WHAT IS TERMINAL VELOCITY?


When something is dropped and is pulled by gravity towards the Earth, it accelerates as it falls until it reaches a velocity from which it can accelerate no further. This is called its terminal velocity. Terminal velocity happens when the force of the air resistance against the falling object increases to the point where it equals the force of gravity pulling the object. The terminal velocity of an object depends on how much air resistance it experiences. This is not affected by its weight but by its surface area and the streamlining of its shape.



Terminal velocity is achieved, therefore, when the speed of a moving object is no longer increasing or decreasing; the object’s acceleration (or deceleration) is zero. The force of air resistance is approximately proportional to the speed of the falling object, so that air resistance increases for an object that is accelerating, having been dropped from rest until terminal velocity is reached. At terminal velocity, air resistance equals in magnitude the weight of the falling object. Because the two are oppositely directed forces, the total force on the object is zero, and the speed of the object has become constant.



Terminal velocity, steady speed achieved by an object freely falling through a gas or liquid. A typical terminal velocity for a parachutist who delays opening the chute is about 150 miles (240 kilometres) per hour. Raindrops fall at a much lower terminal velocity, and a mist of tiny oil droplets settles at an exceedingly small terminal velocity. An object dropped from rest will increase its speed until it reaches terminal velocity; an object forced to move faster than its terminal velocity will, upon release, slow down to this constant velocity.








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WHAT IS ACCELERATION?


Acceleration is a change in the velocity of an object. We often think of it as “speeding up”, but there is also negative acceleration, known as deceleration. Acceleration is measured in metres per second per second (m/s2). A change of direction is also acceleration, as the velocity is changed.



A sprinter accelerates from zero velocity by pushing against the blocks. This propels her forward, but she will still be accelerating for several metres before she reaches her fastest velocity. Her momentum carries her forward even after she has passed the finish line, but as she stops using energy to push her feet against the ground, she gradually slows and stops.



Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.



If you’re not changing your speed and you’re not changing your direction, then you simply cannot be accelerating—no matter how fast you’re going. So, a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration, even though the jet is moving really fast, since the velocity isn’t changing. When the jet lands and quickly comes to a stop, it will have acceleration since it’s slowing down.



Or, you can think about it this way. In a car you could accelerate by hitting the gas or the brakes, either of which would cause a change in speed. But you could also use the steering wheel to turn, which would change your direction of motion. Any of these would be considered acceleration since they change velocity.



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WHAT IS RELATIVE VELOCITY?


Relative velocity is the velocity that one object has when viewed from another moving object. It is something that we are frequently aware of throughout the day, although we are not thinking in scientific terms. For example, if you are sitting still and a dog walks past, it seems to be moving quite quickly. If you later go for a run and pass the dog, still moving at the same velocity, it will seem to be travelling much more slowly.



When you are traveling in a car or bus or train, you see the trees, buildings and many other things outside going backwards. But are they really going backwards? No, you know it pretty well that it’s your vehicle that is moving while the trees are stationary on the ground. But then why do the trees appear to be moving backwards? Also the co-passengers with you who are moving appear stationary to you despite moving.



It’s because in your frame both you and your co-passengers are moving together. Which means there is no relative velocity between you and the passengers? Whereas the trees are stationary while you are moving. Therefore trees are moving at some relative velocity with respect to you and the other passenger. And that relative velocity is the difference of velocities between you and the tree. The relative velocity is the velocity of an object or observer B in the rest frame of another object or the observer A.







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WHAT IS THE DIFFERENCE BETWEEN SPEED AND VELOCITY?


Speed is a measure of how quickly something is moving. Usually when we are talking about speed, we mean average speed. This is the time that it takes to travel from one point to another divided by the distance travelled. So speed is expressed in units such as kilometres per hour (km/h) or metres per second (m/s). Velocity, however, is a vector quantity. It measures the direction of movement as well as the speed.



Speed is how fast an object is moving, while velocity is the rate at which an object changes position in a certain direction. Speed is calculated by the displacement of space per a unit of time. Velocity is calculated by the displacement of space per a unit of time in a certain direction. In short, velocity factors in direction, but speed does not.



Speed refers to how fast an object is moving. It is calculated by the displacement of space per a unit of time. Velocity refers to the rate at which an object changes position in a certain direction. It is calculated by the displacement of space per a unit of time in a certain direction.



This definition might sound the same, but there is a crucial difference. It deals with direction. Velocity deals with direction and speed does not. Let me give you an example.



