A rotation is a circular movement of an object around a center of rotation. A three-dimensional object can always be rotated around an infinite number of imaginary lines called rotation axes. If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation about an external point, e.g. the Earth about the Sun, is called a revolution or orbital revolution when it is produced by gravity. The axis is called a pole. Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed; this definition applies to rotations within both two and three dimensions All rigid body movements are rotations, translations, or combinations of the two. A rotation is a progressive radial orientation to a common point; that common point lies within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question the body is said to orbit. There is no fundamental difference between a “rotation” and an “orbit” and or "spin".
The key distinction is where the axis of the rotation lies, either within or outside of a body in question. This distinction can be demonstrated for "non rigid" bodies. If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results; the reverse of a rotation is a rotation. Thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, e.g. a translation. Rotations around the x, y and z axes are called principal rotations. Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, followed by a rotation around the z axis; that is to say, any spatial rotation can be decomposed into a combination of principal rotations. In flight dynamics, the principal rotations are known as yaw and roll; this terminology is used in computer graphics. In astronomy, rotation is a observed phenomenon.
Stars and similar bodies all spin around on their axes. The rotation rate of planets in the solar system was first measured by tracking visual features. Stellar rotation is measured by tracking active surface features; this rotation induces a centrifugal acceleration in the reference frame of the Earth which counteracts the effect of gravity the closer one is to the equator. One effect is that an object weighs less at the equator. Another is that the Earth is deformed into an oblate spheroid. Another consequence of the rotation of a planet is the phenomenon of precession. Like a gyroscope, the overall effect is a slight "wobble" in the movement of the axis of a planet; the tilt of the Earth's axis to its orbital plane is 23.44 degrees, but this angle changes slowly. While revolution is used as a synonym for rotation, in many fields astronomy and related fields, revolution referred to as orbital revolution for clarity, is used when one body moves around another while rotation is used to mean the movement around an axis.
Moons revolve around their planet, planets revolve about their star. The motion of the components of galaxies is complex, but it includes a rotation component. Most planets in our solar system, including Earth, spin in the same direction; the exceptions are Uranus. Uranus rotates nearly on its side relative to its orbit. Current speculation is that Uranus started off with a typical prograde orientation and was knocked on its side by a large impact early in its history. Venus may be thought of as rotating backwards; the dwarf planet Pluto is anomalous in other ways. The speed of rotation is given by period; the time-rate of change of angular frequency is angular acceleration, caused by torque. The ratio of the two is given by the moment of inertia; the angular velocity vector describes the direction of the axis of rotation. The torque is an axial vector; the physics of the rotation around a fixed axis is mathematically described with the axis–angle representation of rotations. According to the right-hand rule, the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a screw.
The laws of physics are believed to be invariant under any fixed rotation. In modern physical cosmology, the cosmological principle is the notion that the distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe and have no preferred direction, should, produce no observable irregularities in the large scale structuring over the course of evolution of the matter field, laid down by the Big Bang. In particular, for a system which behaves the same regardless of how it is oriented in space, its Lagrangian is rotationally invariant. According to Noether's theorem, if the action (the integral over ti
Surveying or land surveying is the technique and science of determining the terrestrial or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor; these points are on the surface of the Earth, they are used to establish maps and boundaries for ownership, such as building corners or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. Surveyors work with elements of geometry, regression analysis, engineering, programming languages, the law, they use equipment, such as total stations, robotic total stations, theodolites, GNSS receivers, retroreflectors, 3D scanners, handheld tablets, digital levels, subsurface locators, drones, GIS, surveying software. Surveying has been an element in the development of the human environment since the beginning of recorded history; the planning and execution of most forms of construction require it. It is used in transport, communications and the definition of legal boundaries for land ownership.
It is an important tool for research in many other scientific disciplines. The International Federation of Surveyors defines the function of surveying as: A surveyor is a professional person with the academic qualifications and technical expertise to conduct one, or more, of the following activities. Surveying has occurred since humans built the first large structures. In ancient Egypt, a rope stretcher would use simple geometry to re-establish boundaries after the annual floods of the Nile River; the perfect squareness and north-south orientation of the Great Pyramid of Giza, built c. 2700 BC, affirm the Egyptians' command of surveying. The Groma instrument originated in Mesopotamia; the prehistoric monument at Stonehenge was set out by prehistoric surveyors using peg and rope geometry. The mathematician Liu Hui described ways of measuring distant objects in his work Haidao Suanjing or The Sea Island Mathematical Manual, published in 263 AD; the Romans recognized land surveying as a profession.
