. Aviation between the World Wars, 1918 to 1939. Second World War, 1939 to 1945. Postwar era called the jet age, 1945 to the present day. Aerostats use buoyancy to float in the air in much the same way, they are characterized by one or more large gasbags or canopies, filled with a low-density gas such as helium, hydrogen, or hot air, less dense than the surrounding air. When the weight of this is added to the weight of the aircraft structure, it adds up to the same weight as the air that the craft displaces. Small hot-air balloons called sky lanterns were first invented in ancient China prior to the 3rd century BC and used in cultural celebrations, were only the second type of aircraft to fly, the first being kites which were first invented in ancient China over two thousand years ago. A balloon was any aerostat, while the term airship was used for large, powered aircraft designs – fixed-wing. In 1919 Frederick Handley Page was reported as referring to "ships of the air," with smaller passenger types as "Air yachts."
In the 1930s, large intercontinental flying boats were sometimes referred to as "ships of the air" or "flying-ships". – though none had yet been built. The advent of powered balloons, called dirigible balloons, of rigid hulls allowing a great increase in size, began to change the way these words were used. Huge powered aerostats, characterized by a rigid outer framework and separate aerodynamic skin surrounding the gas bags, were produced, the Zeppelins being the largest and most famous. There were still no fixed-wing aircraft or non-rigid balloons large enough to be called airships, so "airship" came to be synonymous with these aircraft. Several accidents, such as the Hindenburg disaster in 1937, led to the demise of these airships. Nowadays a "balloon" is an unpowered aerostat and an "airship" is a powered one. A powered, steerable aerostat is called a dirigible. Sometimes this term is applied only to non-rigid balloons, sometimes dirigible balloon is regarded as the definition of an airship.
Non-rigid dirigibles are characterized by a moderately aerodynamic gasbag with stabilizing fins at the back. These soon became known as blimps. During the Second World War, this shape was adopted for tethered balloons; the nickname blimp was adopted along with the shape. In modern times, any small dirigible or airship is called a blimp, though a blimp may be unpowered as well as powered. Heavier-than-air aircraft, such as airplanes, must find some way to push air or gas downwards, so that a reaction occurs to push the aircraft upwards; this dynamic movement through the air is the origin of the term aerodyne. There are two ways to produce dynamic upthrust: aerodynamic lift, powered lift in the form of engine thrust. Aerodynamic lift involving wings is the most common, with fixed-wing aircraft being kept in the air by the forward movement of wings, rotorcraft by spinning wing-shaped rotors sometimes called rotary wings. A wing is a flat, horizontal surface shaped in cross-section as an aerofoil. To fly, air must generate lift.
A flexible wing is a wing made of fabric or thin sheet material stretched over a rigid frame. A kite is tethered to the ground and relies on the speed of the wind over its wings, which may be flexible or rigid, fixed, or rotary. With powered lift, the aircraft directs its engine thrust vertically downward. V/STOL aircraft, such as the Harrier Jump Jet and F-35B take off and land vertically using powered lift and transfer to aerodynamic lift in steady flight. A pure rocket is not regarded as an aerodyne, because it does not depend on the air for its lift. Rocket-powered missiles that obtain aerodynamic lift at high speed due to airflow over their bodies are a marginal case; the forerunner of the fixed-wing aircraft is the kite. Whereas a fixed-wing aircraft relies on its forward speed to create airflow over the wings, a kite is tethered to the ground and relies on the wind blowing over its wings to provide lift. Kites were the first kind of aircraft to fly, were invented in China around 500 BC.
Much aerodynamic research was done with kites before test aircraft, wind tunnels, computer modelling programs became available. The first heavier-than-air craft capable of controlled free-flight were gliders. A glider designed by Geo
In physics and related fields, a wave is a disturbance of a field in which a physical attribute oscillates at each point or propagates from each point to neighboring points, or seems to move through space. The waves most studied in physics are mechanical and electromagnetic. A mechanical wave is a local deformation in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves in air are variations of the local pressure that propagate by collisions between gas molecules. Other examples of mechanical waves are seismic waves, gravity waves and shock waves. An electromagnetic wave consists of a combination of variable electric and magnetic fields, that propagates through space according to Maxwell's equations. Electromagnetic waves can travel through vacuum. Other types of waves include gravitational waves, which are disturbances in a gravitational field that propagate according to general relativity.