If you were driving at 50 miles per hour to get to a store, you would say that your speed is 50 miles per hours. If you were driving in a circle and ended at the same place, you would say that your velocity is zero, because there was no directional gain. The key to remember is that velocity is a vector, which means there is a directional component.






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WHAT IS ANIMATRONICS?


A method of animating models by using specially developed robotic techniques is called animatronics. It is especially useful for museum displays and cinema work, where animatronic models of such creatures as dinosaurs, monsters or aliens can “act” alongside human actors.



An Animatronic is an electro-mechanically animated puppet. It is a modern variant of the automaton and is often used for the portrayal of characters in films and in theme park attractions.



Before the term "animatronics" became common, they were usually referred to as "robots". Since then, robots have become known as more practical programmable machines that do not necessarily resemble living creatures. Robots (or other artificial beings) designed to convincingly resemble humans are known as "androids".



Animatronics is a multi-disciplinary field which integrates puppetry, anatomy and mechatronics. Animatronic figures can be implemented using both computer control and human control, including teleoperation. Motion actuators are often used to imitate muscle movements and create realistic motions in limbs. Figures are usually covered with body shells and flexible skins made of hard and soft plastic materials and finished with details like colors, hair and feathers and other components to make the figure more lifelike.





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WHAT IS VIRTUAL REALITY?


Virtual reality is a series of effects produced by a computer that enables someone wearing special equipment to feel as if they are really within an artificially created world. The person experiencing the effect wears a helmet through which sounds and pictures are relayed, but this is not like watching a movie. The computer technology makes it possible to turn round and “see” what is behind you. You can also move through the created world, exploring and having adventures. Wearing electronically controlled gloves and other clothing even makes it possible for you to “feel” objects in the virtual world.



Virtual Reality (VR) is the use of computer technology to create a simulated environment. Unlike traditional user interfaces, VR places the user inside an experience. Instead of viewing a screen in front of them, users are immersed and able to interact with 3D worlds. By simulating as many senses as possible, such as vision, hearing, touch, even smell, the computer is transformed into a gatekeeper to this artificial world. The only limits to near-real VR experiences are the availability of content and cheap computing power.



Virtual Reality and Augmented Reality are two sides of the same coin. You could think of Augmented Reality as VR with one foot in the real world: Augmented Reality simulates artificial objects in the real environment; Virtual Reality creates an artificial environment to inhabit.



In Augmented Reality, the computer uses sensors and algorithms to determine the position and orientation of a camera. AR technology then renders the 3D graphics as they would appear from the viewpoint of the camera, superimposing the computer-generated images over a user’s view of the real world.



In Virtual Reality, the computer uses similar sensors and math. However, rather than locating a real camera within a physical environment, the position of the user’s eyes are located within the simulated environment. If the user’s head turns, the graphics react accordingly. Rather than compositing virtual objects and a real scene, VR technology creates a convincing, interactive world for the user.



Virtual Reality’s most immediately-recognizable component is the head-mounted display (HMD). Human beings are visual creatures, and display technology is often the single biggest difference between immersive Virtual Reality systems and traditional user interfaces. For instance, CAVE automatic virtual environments actively display virtual content onto room-sized screens. While they are fun for people in universities and big labs, consumer and industrial wearable’s are the Wild West.




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HOW HAVE ROBOTS BEEN USED IN SPACE TRAVEL?


Robots have already been sent to distant planets, such as Mars. They are able to land on surfaces that might be hostile to human beings, to take soil and atmospheric samples, analyze them and send the results back to Earth. Missions “manned” by robots are much cheaper than those including humans and robots do not necessarily have to be brought home again! Robotics is the study of robots. Robots are machines that can be used to do jobs. Some robots can do work by themselves. Other robots must always have a person telling them what to do.



NASA uses robots in many different ways. Robotic arms on spacecraft can move large objects in space. Robotic spacecraft can visit other worlds. Robotic airplanes can fly without a pilot aboard. NASA is studying new types of robots. These will work with people and help them.



Robots help explore space. Spacecraft that explore other worlds, like the moon or Mars, are robots. These include orbiters, landers and rovers on other planets. The Mars rovers Spirit and Opportunity are robots. Other robotic spacecraft fly by or orbit other worlds. These robots study planets from space. The Cassini spacecraft is this type of robot. Cassini studies Saturn and its moons and rings. The Voyager and Pioneer spacecraft are now traveling beyond our solar system. They are also robots. People use computers to send messages to the spacecraft. The robots have antennas that pick up the message commands. Then the robot does what the person has told it to do. 