They established the basic measurements under which the Roman Empire was divided, such as a tax register of conquered lands. Roman surveyors were known as Gromatici. In medieval Europe, beating the bounds maintained the boundaries of a village or parish; this was the practice of gathering a group of residents and walking around the parish or village to establish a communal memory of the boundaries. Young boys were included to ensure the memory lasted as long as possible. In England, William the Conqueror commissioned the Domesday Book in 1086, it recorded the names of all the land owners, the area of land they owned, the quality of the land, specific information of the area's content and inhabitants. It did not include maps showing exact locations. Abel Foullon described a plane table in 1551, but it is thought that the instrument was in use earlier as his description is of a developed instrument. Gunter's chain was introduced in 1620 by English mathematician Edmund Gunter, it enabled plots of land to be surveyed and plotted for legal and commercial purposes.
Leonard Digges described a Theodolite that measured horizontal angles in his book A geometric practice named Pantometria. Joshua Habermel created a theodolite with a compass and tripod in 1576. Johnathon Sission was the first to incorporate a telescope on a theodolite in 1725. In the 18th century, modern techniques and instruments for surveying began to be used. Jesse Ramsden introduced the first precision theodolite in 1787, it was an instrument for measuring angles in vertical planes. He created his great theodolite using an accurate dividing engine of his own design. Ramsden's theodolite represented a great step forward in the instrument's accuracy. William Gascoigne invented an instrument that used a telescope with an installed crosshair as a target device, in 1640. James Watt developed an optical meter for the measuring of distance in 1771. Dutch mathematician Willebrord Snellius introduced the modern systematic use of triangulation. In 1615 he surveyed the distance from Alkmaar to Breda 72 miles.
He underestimated this distance by 3.5%. The survey was a chain of quadrangles containing 33 triangles in all. Snell showed, he showed how to resection, or calculate, the position of a point inside a triangle using the angles cast between the vertices at the unknown point. These could be measured more than bearings of the vertices, which depended on a compass, his work established the idea of surveying a primary network of control points, locating subsidiary points inside the primary network later. Between 1733 and 1740, Jacques Cassini and his son César undertook the first triangulation of France, they included a re-surveying of the meridian arc, leading to the publication in 1745 of the first map of France constructed on rigorous principles. By this time triangulation methods were well established for local map-making, it was only towards the end of the 18th century that detailed triangulation network surveys mapped whole countries. In 1784, a team from Gene
A vine is any plant with a growth habit of trailing or scandent stems, lianas or runners. The word vine can refer to such stems or runners themselves, for instance, when used in wicker work. In parts of the world, the term "vine" applies to grapevines, while the term "climber" is used for all climbing plants. Certain plants always grow as vines. For instance, poison ivy and bittersweet can grow as low shrubs when support is not available, but will become vines when support is available. A vine displays a growth form based on long stems; this has two purposes. A vine may use rock exposures, other plants, or other supports for growth rather than investing energy in a lot of supportive tissue, enabling the plant to reach sunlight with a minimum investment of energy; this has been a successful growth form for plants such as kudzu and Japanese honeysuckle, both of which are invasive exotics in parts of North America. There are some tropical vines that develop skototropism, grow away from the light, a type of negative phototropism.
Growth away from light allows the vine to reach a tree trunk, which it can climb to brighter regions. The vine growth form may enable plants to colonize large areas even without climbing high; this is the case with ground ivy. It is an adaptation to life in areas where small patches of fertile soil are adjacent to exposed areas with more sunlight but little or no soil. A vine can root in the soil but have most of its leaves in the brighter, exposed area, getting the best of both environments; the evolution of a climbing habit has been implicated as a key innovation associated with the evolutionary success and diversification of a number of taxonomic groups of plants. It has evolved independently in several plant families, using many different climbing methods, such as: twining the stem around a support by way of adventitious, clinging roots with twining petioles using tendrils, which can be specialized shoots, leaves, or inflorescences using tendrils which produce adhesive pads at the end that attach themselves quite to the support using thorns or other hooked structures, such as hooked branches The climbing fetterbush is a woody shrub-vine which climbs without clinging roots, tendrils, or thorns.
It directs its stem into a crevice in the bark of fibrous barked trees where the stem adopts a flattened profile and grows up the tree underneath the host tree's outer bark. The fetterbush sends out branches that emerge near the top of the tree. Most vines are flowering plants; these may be divided into woody vines or lianas, such as wisteria and common ivy, herbaceous vines, such as morning glory. One odd group of vining plants is the fern genus Lygodium, called climbing ferns; the stem does not climb. The fronds unroll from the tip, theoretically never stop growing. A twining vine known as a bine, is one that climbs by its shoots growing in a helix, in contrast to vines that climb using tendrils or suckers. Many bines have rough downward-pointing bristles to aid their grip. Hops are a commercially important example of a bine; the direction of rotation of the shoot tip during climbing is autonomous and does not derive from the shoot's following the sun around the sky – the direction of twist does not therefore depend upon which side of the equator the plant is growing on.