Mechanical and electromagnetic waves may seem to travel through space. In mathematics and electronics waves are studied as signals. On the other hand, some waves do not appear to move at all, like hydraulic jumps. Some, like the probability waves of quantum mechanics, may be static in both space. A plane seems to travel in a definite direction, has constant value over any plane perpendicular to that direction. Mathematically, the simplest waves are the sinusoidal ones. Complicated waves can be described as the sum of many sinusoidal plane waves. A plane wave can be transverse, if its effect at each point is described by a vector, perpendicular to the direction of propagation or energy transfer. While mechanical waves can be both transverse and longitudinal, electromagnetic waves are transverse in free space. Consider a traveling transverse wave on a string. Consider the string to have a single spatial dimension. Consider this wave as traveling in the x direction in space. For example, let the positive x direction be to the right, the negative x direction be to the left.
With constant amplitude u with constant velocity v, where v is independent of wavelength independent of amplitude. With constant waveform, or shapeThis wave can be described by the two-dimensional functions u = F u = G or, more by d'Alembert's formula: u = F + G. representing two component waveforms F and G traveling through the medium in opposite directions. A generalized representation of this wave can be obtained as the partial differential equation 1 v 2 ∂ 2 u ∂ t 2 = ∂ 2 u ∂ x 2. General solutions are based upon Duhamel's principle; the form or shape of F in d'Alembert's formula involves the argument x − vt. Constant values of this argument correspond to constant values of F, these constant values occur if x increases at the same rate that vt increases; that is, the wave shaped like the function F will move in the positive x-direction at velocity v. In the case of a periodic function F with period λ, that is, F = F, the periodicity of F in space means that a snapshot of the wave at a given time t finds the wave varying periodically in space with period λ.
In a similar fashion, this periodicity of F implies a periodicity in time as well: F = F provided vT = λ, so an observation of the wave at a fixed location x finds the wave undulating periodically in time with period T = λ/v. The amplitude of a wave may be constant, or may be modulated so as to vary with time and/or position; the outline of the variation in amplitude is called the envelope of the w
The business cycle known as the economic cycle or trade cycle, is the downward and upward movement of gross domestic product around its long-term growth trend. The length of a business cycle is the period of time containing a single boom and contraction in sequence; these fluctuations involve shifts over time between periods of rapid economic growth and periods of relative stagnation or decline. Business cycles are measured by considering the growth rate of real gross domestic product. Despite the often-applied term cycles, these fluctuations in economic activity do not exhibit uniform or predictable periodicity; the common or popular usage boom-and-bust cycle refers to fluctuations in which the expansion is rapid and the contraction severe. The first systematic exposition of economic crises, in opposition to the existing theory of economic equilibrium, was the 1819 Nouveaux Principes d'économie politique by Jean Charles Léonard de Sismondi. Prior to that point classical economics had either denied the existence of business cycles, blamed them on external factors, notably war, or only studied the long term.
Sismondi found vindication in the Panic of 1825, the first unarguably international economic crisis, occurring in peacetime. Sismondi and his contemporary Robert Owen, who expressed similar but less systematic thoughts in 1817 Report to the Committee of the Association for the Relief of the Manufacturing Poor, both identified the cause of economic cycles as overproduction and underconsumption, caused in particular by wealth inequality, they advocated government intervention and socialism as the solution. This work did not generate interest among classical economists, though underconsumption theory developed as a heterodox branch in economics until being systematized in Keynesian economics in the 1930s. Sismondi's theory of periodic crises was developed into a theory of alternating cycles by Charles Dunoyer, similar theories, showing signs of influence by Sismondi, were developed by Johann Karl Rodbertus. Periodic crises in capitalism formed the basis of the theory of Karl Marx, who further claimed that these crises were increasing in severity and, on the basis of which, he predicted a communist revolution.
