Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
The Lockheed Corporation was an American aerospace company. Lockheed was founded in 1926 and merged with Martin Marietta to form Lockheed Martin in 1995; the founder, Allan Lockheed, had earlier founded the named but otherwise unrelated Loughead Aircraft Manufacturing Company, operational from 1912 through 1920. Allan Loughead and his brother Malcolm Loughead had operated an earlier aircraft company, Loughead Aircraft Manufacturing Company, operational from 1912 to 1920; the company built and operated aircraft for paying passengers on sightseeing tours in California and had developed a prototype for the civil market, but folded in 1920 due to the flood of surplus aircraft deflating the market after World War I. Allan went into the real estate market while Malcolm had meanwhile formed a successful company marketing brake systems for automobiles. In 1926, Allan Lockheed, John Northrop, Kenneth Kay and Fred Keeler secured funding to form the Lockheed Aircraft Company in Hollywood; this new company utilized some of the same technology developed for the Model S-1 to design the Vega Model.
In March 1928, the company relocated to Burbank, by year's end reported sales exceeding one million dollars. From 1926 to 1928 the company produced over 80 aircraft and employed more than 300 workers who by April 1929 were building five aircraft per week. In July 1929, majority shareholder Fred Keeler sold 87% of the Lockheed Aircraft Company to Detroit Aircraft Corporation. In August 1929, Allan Loughead resigned; the Great Depression ruined the aircraft market, Detroit Aircraft went bankrupt. A group of investors headed by brothers Robert and Courtland Gross, Walter Varney, bought the company out of receivership in 1932; the syndicate bought the company for a mere $40,000. Allan Loughead himself had planned to bid for his own company, but had raised only $50,000, which he felt was too small a sum for a serious bid. In 1934, Robert E. Gross was named chairman of the new company, the Lockheed Aircraft Corporation, headquartered at what is now the airport in Burbank, California, his brother Courtlandt S. Gross was a co-founder and executive, succeeding Robert as chairman following his death in 1961.
The company was named the Lockheed Corporation in 1977. The first successful construction, built in any number was the Vega first built in 1927, best known for its several first- and record-setting flights by, among others, Amelia Earhart, Wiley Post, George Hubert Wilkins. In the 1930s, Lockheed spent $139,400 to develop the Model 10 Electra, a small twin-engined transport; the company sold 40 in the first year of production. Amelia Earhart and her navigator, Fred Noonan, flew it in their failed attempt to circumnavigate the world in 1937. Subsequent designs, the Lockheed Model 12 Electra Junior and the Lockheed Model 14 Super Electra expanded their market; the Lockheed Model 14 formed the basis for the Hudson bomber, supplied to both the British Royal Air Force and the United States military before and during World War II. Its primary role was submarine hunting; the Model 14 Super Electra were sold abroad, more than 100 were license-built in Japan for use by the Imperial Japanese Army. At the beginning of World War II, Lockheed – under the guidance of Clarence Johnson, considered one of the best-known American aircraft designers – answered a specification for an interceptor by submitting the P-38 Lightning fighter aircraft, a twin-engined, twin-boom design.
The P-38 was the only American fighter aircraft in production throughout American involvement in the war, from Pearl Harbor to Victory over Japan Day. It filled ground-attack, air-to-air, strategic bombing roles in all theaters of the war in which the United States operated; the P-38 was responsible for shooting down more Japanese aircraft than any other U. S. Army Air Forces type during the war; the Lockheed Vega factory was located next to Burbank's Union Airport which it had purchased in 1940. During the war, the entire area was camouflaged to fool enemy aerial reconnaissance; the factory was hidden beneath a huge burlap tarpaulin painted to depict a peaceful semi-rural neighborhood, replete with rubber automobiles. Hundreds of fake trees, shrubs and fire hydrants were positioned to give a three-dimensional appearance; the trees and shrubs were created from chicken wire treated with an adhesive and covered with feathers to provide a leafy texture. Lockheed ranked tenth among United States corporations in the value of wartime production contracts.