This is shown by the fact that some bines always twine clockwise, including runner bean and bindweed, while others twine anticlockwise, including French bean and climbing honeysuckles. The contrasting rotations of bindweed and honeysuckle was the theme of the satirical song "Misalliance", written and sung by Michael Flanders and Donald Swann; the term "vine" applies to cucurbitaceae like cucumbers where botanists refer to creeping vines. Gardeners can use the tendency of climbing plants to grow quickly. If a plant display is wanted a climber can achieve this. Climbers can be trained over walls, fences, etc. Climbers can be grown over other plants to provide additional attraction. Artificial support can be provided; some climbers climb by themselves. Vines differ in size and evolutionary origin. Darwin classified climbing groups based on their climbing method, he classified five classes of vines – twining plants, leaf climbers, tendril bearers, root climbers and hook climbers. Vines are unique in that they have multiple evolutionary origins and a wide range of phenotypic plasticity.
They reside in tropical locations and have the unique ability to climb. Vines are able to grow in both deep shade and full sun due to their wide range of phenotypic plasticity; this climbing action prevents shading by neighbors and allows the vine to grow out of reach of herbivores. The environment where a vine can grow is determined by the climbing mechanism of a vine and how far it can spread across supports. There are many theories suppor
Leonardo da Vinci
Leonardo di ser Piero da Vinci, more Leonardo da Vinci or Leonardo, was an Italian polymath of the Renaissance whose areas of interest included invention, painting, architecture, music, engineering, anatomy, astronomy, writing and cartography. He has been variously called the father of palaeontology and architecture, he is considered one of the greatest painters of all time. Sometimes credited with the inventions of the parachute and tank, he epitomised the Renaissance humanist ideal. Many historians and scholars regard Leonardo as the prime exemplar of the "Universal Genius" or "Renaissance Man", an individual of "unquenchable curiosity" and "feverishly inventive imagination", he is considered one of the most diversely talented individuals to have lived. According to art historian Helen Gardner, the scope and depth of his interests were without precedent in recorded history, "his mind and personality seem to us superhuman, while the man himself mysterious and remote". Marco Rosci notes that, while there is much speculation regarding his life and personality, his view of the world was logical rather than mysterious, although the empirical methods he employed were unorthodox for his time.
Leonardo was born out of wedlock to notary Piero da Vinci and a peasant woman named Caterina in Vinci in the region of Florence, he was educated in the studio of Florentine painter Andrea del Verrocchio. Much of his earlier working life was spent in the service of Ludovico il Moro in Milan, he worked in Rome and Venice, he spent his last years in France at the home awarded to him by Francis I of France. Leonardo is renowned as a painter; the Mona Lisa is the most famous of his works and the most parodied portrait, The Last Supper is the most reproduced religious painting of all time. His drawing of the Vitruvian Man is regarded as a cultural icon, being reproduced on items as varied as the euro coin, T-shirts, his painting Salvator Mundi sold for $450.3 million at a Christie's auction in New York on 15 November 2017, the highest price paid for a work of art. 15 of his paintings have survived. These few works compose a contribution to generations of artists rivalled only by that of his contemporary Michelangelo, together with his notebooks, which contain drawings, scientific diagrams, his thoughts on the nature of painting.
Leonardo is revered for his technological ingenuity. He conceptualised flying machines, a type of armoured fighting vehicle, concentrated solar power, an adding machine, the double hull. Few of his designs were constructed or feasible during his lifetime, as the modern scientific approaches to metallurgy and engineering were only in their infancy during the Renaissance; some of his smaller inventions, entered the world of manufacturing unheralded, such as an automated bobbin winder and a machine for testing the tensile strength of wire. A number of his most practical inventions are displayed as working models at the Museum of Vinci, he made substantial discoveries in anatomy, civil engineering, geology and hydrodynamics, but he did not publish his findings and they had no direct influence on science. Leonardo was born on 15 April 1452 "at the third hour of the night" in the Tuscan hill town of Vinci, in the lower valley of the Arno river in the territory of the Medici-ruled Republic of Florence.