Though only passing references in Das Kapital refer to crises, they were extensively discussed in Marx's posthumously published books in Theories of Surplus Value. In Progress and Poverty, Henry George focused on land's role in crises – land speculation – and proposed a single tax on land as a solution. In 1860 French economist Clément Juglar first identified economic cycles 7 to 11 years long, although he cautiously did not claim any rigid regularity. Economist Joseph Schumpeter argued that a Juglar cycle has four stages: Expansion Crisis Recession Recovery Schumpeter's Juglar model associates recovery and prosperity with increases in productivity, consumer confidence, aggregate demand, prices. In the 20th century and others proposed a typology of business cycles according to their periodicity, so that a number of particular cycles were named after their discoverers or proposers: The Kitchin inventory cycle of 3 to 5 years The Juglar fixed-investment cycle of 7 to 11 years (often identified as "the" business cycle The Kuznets infrastructural investment cycle of 15 to 25 years (after Simon Kuznets – called "building cycle" The Kondratiev wave or long technological cycle of 45 to 60 years Some say interest in the different typologies of cycles has waned since the development of modern macroeconomics, which gives little support to the idea of regular periodic cycles.
Others realize. Since 1960, World GDP has increased by fifty-nine times, these multiples have not kept up with annual inflation over the same period. Social Contract collapses for nations when incomes are not kept in balance with cost-of-living over the timeline of the monetary system cycle - until hardships/populism/revolution are always seen in late capitalism; the Bible and Hammurabi's Code both explain economic remediations for cyclic sixty-year recurring great depressions, via fiftieth-year Jubilee debt and wealth resets. Thirty major debt forgiveness events are recorded in history including the debt forgiveness given to most european nations in the 1930s to 1954. There were great increases in productivity, industrial production and real per capita product throughout the period from 1870 to 1890 that included the Long Depression and two other recessions. There were significant increases in productivity in the years leading up to the Great Depression. Both the Long and Great Depressions were characterized by market saturation.
Over the period since the Industrial Revolution, technological progress has had a much larger effect on the economy than any fluctuations in credit or debt, the primary exception being the Great Depression, which caused a multi-year steep economic decline. The effect of technological progress can be seen by the purchasing power of an average hour's work, which has grown from $3 in 1900 to $22 in 1990, measured in 2010 dollars. There were similar increases in real wages during the 19th century. A table of innovations and long
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position; when released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period; the period depends on the length of the pendulum and to a slight degree on the amplitude, the width of the pendulum's swing. From the first scientific investigations of the pendulum around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping, was the world's most accurate timekeeping technology until the 1930s; the pendulum clock invented by Christian Huygens in 1658 became the world's standard timekeeper, used in homes and offices for 270 years, achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.
Pendulums are used in scientific instruments such as accelerometers and seismometers. They were used as gravimeters to measure the acceleration of gravity in geophysical surveys, as a standard of length; the word "pendulum" is new Latin, from the Latin pendulus, meaning'hanging'. The simple gravity pendulum is an idealized mathematical model of a pendulum; this is a weight on the end of a massless cord suspended without friction. When given an initial push, it will swing forth at a constant amplitude. Real pendulums are subject to friction and air drag, so the amplitude of their swings declines; the period of swing of a simple gravity pendulum depends on its length, the local strength of gravity, to a small extent on the maximum angle that the pendulum swings away from vertical, θ0, called the amplitude. It is independent of the mass of the bob. If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is: T ≈ 2 π L g θ 0 ≪ 1 r a d i a n where L is the length of the pendulum and g is the local acceleration of gravity.
For small swings the period of swing is the same for different size swings: that is, the period is independent of amplitude. This property, called isochronism, is the reason. Successive swings of the pendulum if changing in amplitude, take the same amount of time. For larger amplitudes, the period increases with amplitude so it is longer than given by equation. For example, at an amplitude of θ0 = 23 ° it is 1 % larger; the period increases asymptotically as θ0 approaches 180°, because the value θ0 = 180° is an unstable equilibrium point for the pendulum. The true period of an ideal simple gravity pendulum can be written in several different forms, one example being the infinite series: T = 2 π L g where θ 0 is in radians; the difference between this true period and the period for small swings above is called the circular error. In the case of a typical grandfather clock whose pendulum has a swing of 6° and thus an amplitude of 3°, the difference between the true period and the small angle approximation amounts to about 15 seconds per day.