NASA is developing new robots to help people in space. One of these ideas is called Robonaut. Robonaut looks like the upper body of a person. It has a chest, head and arms. Robonaut could work outside a spacecraft. It could do work like an astronaut on a spacewalk. With wheels or another way of moving, Robonaut could work on another world. Robonaut could help astronauts on the moon or Mars.



Another robot idea is called SPHERES. These small robots look a little like soccer balls. SPHERES are being used on the space station to test how well they can move there. Someday, robots could fly around the station helping astronauts.



NASA is studying other ideas for robots. A small robotic arm could be used inside the station. A robot like that might help in an emergency. If an astronaut were seriously hurt, a doctor on Earth could use the arm to perform surgery. This technology could help on Earth, as well. Doctors could help people in faraway places where there are no doctors.



Robots also can be used as scouts to check out new areas to be explored. Scout robots can take photographs and measure the terrain. This helps scientists and engineers make better plans for exploring. Scout robots can be used to look for dangers and to find the best places to walk drive or stop. This helps astronauts work more safely and quickly. Having humans and robots work together makes it easier to study other worlds.




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HOW ARE ROBOTS USED IN INDUSTRY?


As well as being useful in dealing with chemicals that would be dangerous to humans, robots have their uses in manufacturing industry. On production lines, the same action is done over and over again as part-made products pass along a conveyor belt. This is very tedious for human workers. Specialist robots, which can perform only one action, are ideal for this work, but humans are still needed to control them and to act if something goes wrong, as most robots are not designed to respond to unusual situations.



An industrial robot is a robot system used for manufacturing. Industrial robots are automated, programmable and capable of movement on three or more axes.



Typical applications of robots include welding, painting, assembly, disassembly, pick and place for printed circuit boards, packaging and labeling, palletizing, product inspection, and testing; all accomplished with high endurance, speed, and precision. They can assist in material handling. In the year 2015, an estimated 1.64 million industrial robots were in operation worldwide according to International Federation of Robotics (IFR).



The most commonly used robot configurations are articulated robots, SCARA robots, delta robots and Cartesian coordinate robots, (gantry robots or x-y-z robots). In the context of general robotics, most types of robots would fall into the category of robotic arms (inherent in the use of the word manipulator in ISO standard 8373). Robots exhibit varying degrees of autonomy:



Some robots are programmed to faithfully carry out specific actions over and over again (repetitive actions) without variation and with a high degree of accuracy. These actions are determined by programmed routines that specify the direction, acceleration, velocity, deceleration, and distance of a series of coordinated motions.



Other robots are much more flexible as to the orientation of the object on which they are operating or even the task that has to be performed on the object itself, which the robot may even need to identify. For example, for more precise guidance, robots often contain machine vision sub-systems acting as their visual sensors, linked to powerful computers or controllers. Artificial intelligence, or what passes for it,] is becoming an increasingly important factor in the modern industrial robot.



Arc Welding



Arc-welding robots are common in steel production and automobile manufacturing plants. While human operators most often do the preparatory work, robots handle the parts and perform the weld. In addition to improving weld consistency, decreasing cycle times and enhancing production efficiency, welding robots have distinct health and safety advantages. Welding, which involves applying intense heat to connect two pieces of metal, exposes human workers to hazardous fumes and risks of arc burns. Replacing human workers with welding robots eliminates these risks.



Assembly Lines



Assembly robots are especially common in industries that use lean manufacturing processes. According to the ABB Group, a global power and technology company, an automated assembly line supports lean manufacturing businesses ranging from food processors to automotive manufacturing plants in a number of ways. Robots reduce waste, and decrease both wait and changeover time as they increase accuracy, consistency and assembly line speed. In addition, robots save human operators from tedious assembly line jobs.



Picking and Packing



The faster and more efficiently you can pick and pack products as they come off the assembly line, the better. However, picking and packing jobs require dexterity, consistency and flexibility, which over time can not only tax the health and safety of human workers but also decrease efficiency and speed. Picking and packing robots ensure consistent throughput, a measure of productivity within a given amount of time, which is why picking and packing robots are common in manufacturing industries.



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WILL ROBOTS EVER BE ABLE TO THINK FOR THEMSELVES?