All told and its subsidiary Vega produced 19,278 aircraft during World War II, representing six percent of war production, including 2,600 Venturas, 2,750 Boeing B-17 Flying Fortress bombers, 2,900 Hudson bombers, 9,000 Lightnings. During World War II, Lockheed, in cooperation with Trans-World Airlines, had developed the L-049 Constellation, a radical new airliner capable of flying 43 passengers between New York and London at a speed of 300 mph in 13 hours. Once the Constellation went into production, the military received the first production models; the Constellations' performance set new standards which transformed the civilian transportation market. Its signature tri-tail was the result of many initial customers not
Physics is the natural science that studies matter, its motion, behavior through space and time, that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, its main goal is to understand how the universe behaves. Physics is one of the oldest academic disciplines and, through its inclusion of astronomy the oldest. Over much of the past two millennia, chemistry and certain branches of mathematics, were a part of natural philosophy, but during the scientific revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, the boundaries of physics which are not rigidly defined. New ideas in physics explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics enable advances in new technologies.
For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have transformed modern-day society, such as television, domestic appliances, nuclear weapons. Astronomy is one of the oldest natural sciences. Early civilizations dating back to beyond 3000 BCE, such as the Sumerians, ancient Egyptians, the Indus Valley Civilization, had a predictive knowledge and a basic understanding of the motions of the Sun and stars; the stars and planets were worshipped, believed to represent gods. While the explanations for the observed positions of the stars were unscientific and lacking in evidence, these early observations laid the foundation for astronomy, as the stars were found to traverse great circles across the sky, which however did not explain the positions of the planets. According to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, all Western efforts in the exact sciences are descended from late Babylonian astronomy.
Egyptian astronomers left monuments showing knowledge of the constellations and the motions of the celestial bodies, while Greek poet Homer wrote of various celestial objects in his Iliad and Odyssey. Natural philosophy has its origins in Greece during the Archaic period, when pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause, they proposed ideas verified by reason and observation, many of their hypotheses proved successful in experiment. The Western Roman Empire fell in the fifth century, this resulted in a decline in intellectual pursuits in the western part of Europe. By contrast, the Eastern Roman Empire resisted the attacks from the barbarians, continued to advance various fields of learning, including physics. In the sixth century Isidore of Miletus created an important compilation of Archimedes' works that are copied in the Archimedes Palimpsest. In sixth century Europe John Philoponus, a Byzantine scholar, questioned Aristotle's teaching of physics and noting its flaws.
He introduced the theory of impetus. Aristotle's physics was not scrutinized until John Philoponus appeared, unlike Aristotle who based his physics on verbal argument, Philoponus relied on observation. On Aristotle's physics John Philoponus wrote: “But this is erroneous, our view may be corroborated by actual observation more than by any sort of verbal argument. For if you let fall from the same height two weights of which one is many times as heavy as the other, you will see that the ratio of the times required for the motion does not depend on the ratio of the weights, but that the difference in time is a small one, and so, if the difference in the weights is not considerable, that is, of one is, let us say, double the other, there will be no difference, or else an imperceptible difference, in time, though the difference in weight is by no means negligible, with one body weighing twice as much as the other”John Philoponus' criticism of Aristotelian principles of physics served as an inspiration for Galileo Galilei ten centuries during the Scientific Revolution.
Galileo cited Philoponus in his works when arguing that Aristotelian physics was flawed. In the 1300s Jean Buridan, a teacher in the faculty of arts at the University of Paris, developed the concept of impetus, it was a step toward the modern ideas of momentum. Islamic scholarship inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further placing emphasis on observation and a priori reasoning, developing early forms of the scientific method; the most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn al-Haytham, in which he conclusively disproved the ancient Greek idea about vision, but came up with a new theory. In the book, he presented a study of the phenomenon of the camera obscura (his thousand-year-old
Engineers, as practitioners of engineering, are professionals who invent, analyze and test machines, systems and materials to fulfill objectives and requirements while considering the limitations imposed by practicality, regulation and cost. The word engineer is derived from the Latin words ingenium; the foundational qualifications of an engineer include a four-year bachelor's degree in an engineering discipline, or in some jurisdictions, a master's degree in an engineering discipline plus four to six years of peer-reviewed professional practice and passage of engineering board examinations. The work of engineers forms the link between scientific discoveries and their subsequent applications to human and business needs and quality of life. In 1961, the Conference of Engineering Societies of Western Europe and the United States of America defined "professional engineer" as follows: A professional engineer is competent by virtue of his/her fundamental education and training to apply the scientific method and outlook to the analysis and solution of engineering problems.