He was the out-of-wedlock son of the wealthy Messer Piero Fruosino di Antonio da Vinci, a Florentine legal notary, Caterina, a peasant. Leonardo had no surname in the modern sense—"da Vinci" meaning "of Vinci"; the inclusion of the title "ser" indicated. Little is known about Leonardo's early life, he spent his first five years in the hamlet of Anchiano in the home of his mother, from 1457 lived in the household of his father and uncle in the small town of Vinci. His father had married a 16-year-old girl named Albiera Amadori, who loved Leonardo but died young in 1465 without children; when Leonardo was 16, his father married again to 20-year-old Francesca Lanfredini, who died without children. Piero's legitimate heirs were born from his third wife Margherita di Guglielmo and his fourth and final wife, Lucrezia Cortigiani. In all, Leonardo had 12 half-siblings, who were much younger than he was and with whom he had few contacts, but they caused him difficulty after his father's death in the dispute over the inheritance.
Leonardo received an informal education in Latin and mathematics. In life, Leonardo recorded only two childhood incidents. One, which he regarded as an omen, was when a kite dropped from the sky and hovered over his cradle, its tail feathers brushing his face; the second occurred while he was exploring in the mountains: he discovered a cave and was both terrified that some great monster might lurk there and driven by curiosity to find out what was inside. Leonardo's early life has been the subject of historical conjecture. Vasari, the 16th-century biographer of Renaissance painters, tells a story of Leonardo as a young man: A local peasant made himself a round shield and requested that Ser Piero have it painted for him. Leonardo responded with a
Jacques Besson was a French Protestant inventor and philosopher, chiefly remembered for his popular treatise on machines Theatrum Instrumentorum, which saw many reprints in different languages. Little information has survived about Besson's early life, he was most born around 1540. In the early 1550s he is recorded as teaching mathematics in Paris, following which the next account of him dates from April 1557, when he is recorded in the minutes of the town council of Lausanne, Switzerland, as being paid for models of pumps and fountains. In 1559 he published his first treatise in Zurich, the De absoluta ratione extrahendi olea et aquas e medicamentis simplicibus, featuring an introduction by Conrad Gesner; that same year he moved to Geneva where in 1561 he requested permission to become a citizen of Geneva. His entry in Geneva's Livre de Bourgeois notes that citizenship was awarded as a result of his services "in teaching the art and science of mathematics"In 1562 Besson became the pastor of the Protestant Reformed Church in Villeneuve-de-Berg, Olivier de Serres having sent a request to the Company of Pastors for a minister.
However, less than two years he was forced out by a rival. By 1565 he was back in Paris, where in 1567 he published his second treatise, Le Cosmolabe, which described an elaborate instrument based on the astrolabe which could be used for navigation, surveying and astronomy. Le Cosmolabe introduced a number of mechanical inventions that he hoped to describe in more detail in a future work. Besson was described as a professor of mathematics from Orléans; when King Charles IX of France made a royal visit to Orléans in 1569, Besson presented to the King a draft of his new treatise, what was to become the Theatrum Instrumentorum. and returned with him to Paris as "master of the King's Engines". Charles gave Besson exclusive rights to his designs in that same year. While employed by the court, Besson created an ingenious screw-cutting lathe, semi-automatic, in that the operator only needed to pull and release a cord. Besson's Theatrum Instrumentorum, was completed and published in 1571 or 1572, it was a unique work.
In contrast, Besson's work was a collection of his own new inventions with detailed illustrations of each engraved by Jacques Androuet du Cerceau to his specifications. Some of his designs suggested important improvements to the waterwheel; the Latin captions to the detailed drawings were sparse, which would seem to indicate that the text was produced in a hurry. The title page does not give the name of the printer or the date of publication; the rush in publishing the book may have been due to the crackdown on French Protestants that culminated in the St. Bartholomew's Day Massacre of 1572. Although Besson was favoured by King Charles IX, he feared the increasing anti-Protestant sentiment in France, emigrated to England shortly after the St. Bartholomew's Day Massacre of 1572, where he died in 1573; the Theatrum Instrumentorum had proved so popular that a second edition appeared in 1578, with more detailed descriptions of the instruments and machines by François Béroalde de Verville. The copper plates from the original edition were reused, except for four which were replaced by new engravings produced by René Boyvin.