For small swings the pendulum approximates a harmonic oscillator, its motion as a function of time, t, is simple harmonic motion: θ = θ 0 cos where φ is a constant value, dependent on initial conditions. For real pendulums, the period varies with factors such as the buoyancy and viscous resistance of the air, the mass of the string or rod, the size and shape of the bob and how it is attached to the string, flexibility and stretching of the string. In precision applications, corrections for these factors may need to be applied to eq. to give the period accurately. Any swinging rigid body free to rotate about a fixed horizontal axis is called a compound pendulum or physical pendulum; the appropriate equivalent length L for calculating the period of any such pendulum is the distance from the pivot to the center of oscillation. This point is located under the center of mass at a distance from the pivot traditionally called the radius of oscillation, which depends on the mass distribution of the pendulum.
If most of the mass is concentrated in a small bob compared to the pendulum length, the center of oscillation is close to the center of mass. The radiu
Ecology is the branch of biology which studies the interactions among organisms and their environment. Objects of study include interactions of organisms that include biotic and abiotic components of their environment. Topics of interest include the biodiversity, distribution and populations of organisms, as well as cooperation and competition within and between species. Ecosystems are dynamically interacting systems of organisms, the communities they make up, the non-living components of their environment. Ecosystem processes, such as primary production, nutrient cycling, niche construction, regulate the flux of energy and matter through an environment; these processes are sustained by organisms with specific life history traits. Biodiversity means the varieties of species and ecosystems, enhances certain ecosystem services. Ecology is not synonymous with natural history, or environmental science, it overlaps with the related sciences of evolutionary biology and ethology. An important focus for ecologists is to improve the understanding of how biodiversity affects ecological function.
Ecologists seek to explain: Life processes and adaptations The movement of materials and energy through living communities The successional development of ecosystems The abundance and distribution of organisms and biodiversity in the context of the environment. Ecology has practical applications in conservation biology, wetland management, natural resource management, city planning, community health, economics and applied science, human social interaction. For example, the Circles of Sustainability approach treats ecology as more than the environment'out there', it is not treated as separate from humans. Organisms and resources compose ecosystems which, in turn, maintain biophysical feedback mechanisms that moderate processes acting on living and non-living components of the planet. Ecosystems sustain life-supporting functions and produce natural capital like biomass production, the regulation of climate, global biogeochemical cycles, water filtration, soil formation, erosion control, flood protection, many other natural features of scientific, economic, or intrinsic value.
The word "ecology" was coined in 1866 by the German scientist Ernst Haeckel. Ecological thought is derivative of established currents in philosophy from ethics and politics. Ancient Greek philosophers such as Hippocrates and Aristotle laid the foundations of ecology in their studies on natural history. Modern ecology became a much more rigorous science in the late 19th century. Evolutionary concepts relating to adaptation and natural selection became the cornerstones of modern ecological theory; the scope of ecology contains a wide array of interacting levels of organization spanning micro-level to a planetary scale phenomena. Ecosystems, for example, contain interacting life forms. Ecosystems are dynamic, they do not always follow a linear successional path, but they are always changing and sometimes so that it can take thousands of years for ecological processes to bring about certain successional stages of a forest. An ecosystem's area can vary from tiny to vast. A single tree is of little consequence to the classification of a forest ecosystem, but critically relevant to organisms living in and on it.