He/she is able to assume personal responsibility for the development and application of engineering science and knowledge, notably in research, construction, superintending, managing and in the education of the engineer. His/her work is predominantly intellectual and varied and not of a routine mental or physical character, it requires the exercise of original thought and judgement and the ability to supervise the technical and administrative work of others. His/her education will have been such as to make him/her capable of and continuously following progress in his/her branch of engineering science by consulting newly published works on a worldwide basis, assimilating such information and applying it independently. He/she is thus placed in a position to make contributions to the development of engineering science or its applications. His/her education and training will have been such that he/she will have acquired a broad and general appreciation of the engineering sciences as well as thorough insight into the special features of his/her own branch.
In due time he/she will be able to give authoritative technical advice and to assume responsibility for the direction of important tasks in his/her branch. Engineers develop new technological solutions. During the engineering design process, the responsibilities of the engineer may include defining problems and narrowing research, analyzing criteria and analyzing solutions, making decisions. Much of an engineer's time is spent on researching, locating and transferring information. Indeed, research suggests engineers spend 56% of their time engaged in various information behaviours, including 14% searching for information. Engineers must weigh different design choices on their merits and choose the solution that best matches the requirements and needs, their crucial and unique task is to identify and interpret the constraints on a design in order to produce a successful result. Engineers apply techniques of engineering analysis in production, or maintenance. Analytical engineers may supervise production in factories and elsewhere, determine the causes of a process failure, test output to maintain quality.
They estimate the time and cost required to complete projects. Supervisory engineers are responsible for entire projects. Engineering analysis involves the application of scientific analytic principles and processes to reveal the properties and state of the system, device or mechanism under study. Engineering analysis proceeds by separating the engineering design into the mechanisms of operation or failure, analyzing or estimating each component of the operation or failure mechanism in isolation, recombining the components, they may analyze risk. Many engineers use computers to produce and analyze designs, to simulate and test how a machine, structure, or system operates, to generate specifications for parts, to monitor the quality of products, to control the efficiency of processes. Most engineers specialize in one or more engineering disciplines. Numerous specialties are recognized by professional societies, each of the major branches of engineering has numerous subdivisions. Civil engineering, for example, includes structural and transportation engineering and materials engineering include ceramic and polymer engineering.
Mechanical engineering cuts across just about every discipline since its core essence is applied physics. Engineers may specialize in one industry, such as motor vehicles, or in one type of technology, such as turbines or semiconductor materials. Several recent studies have investigated. Research suggests that there are several key themes present in engineers' work: technical work, social work, computer-based work and information behaviours. Among other more detailed findings, a recent work sampling study found that engineers spend 62.92% of their time engaged in technical work, 40.37% in social work, 49.66% in computer-based work. Furthermore, there was considerable overlap between these different types of work, with engineers spending 24.96% of their time engaged in technical and social work, 37.97% in technical and non-social, 15.42% in non-technical and social, 21.66% in non-technical and non-social. Engineering is an information-intensive field, with research finding that engineers spend 55
Los Angeles the City of Los Angeles and known by its initials L. A. is the most populous city in California, the second most populous city in the United States, after New York City, the third most populous city in North America. With an estimated population of four million, Los Angeles is the cultural and commercial center of Southern California; the city is known for its Mediterranean climate, ethnic diversity and the entertainment industry, its sprawling metropolis. Los Angeles is the largest city on the West Coast of North America. Los Angeles is in a large basin bounded by the Pacific Ocean on one side and by mountains as high as 10,000 feet on the other; the city proper, which covers about 469 square miles, is the seat of Los Angeles County, the most populated county in the country. Los Angeles is the principal city of the Los Angeles metropolitan area, the second largest in the United States after that of New York City, with a population of 13.1 million. It is part of the Los Angeles-Long Beach combined statistical area the nation's second most populous area with a 2015 estimated population of 18.7 million.
Los Angeles is one of the most substantial economic engines within the United States, with a diverse economy in a broad range of professional and cultural fields. Los Angeles is famous as the home of Hollywood, a major center of the world entertainment industry. A global city, it has been ranked 6th in the Global Cities Index and 9th in the Global Economic Power Index; the Los Angeles metropolitan area has a gross metropolitan product of $1.044 trillion, making it the third-largest in the world, after the Tokyo and New York metropolitan areas. Los Angeles hosted the 1932 and 1984 Summer Olympics and will host the event for a third time in 2028; the city hosted the Miss Universe pageant twice, in 1990 and 2006, was one of 9 American cities to host the 1994 FIFA men's soccer World Cup and one of 8 to host the 1999 FIFA women's soccer World Cup, hosting the final match for both tournaments. Home to the Chumash and Tongva, Los Angeles was claimed by Juan Rodríguez Cabrillo for Spain in 1542 along with the rest of what would become Alta California.