In many ways, robots already do think for themselves, in the sense that they may have the ability to assess all the information available in a particular situation and make a decision based on what they “know”. Some robots can also “learn”, so that if an action is unsuccessful, they do not repeat it. But any robot is only as good as the electronic circuits that cause it to move and the engineering that has enabled it to respond physically to electronic signals. As computer technology becomes more sophisticated, so will robots. It is likely that they will play an important role in all our lives in the twenty-first century.



Generally, we say that robots don't have feelings and so they can't behave like humans. But the most important thing is the evolution through which we learn or develop a lot of new things about which we were never aware before that point. Perhaps the so called early humans, Homo erectus didn't have feelings and as the time passed by they were exposed to different situations and in trying to adapt to them they developed the feelings like hunger, pain, fear, love and so on. So if we give enough time and if robots have the ability to evolve in time, they could one day become as intelligent as humans and may have the feelings. Is this not possible?



This is of course not entirely true. A robot could mimic feelings, regardless of it actually feeling them, and could thus behave human-like. Also look up on the Turing-test on this one. But to cut down to the chase, we, humans, got certain hardware, biological equivalents to software and our neural system is a closed system, so yeah, we are theoretically able to fully create that, which includes everything from perception, to feelings, to creativity. The reason that we cannot do that right now, depends on our current understanding of the brain and (perhaps) the state of current technological equipment.



Finally, I'd like to respond to a couple of remarks from John Galvin: "AI, Robotics and so forth will always be bonded by the code created for them, and for such an AI to be consider equal to our mortal intelligence would require a programmer of greater intelligence"



We too are bonded by code (DNA, basically) and there is absolutely no reason to believe that we cannot figure out our own code (not saying it's easy though). So, once fully understood, there is no reason to assume that we cannot make ourselves. Heck, we're already reproducing ourselves by the billions; we just gotta look beyond the GUI of sexual intercourse.



Finally, you talk about the 7 logical gates a computer uses. Our current understanding of the brain tells us that neurons do precisely just that. Obviously, a computer is able to perform billions of actions with just those 7 gates; it's just that we don't exactly know how the brain uses those 7 gates to do what it does.



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WHAT IS A ROBOT?


A robot is a machine—especially one programmable by a computer— capable of carrying out a complex series of actions automatically. Robots can be guided by an external control device or the control may be embedded within. Robots may be constructed on the lines of human form, but most robots are machines designed to perform a task with no regard to their aesthetics.



Robots that resemble humans are known as androids; however, many robots aren't built on the human model. Industrial robots, for example, are often designed to perform repetitive tasks that aren't facilitated by a human-like construction. A robot can be remotely controlled by a human operator, sometimes from a great distance. A telechir is a complex robot that is remotely controlled by a human operator for a telepresence system, which gives that individual the sense of being on location in a remote, dangerous or alien environment and the ability to interact with it. Telepresence robots, which simulate the experience and some of the capabilities of being physically present, can enable remote business consultations, healthcare, home monitoring and childcare, among many other possibilities.



An autonomous robot acts as a stand-alone system, complete with its own computer (called the controller). The most advanced example is the smart robot, which has a built-in artificial intelligence (Al) system that can learn from its environment and its experience and build on its capabilities based on that knowledge.



Swarm robots, sometimes referred to as insect robots, work in fleets ranging in number from a few to thousands, with all fleet members under the supervision of a single controller. The term arises from the similarity of the system to a colony of insects, where the individuals and behaviors are simple but the fleet as a whole can be sophisticated.



Robots are sometimes grouped according to the time frame in which they were first widely used. First-generation robots date from the 1970s and consist of stationary, nonprogrammable, electromechanical devices without sensors. Second-generation robots were developed in the 1980s and can contain sensors and programmable controllers. Third-generation robots were developed between approximately 1990 and the present. These machines can be stationary or mobile, autonomous or insect type, with sophisticated programming, speech recognition and/or synthesis, and other advanced features. Fourth-generation robots are in the research-and-development phase, and include features such as artificial intelligence, self-replication, self-assembly, and nanoscale size (physical dimensions on the order of nanometers, or units of 10- meter).



Some advanced robots are called androids because of their superficial resemblance to human beings. Androids are mobile, usually moving around on wheels or a track drive (robots legs are unstable and difficult to engineer). The android is not necessarily the end point of robot evolution. Some of the most esoteric and powerful robots do not look or behave anything like humans. The ultimate in robotic intelligence and sophistication might take on forms yet to be imagined.