Several generations of an aphid population can exist over the lifespan of a single leaf. Each of those aphids, in turn, support diverse bacterial communities; the nature of connections in ecological communities cannot be explained by knowing the details of each species in isolation, because the emergent pattern is neither revealed nor predicted until the ecosystem is studied as an integrated whole. Some ecological principles, however, do exhibit collective properties where the sum of the components explain the properties of the whole, such as birth rates of a population being equal to the sum of individual births over a designated time frame; the main subdisciplines of ecology, population ecology and ecosystem ecology, exhibit a difference not only of scale, but of two contrasting paradigms in the field. The former focus on organisms distribution and abundance, while the focus on materials and energy fluxes; the scale of ecological dynamics can operate like a closed system, such as aphids migrating on a single tree, while at the same time remain open with regard to broader scale influences, such as atmosphere or climate.
Hence, ecologists classify ecosystems hierarchically by analyzing data collected from finer scale units, such as vegetation associations and soil types, integrate this information to identify emergent patterns of uniform organization and processes that operate on local to regional and chronological scales. To structure the study of ecology into a conceptually manageable framework, the biological world is organized into a nested hierarchy, ranging in scale from genes, to cells, to tissues, to organs, to organisms, to species, to populations, to communities, to ecosystems, to biomes, up to the level of the biosphere; this framework exhibits non-linear behaviors.
A Wilberforce pendulum, invented by British physicist Lionel Robert Wilberforce around 1896, consists of a mass suspended by a long helical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanical oscillator used as a demonstration in physics education; the mass can both bob up and down on the spring, rotate back and forth about its vertical axis with torsional vibrations. When adjusted and set in motion, it exhibits a curious motion in which periods of purely rotational oscillation alternate with periods of purely up and down oscillation; the energy stored in the device shifts back and forth between the translational'up and down' oscillation mode and the torsional'clockwise and counterclockwise' oscillation mode, until the motion dies away. Despite the name, in normal operation it does not swing forth as ordinary pendulums do; the mass has opposing pairs of radial'arms' sticking out horizontally, threaded with small weights that can be screwed in or out to adjust the moment of inertia to'tune' the torsional vibration period.
The device's intriguing behavior is caused by a slight coupling between the two motions or degrees of freedom, due to the geometry of the spring. When the weight is moving up and down, each downward excursion of the spring causes it to unwind giving the weight a slight twist; when the weight moves up, it causes the spring to wind tighter, giving the weight a slight twist in the other direction. So when the weight is moving up and down, each oscillation gives a slight alternating rotational torque to the weight. In other words, during each oscillation some of the energy in the translational mode leaks into the rotational mode; the up and down movement gets less, the rotational movement gets greater, until the weight is just rotating and not bobbing. When the weight is rotating back and forth, each twist of the weight in the direction that unwinds the spring reduces the spring tension causing the weight to sag a little lower. Conversely, each twist of the weight in the direction of winding the spring tighter causes the tension to increase, pulling the weight up slightly.
So each oscillation of the weight back and forth causes it to bob up and down more, until all the energy is transferred back from the rotational mode into the translational mode and it is just bobbing up and down, not rotating. The frequency at which the two modes alternate is equal to the difference between the oscillation frequencies of the modes; the closer in frequency the two motions are, the slower will be the alternation between them. This behavior, common to all coupled oscillators, is analogous to the phenomenon of beats in musical instruments, in which two tones combine to produce a'beat' tone at the difference between their frequencies. For example, if the pendulum bobs up and down at a rate of fT = 4 Hz, rotates back and forth about its axis at a rate of fR = 4.1 Hz, the alternation rate falt will be: f a l t = f R − f T = 0.1 H z T a l t = 1 / f a l t = 10 s So the motion will change from rotational to translational in 5 seconds and back to rotational in the next 5 seconds. The pendulum is adjusted by moving the moment of inertia adjustment weights in or out equal amounts on each side, until the rotational frequency is close to the translational frequency, so the alternation period will be slow enough to allow the change between the two modes to be seen.