The city was founded on September 4, 1781, by Spanish governor Felipe de Neve. It became a part of Mexico in 1821 following the Mexican War of Independence. In 1848, at the end of the Mexican–American War, Los Angeles and the rest of California were purchased as part of the Treaty of Guadalupe Hidalgo, becoming part of the United States. Los Angeles was incorporated as a municipality on April 4, 1850, five months before California achieved statehood; the discovery of oil in the 1890s brought rapid growth to the city. The completion of the Los Angeles Aqueduct in 1913, delivering water from Eastern California assured the city's continued rapid growth; the Los Angeles coastal area was settled by the Chumash tribes. A Gabrieleño settlement in the area was called iyáangẚ, meaning "poison oak place". Maritime explorer Juan Rodríguez Cabrillo claimed the area of southern California for the Spanish Empire in 1542 while on an official military exploring expedition moving north along the Pacific coast from earlier colonizing bases of New Spain in Central and South America.
Gaspar de Portolà and Franciscan missionary Juan Crespí, reached the present site of Los Angeles on August 2, 1769. In 1771, Franciscan friar Junípero Serra directed the building of the Mission San Gabriel Arcángel, the first mission in the area. On September 4, 1781, a group of forty-four settlers known as "Los Pobladores" founded the pueblo they called El Pueblo de Nuestra Señora la Reina de los Ángeles,'The Town of Our Lady the Queen of the Angels'; the present-day city has the largest Roman Catholic Archdiocese in the United States. Two-thirds of the Mexican or settlers were mestizo or mulatto, a mixture of African and European ancestry; the settlement remained a small ranch town for decades, but by 1820, the population had increased to about 650 residents. Today, the pueblo is commemorated in the historic district of Los Angeles Pueblo Plaza and Olvera Street, the oldest part of Los Angeles. New Spain achieved its independence from the Spanish Empire in 1821, the pueblo continued as a part of Mexico.
During Mexican rule, Governor Pío Pico made Los Angeles Alta California's regional capital. Mexican rule ended during the Mexican–American War: Americans took control from the Californios after a series of battles, culminating with the signing of the Treaty of Cahuenga on January 13, 1847. Railroads arrived with the completion of the transcontinental Southern Pacific line to Los Angeles in 1876 and the Santa Fe Railroad in 1885. Petroleum was discovered in the city and surrounding area in 1892, by 1923, the discoveries had helped California become the country's largest oil producer, accounting for about one-quarter of the world's petroleum output. By 1900, the population had grown to more than 102,000; the completion of the Los Angeles Aqueduct in 1913, under the supervision of William Mulholland, assured the continued growth of the city. Due to clauses in the city's charter that prevented the City of Los Angeles from selling or providing water from the aqueduct to any area outside its borders, many adjacent city and communities became compelled to annex themselves into Los Angeles.
Los Angeles created the first municipal zoning ordinance in the United States. On September 14, 1908, the Los Angeles City Council promulgated residential and industrial land use zones; the new ordinance established three residential zones of a single type, where industrial uses were
Willis Moore Hawkins was an aeronautical engineer for Lockheed for more than fifty years. He was hired in 1937 after receiving his bachelor's degree in aeronautical engineering from the University of Michigan. Prior to that, he was in the first graduating class of The Leelanau School, a boarding school in Glen Arbor, Michigan, he contributed to the designs of a number of historic Lockheed aircraft, including the Constellation, P-80 Shooting Star, XF-90, F-94 Starfire, F-104 Starfighter. During World War II, he was part of the group of Lockheed designers who designed the first American attempt at a jet plane, the Lockheed L-133. In 1951, he led the design team that created the proposal for the Lockheed Model 82, which would become the C-130 Hercules, with Joseph F. Ware, Jr. as Flight Test Engineer in charge. Hawkins served as President, he was elected a Vice President of the Lockheed Corporation in 1960 and served on the corporation’s board of directors. Hawkins served as Assistant Secretary for Research and Development for the US Army from 1962 to 1965, where he was instrumental in starting development of the M1 Abrams main battle tank.