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HOW ARE ROBOTS USED FOR DANGEROUS JOBS?


There are many situations in which human beings can operate safely only by wearing bulky protective clothing and working for short periods at a time. Sometimes even that is not enough to protect them. If it is suspected that a booby-trapped bomb has been left in an abandoned vehicle, for example, a controlled explosion may be the only way of deactivating it. No matter how much protection a bomb disposal expert has, the explosion could be fatal if he or she is nearby. The answer is to use a robot carrying an explosive charge. The robot can be sent into the danger zone while experts remain at a safe distance. Although no one wants to destroy an expensive machine, the alternative is much worse.



Dirty jobs are often unsanitary or hazardous work that can impact human health. Even though these jobs are unfavorable, someone has to do them. They include waste management, livestock nurturing, and mine exploration. The robot can take away the risk from humans and keep them safe from harm.



One example is the need for sewer scrapers. When there is a problem with a sewer pipe, a crew shuts it off, digs to access the pipe, then fixes the infrastructure. But a robot can clean, map, and inspect pipes before the problems arise. Robots can also collect data like distance, pressure, temperature, and composition to get visibility of pollutants, infectious diseases, and drug use.



Dangerous jobs put humans in harmful situations. To prevent the loss of human life, robots can be used. They are able to measure and detect variables beyond human perception. Robots can defuse bombs, traverse distant planets, and inspect unstable structures. Robots are being used to inspect bridges. A high degree of expertise, risk, and cost is associated with manned bridge inspections. Multirotor drones are able to completely remove humans from dangerous situations. They inspect hard-to-access areas with advanced speed and maneuverability.



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HOW ARE ANGLES MEASURED?


Angles are measured in degrees, using a protractor. There are 360° in a circle, and 90° in a right angle. A triangle has a total of 180° in its three inner angles, so that if the size of two angles is known, it is always possible to work out the third. Since pairs of inner and outer angles must add up to 360°, it is also possible to work out the inner angles if two of the outer angles are known.



The concept of angle is one of the most important concepts in geometry. The concepts of equality, sums, and differences of angles are important and used throughout geometry, but the subject of trigonometry is based on the measurement of angles.



Angles: 15, 30, 45 degrees.



There are two commonly used units of measurement for angles. The more familiar unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°. we’ll only consider angles between 0° and 360°.



Degrees may be further divided into minutes and seconds, but that division is not as universal as it used to be. Each degree is divided into 60 equal parts called minutes. So seven and a half degrees can be called 7 degrees and 30 minutes, written 7° 30'. Each minute is further divided into 60 equal parts called seconds, and, for instance, 2 degrees 5 minutes 30 seconds is written 2° 5' 30". The division of degrees into minutes and seconds of angle is analogous to the division of hours into minutes and seconds of time.



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HOW CAN STANDARD UNITS BE USED FOR VERY SMALL AND VERY LARGE MEASUREMENTS?


Metric units can be multiplied or divided by 10 as often as is needed to create units of a useful size for measuring the object under consideration. For example, a unit of 1000 metres, which is the same as 10 x 10 metres, and can be written as 102 metres, is called a kilometre. The prefix “kilo”, meaning one thousand, can be applied to other units. A kilogram (kg) is equal to one thousand grams. Similarly, there is a prefix meaning one thousandth (10-3): milli. So one milligram is the same as a thousandth of a gram. On the right is a list of other prefixes and their meanings.



Length is the measurement of the extent of something along its greatest dimension. The SI basic unit of length, or linear measure, is the meter (m). All measurements of length may be made in meters, though the prefixes listed in various tables will often be more convenient. The width of a room may be expressed as about 5 meters (m), whereas a large distance, such as the distance between New York City and Chicago, is better expressed as 1150 kilometers (km). Very small distances can be expressed in units such as the millimeter or the micrometer. The width of a typical human hair is about 20 micrometers (?m).



Volume is the amount of space occupied by a sample of matter. The volume of a regular object can be calculated by multiplying its length by its width by its height. Since each of those is a linear measurement, we say that units of volume are derived from units of length. The SI unit of volume is the cubic meter (m 3 ), which is the volume occupied by a cube that measures 1 m on each side. This very large volume is not very convenient for typical use in a chemistry laboratory. A liter (L) is the volume of a cube that measures 10 cm (1 dm) on each side. A liter is thus equal to both 1000 cm3 (10 cm × 10 cm × 10 cm) and to 1 dm3. A smaller unit of volume that is commonly used is the milliliter (mL—note the capital L which is a standard practice). A milliliter is the volume of a cube that measures 1 cm on each side. Therefore, a milliliter is equal to a cubic centimeter (cm3). There are 1000 mL in 1 L, which is the same as saying that there are 1000 cm3 in 1 dm3.