Works by or about Jacques Besson at Internet Archive http://www.sil.si.edu/DigitalCollections/HST/Besson/besson.htm http://www.britannica.com/eb/article-9078938/Jacques-Besson http://www.sil.si.edu/DigitalCollections/HST/Besson/besson-introduction.htm http://libcoll.mpiwg-berlin.mpg.de/elib/rara/YD9NH338 Media related to Jacques Besson at Wikimedia Commons
Late Middle Ages
The Late Middle Ages or Late Medieval Period was the period of European history lasting from 1250 to 1500 AD. The Late Middle Ages followed the High Middle Ages and preceded the onset of the early modern period. Around 1300, centuries of prosperity and growth in Europe came to a halt. A series of famines and plagues, including the Great Famine of 1315–1317 and the Black Death, reduced the population to around half of what it was before the calamities. Along with depopulation came social unrest and endemic warfare. France and England experienced serious peasant uprisings, such as the Jacquerie and the Peasants' Revolt, as well as over a century of intermittent conflict, the Hundred Years' War. To add to the many problems of the period, the unity of the Catholic Church was temporarily shattered by the Western Schism. Collectively, those events are sometimes called the Crisis of the Late Middle Ages. Despite the crises, the 14th century was a time of great progress in the arts and sciences. Following a renewed interest in ancient Greek and Roman texts that took root in the High Middle Ages, the Italian Renaissance began.
The absorption of Latin texts had started before the Renaissance of the 12th century through contact with Arabs during the Crusades, but the availability of important Greek texts accelerated with the Capture of Constantinople by the Ottoman Turks, when many Byzantine scholars had to seek refuge in the West Italy. Combined with this influx of classical ideas was the invention of printing, which facilitated dissemination of the printed word and democratized learning; those two things would lead to the Protestant Reformation. Toward the end of the period, the Age of Discovery began; the expansion of the Ottoman Empire cut off trading possibilities with the East. Europeans were forced to seek new trading routes, leading to the Spanish expedition under Christopher Columbus to the Americas in 1492 and Vasco da Gama’s voyage to Africa and India in 1498, their discoveries strengthened the power of European nations. The changes brought about by these developments have led many scholars to view this period as the end of the Middle Ages and the beginning of modern history and of early modern Europe.
However, the division is somewhat artificial, since ancient learning was never absent from European society. As a result, there was developmental continuity between the modern age; some historians in Italy, prefer not to speak of the Late Middle Ages at all but rather see the high period of the Middle Ages transitioning to the Renaissance and the modern era. The term "Late Middle Ages" refers to one of the three periods of the Middle Ages, along with the Early Middle Ages and the High Middle Ages. Leonardo Bruni was the first historian to use tripartite periodization in his History of the Florentine People. Flavio Biondo used a similar framework in Decades of History from the Deterioration of the Roman Empire. Tripartite periodization became standard after the German historian Christoph Cellarius published Universal History Divided into an Ancient and New Period. For 18th-century historians studying the 14th and 15th centuries, the central theme was the Renaissance, with its rediscovery of ancient learning and the emergence of an individual spirit.
The heart of this rediscovery lies in Italy, where, in the words of Jacob Burckhardt: "Man became a spiritual individual and recognized himself as such". This proposition was challenged, it was argued that the 12th century was a period of greater cultural achievement; as economic and demographic methods were applied to the study of history, the trend was to see the late Middle Ages as a period of recession and crisis. Belgian historian Henri Pirenne continued the subdivision of Early and Late Middle Ages in the years around World War I, yet it was his Dutch colleague, Johan Huizinga, responsible for popularising the pessimistic view of the Late Middle Ages, with his book The Autumn of the Middle Ages. To Huizinga, whose research focused on France and the Low Countries rather than Italy and decline were the main themes, not rebirth. Modern historiography on the period has reached a consensus between the two extremes of innovation and crisis, it is now acknowledged that conditions were vastly different north and south of the Alps, the term "Late Middle Ages" is avoided within Italian historiography.
The term "Renaissance" is still considered useful for describing certain intellectual, cultural, or artistic developments, but not as the defining feature of an entire European historical epoch. The period from the early 14th century up until – and sometimes including – the 16th century, is rather seen as characterized by other trends: demographic and economic decline followed by recovery, the end of western religious unity and the subsequent emergence of the nation state, the expansion of European influence onto the rest of the world; the limits of Christian Europe were still being defined in the 15th centuries. While the Grand Duchy of Moscow was beginning to repel the Mongols, the Iberian kingdoms completed the Reconquista of the peninsula and turned their attention outwards, the Balkans fell under the dominance of the Ottoman Empire. Meanwhile, the remaining nations of the continent were locked in constant international or internal conflict; the situation led to the consolidation of central authority and the emergence of the nation state.
The financial demands of war necessitated higher levels of taxation, resulting in the emergence of representative bodies – most notably the English Parliament. The growth of secular authority was further aided by t