He retired from Lockheed in 1980, but Lockheed chairman Roy Anderson brought Hawkins back to run the Lockheed—California Company on an interim basis in the 1980s. Hawkins retired for good in 1986, he died in 2004 at the age of 90, after witnessing the celebration of the 50th anniversary of the C-130's first flight on August 23, 1954. An obituary of Willis Hawkins from the Marshall Institute "Willis Hawkins and the Genesis of the Hercules", by Jeff Rhodes, from Code One OAC Willis M. Hawkins Papers, 1920-2009
Technical drawing, drafting or drawing, is the act and discipline of composing drawings that visually communicate how something functions or is constructed. Technical drawing is essential for communicating ideas in engineering. To make the drawings easier to understand, people use familiar symbols, units of measurement, notation systems, visual styles, page layout. Together, such conventions constitute a visual language and help to ensure that the drawing is unambiguous and easy to understand. Many of the symbols and principles of technical drawing are codified in an international standard called ISO 128; the need for precise communication in the preparation of a functional document distinguishes technical drawing from the expressive drawing of the visual arts. Artistic drawings are subjectively interpreted. Technical drawings are understood to have one intended meaning. A drafter, draftsperson, or draughtsman is a person. A professional drafter who makes technical drawings is sometimes called a drafting technician.
A sketch is a executed, freehand drawing, not intended as a finished work. In general, sketching is a quick way to record an idea for use. Architect's sketches serve as a way to try out different ideas and establish a composition before a more finished work when the finished work is expensive and time-consuming. Architectural sketches, for example, are a kind of diagrams; these sketches, like metaphors, are used by architects as a means of communication in aiding design collaboration. This tool helps architects to abstract attributes of hypothetical provisional design solutions and summarize their complex patterns, hereby enhancing the design process. Italic text The basic drafting procedure is to place a piece of paper on a smooth surface with right-angle corners and straight sides—typically a drawing board. A sliding straightedge known as a T-square is placed on one of the sides, allowing it to be slid across the side of the table, over the surface of the paper. "Parallel lines" can be drawn by moving the T-square and running a pencil or technical pen along the T-square's edge.
The T-square is used to hold other devices such as set triangles. In this case, the drafter places one or more triangles of known angles on the T-square—which is itself at right angles to the edge of the table—and can draw lines at any chosen angle to others on the page. Modern drafting tables come equipped with a drafting machine, supported on both sides of the table to slide over a large piece of paper; because it is secured on both sides, lines drawn along the edge are guaranteed to be parallel. In addition, the drafter uses several technical drawing tools to draw circles. Primary among these are the compasses, used for drawing simple arcs and circles, the French curve, for drawing curves. A spline is a rubber coated articulated metal. Drafting templates assist the drafter with creating recurring objects in a drawing without having to reproduce the object from scratch every time; this is useful when using common symbols. Templates are sold commercially by a number of vendors customized to a specific task, but it is not uncommon for a drafter to create his own templates.
This basic drafting system requires an accurate table and constant attention to the positioning of the tools. A common error is to allow the triangles to push the top of the T-square down thereby throwing off all angles. Tasks as simple as drawing two angled lines meeting at a point require a number of moves of the T-square and triangles, in general, drafting can be a time-consuming process. A solution to these problems was the introduction of the mechanical "drafting machine", an application of the pantograph which allowed the drafter to have an accurate right angle at any point on the page quite quickly; these machines included the ability to change the angle, thereby removing the need for the triangles as well. In addition to the mastery of the mechanics of drawing lines and circles onto a piece of paper—with respect to the detailing of physical objects—the drafting effort requires a thorough understanding of geometry and spatial comprehension, in all cases demands precision and accuracy, attention to detail of high order.
Although drafting is sometimes accomplished by a project engineer, architect, or shop personnel, skilled drafters accomplish the task, are always in demand to some degree. Today, the mechanics of the drafting task have been automated and accelerated through the use of computer-aided design systems. There are two types of computer-aided design systems used for the production of technical drawings" two dimensions and three dimensions. 2D CAD systems such as AutoCAD or MicroStation replace the paper drawing discipline. The lines, circles and curves are created within the software, it is down to the technical drawing skill of the user to produce the drawing. There is still much scope for error in the drawing when producing first and third angle orthographic projections, auxiliary projections and cross sections. A 2D CAD system is an electronic drawing board, its greatest strength over direct to paper technical drawing is in the making of revisions. Whereas in a conventional hand dr