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HOW ARE LATITUDE AND LONGITUDE MEASURED?


To pinpoint your position on a map of the world you need to work out your co-ordinates, known as latitude and longitude. Latitude is your position north or south of the Equator. Lines, or parallels, are drawn around the Earth at intervals. The North Pole is assigned the latitude 90º north and the South Pole latitude 90º south.



Lines of longitude, or meridians, are drawn a little differently. The line of longitude corresponding to 0º, which passes through Greenwich in London, is called the Prime (or Greenwich) Meridian. Longitude lines run along the Earth’s surface in a north–south direction, and unlike latitude lines, they divide the globe into segments like those of an orange, rather than regular strips.



It's possible to measure latitude by comparing your position on Earth with the position of either the sun or the North Star (Polaris). Measurements using the sun are possible on a clear day in the northern or southern hemispheres, when the sun is easy to find. However, measurement of latitude isn't as straightforward as you might think. Accurate readings can only be taken at noon, when the sun is at its highest in the sky. To complicate matters further, the sun rises higher in summer than in winter, and this must be allowed for in any calculation.



Being so far away and only one of a myriad stars visible to the naked eye, the North Star isn't as easy to find as the sun. Furthermore, you can only see it at night, which isn't always convenient. Its major limitation, however, is that it isn't visible from the southern hemisphere.



For our purposes, we shall therefore assume that we're in the northern hemisphere. You can use a simple quadrant to measure latitude using either the sun or the North Star.



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WHAT WAS THE EARLIEST SYSTEM OF MEASUREMENT?

It is likely that the first systems of measurement were based on the human body. As every person had a body, they could use themselves as reference! Of course, since people vary greatly in size, this was not a very accurate system.



This article looks at the problems surrounding systems of measurement which grew up over many centuries, and looks at the introduction of the metric system. Is the meaning of measurement? It is associating numbers with physical quantities and so the earliest forms of measurement constitute the first steps towards mathematics. Once the step of associating numbers with physical objects has been made, it becomes possible to compare the objects by comparing the associated numbers. This leads to the development of methods of working with numbers.



The earliest weights seem to have been based on the objects being weighed, for example seeds and beans. Ancient measurement of length was based on the human body, for example the length of a foot, the length of a stride, the span of a hand, and the breadth of a thumb. There were unbelievably many different measurement systems developed in early times, most of them only being used in a small locality. One which gained a certain universal nature was that of the Egyptian cubit developed around 3000 BC. Based on the human body, it was taken to be the length of an arm from the elbow to the extended fingertips. Since different people have different lengths of arm, the Egyptians developed a standard royal cubit which was preserved in the form of a black granite rod against which everyone could standardise their own measuring rods.



To measure smaller lengths required subdivisions of the royal cubit. Although we might think there is an inescapable logic in dividing it in a systematic manner, this ignores the way that measuring grew up with people measuring shorter lengths using other parts of the human body. The digit was the smallest basic unit, being the breadth of a finger. There were 28 digits in a cubit, 4 digits in a palm, 5 digits in a hand, 3 palms (so 12 digits) in a small span, 14 digits (or a half cubit) in a large span, 24 digits in a small cubit, and several other similar measurements. Now one might want measures smaller than a digit, and for this the Egyptians used measures composed of unit fractions.



It is not surprising that the earliest mathematics which comes down to us is concerned with problems about weights and measures for this indeed must have been one of the earliest reasons to develop the subject. Egyptian papyri, for example, contain methods for solving equations which arise from problems about weights and measures.



A later civilisation whose weights and measures had a wide influence was that of the Babylonians around 1700 BC. Their basic unit of length was, like the Egyptians, the cubit. The Babylonian cubit (530 mm), however, was very slightly longer than the Egyptian cubit (524 mm). The Babylonian cubit was divided into 30 kus which is interesting since the kus must have been about a finger's breadth but the fraction 1/30 is one which is also closely connected to the Babylonian base 60 number system. A Babylonian foot was 2/3 of a Babylonian cubit.



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