Pitre, John. "Wilberforce Pendulum". Physics 182S lab. Univ. of Toronto. Retrieved 2008-05-03. Video of Wilberforce pendulum oscillating, by Berkeley Lecture Demonstrations, YouTube.com, retrieved April 25, 2008
Christiaan Huygens was a Dutch physicist, mathematician and inventor, regarded as one of the greatest scientists of all time and a major figure in the scientific revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan; as an inventor, he improved the design of the telescope with the invention of the Huygenian eyepiece. His most famous invention, was the invention of the pendulum clock in 1656, a breakthrough in timekeeping and became the most accurate timekeeper for 300 years; because he was the first to use mathematical formulae to describe the laws of physics, Huygens has been called the first theoretical physicist and the founder of mathematical physics. In 1659, Huygens was the first to derive the now standard formula for the centripetal force in his work De vi centrifuga; the formula played a central role in classical mechanics and became known as the second of Newton's laws of motion.
Huygens was the first to formulate the correct laws of elastic collision in his work De motu corporum ex percussione, but his findings were not published until 1703, after his death. In the field of optics, he is best known for his wave theory of light, which he proposed in 1678 and described in 1690 in his Treatise on Light, regarded as the first mathematical theory of light, his theory was rejected in favor of Isaac Newton's corpuscular theory of light, until Augustin-Jean Fresnel adopted Huygens' principle in 1818 and showed that it could explain the rectilinear propagation and diffraction effects of light. Today this principle is known as the Huygens–Fresnel principle. Huygens invented the pendulum clock in 1656. In addition to this invention, his research in horology resulted in an extensive analysis of the pendulum in his 1673 book Horologium Oscillatorium, regarded as one of the most important 17th-century works in mechanics. While the first part of the book contains descriptions of clock designs, most of the book is an analysis of pendulum motion and a theory of curves.
In 1655, Huygens began grinding lenses with his brother Constantijn in order to build telescopes to conduct astronomical research. He designed a 50-power refracting telescope with which he discovered that the ring of Saturn was "a thin, flat ring, nowhere touching, inclined to the ecliptic." It was with this telescope that he discovered the first of Saturn's moons, Titan. He developed in 1662 what is now called the Huygenian eyepiece, a telescope with two lenses, which diminished the amount of dispersion; as a mathematician, Huygens was a pioneer on probability and wrote his first treatise on probability theory in 1657 with the work Van Rekeningh in Spelen van Gluck. Frans van Schooten, the private tutor of Huygens, translated the work as De ratiociniis in ludo aleae; the work is a systematic treatise on probability and deals with games of chance and in particular the problem of points. The modern concept of probability grew out of the use of expectation values by Huygens and Blaise Pascal; the last years of Huygens, who never married, were characterized by loneliness and depression.
As a rationalist, he refused to believe in an immanent supreme being, could not accept the Christian faith of his upbringing. Although Huygens did not believe in such a supernatural being, he did hypothesize on the possibility of extraterrestrial life in his Cosmotheoros, published shortly before his death in 1695, he speculated that extraterrestrial life was possible on planets similar to Earth and wrote that the availability of water in liquid form was a necessity for life. Christiaan Huygens 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 was Suzanna van Baerle. She died in 1637, shortly after the birth of Huygens' sister; the couple had five children: Constantijn, Lodewijk and Suzanna. Constantijn Huygens was a diplomat and advisor to the House of Orange, a poet and musician, his friends included Marin Mersenne and René Descartes. Huygens was educated at home until turning sixteen years old.
He liked to play with miniatures of other machines. His father gave him a liberal education: he studied languages and music and geography, mathematics and rhetoric, but dancing and horse riding. In 1644 Huygens had as his mathematical tutor Jan Jansz de Jonge Stampioen, who set the 15-year-old a demanding reading list on contemporary science. Descartes was impressed by his skills in geometry, his father sent Huygens to study law and mathematics at the University of Leiden, where he studied from May 1645 to March 1647. Frans van Schooten was an academic at Leiden from 1646, a private tutor to Huygens and his elder brother, replacing Stampioen on the advice of Descartes. Van Schooten brought his mathematical education up to date, in particular introducing him to the work of Fermat on differential geometry. After two years, from March 1647, Huygens continued his studies at the newly founded Orange College, in Breda, where his father was a curator: the change occurred because of a duel between his brother Lodewijk and another student.
Constantijn Huygens was involved in the new College, which lasted only to 1669. Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber, and