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Application of coordinate system and vectors in the real life
- 1. Application of coordinate systems and vectors in the real life Əliəkbər Rəhimli İlkin Nəsrəddin
- 2. Math in daily life Math is one of the most important part of the life. Someone can says that, there are many rulers, theorems and others in math, but do we need them in daily life?! Answer is YES. There many cases that math is the most important part of the life. Mathematics is defined as the science which deals with logic of shape, quantity and arrangement. During ancient times in Egypt, the Egyptians used math's and complex mathematic equations like geometry and algebra. That is how they managed to build the pyramids.
- 3. Some important fiels that we need math there Building bridges Digital music Roller Coaster Design Rocket and Satellites Automotive Design Satellite Navigation Computer Games MRI and Tomography
- 4. Coordinate systems. Cartesian means relating to the French mathematician and philosopher René Descartes (Latin: Cartesius), who, among other things, worked to merge algebra and Euclidean geometry. René Descartes who lived in the 1600s. When he was a child, he was often sick, so the teachers at his boarding school let him stay in bed until noon. He went on staying in bed until noon for almost all his life. While in bed, Descartes thought about math and philosophy. One day, Descartes noticed a fly crawling around on the ceiling. He watched the fly for a long time. He wanted to know how to tell someone else where the fly was. Finally he realized that he could describe the position of the fly by its distance from the walls of the room. When he got out of bed, Descartes wrote down what he had discovered. Then he tried describing the positions of points, the same way he described the position of the fly. Descartes had invented the coordinate plane! In fact, the coordinate plane is sometimes called the Cartesian plane, in his honor. History
- 5. Application of Coordinate Systems 1. Describing position The position of any object in the real world can be described using a simple coordinate system. For example, you could describe your phone’s position as being 2 meters across from the door, 3.5 meters up from the floor, and 4 meters in front of the window. In a coordinate system, each of the three numbers used to describe an object’s position corresponds to a coordinate axis. The place where the zero values along each axis meet is called the origin. In this example, the X equals 2, Y equals 4, and Z equals 3.5.
- 6. Application of Coordinate Systems 2. Location of Air Transport. Anytime one has a need to know the location of something – where something should be or where something actually is – a coordinate plane is a very useful tool. For this reason, applications that make use of mapping are common. An air traffic controller must know the location of every aircraft in the sky within certain geographic boundaries. In order to describe where each aircraft is situated, coordinates are assigned to each vehicle in the air. Alternatively, the “air traffic controller” can assign each “aircraft” certain coordinates, and the “aircraft” can report to the appropriate location. So coordinate system is one of the most important part of air transport. What if coordinate systems doesn’t exist, pilots or others that associated with air craft don’t know the position or location of aircraft so the percent of aircraft crashes will be increase.
- 7. Application of Coordinate Systems 3. Map Projections. A projected coordinate system is any coordinate system designed for a flat surface, such as a printed map or a computer screen. Both 2D and 3D Cartesian coordinate systems provide the mechanism for describing the geographic location and shape of features using x- and y-values. The Cartesian coordinate system uses two axes: one horizontal (x), representing east–west, and one vertical (y), representing north–south. The point at which the axes intersect is called the origin. Locations of geographic objects are defined relative to the origin, using the notation (x,y), where x refers to the distance along the horizontal axis and y refers to the distance along the vertical axis. The origin is defined as (0,0).
- 8. Application of Coordinate Systems 4. Latitude and longitude Describing the correct location and shape of features requires a coordinate framework for defining real-world locations. A geographic coordinate system is used to assign geographic locations to objects. A global coordinate system of latitude-longitude is one such framework. They are measures of the angles (in degrees) from the center of the earth to a point on the earth's surface. This type of coordinate reference system is often referred to as a geographic coordinate system.
- 9. Application of Coordinate Systems 5. Economy In economics, we use math widely, for analysing and managing. During the last century result in connection among math, economist, and statistics the new science occurred, that called “Econometrics”. In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth or income, and was developed by Max O.Lorenz in 1905 for representing inequality of the wealth distribution, and each calculation apply in coordinate system.
- 10. Application of Coordinate Systems 6. Military service Cartesian Coordinate system is also important thing in Military Service. For each target there are coordinates to determine the precise position of them. For example, a soldier want to explode some targets of enemy, so he must know the exact position of the target. If he know the position with coordinates, then it is so easy to explode or wipe out the target of enemy by warship or others. But it is important that they have to know exact coordinates, because if it is not calibrated correctly it will give rise to untold result.
- 11. Vectors. Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis. In the conventional form using cross products, vector calculus does not generalize to higher dimensions, while the alternative approach of geometric algebra, which uses exterior products does generalize. History
- 12. Application of Vectors 1. Cannon A cannon is any piece of artillery that uses gunpowder or other usually explosive-based propellants to launch a projectile. Cannon vary in caliber, range, mobility, rate of fire, angle of fire, and firepower; different forms of cannon combine and balance these attributes in varying degrees, depending on their intended use on the battlefield. Of course for this we need vectors. It is used also in aircraft. The first documented installation of a cannon on an aircraft was on the Voisin Canon in 1911, displayed at the Paris Exposition that year. By World War I, all of the major powers were experimenting with aircraft mounted cannons; however their low rate of fire and great size and weight precluded any of them from being anything other than experimental.
- 13. Application of Vectors 2. Sports (Baseball) Another example of a vector in real life would be an outfielder in a baseball game moving a certain direction for a specific distance to reach a high fly ball before it touches the ground. The outfielder can't just run directly for where he sees the ball first or he is going to miss it by a long shot. The player must anticipate what direction and how far the ball will be from him when it drops and move to that location to have the best chance of catching the ball.
- 14. Application of Vectors 3. Sports ( Football & Basketball & Golf ) In football match, player who want to score a goal, he cant shoot ball 10metres left, and after that 9metres right, it is impossible, so here we need vectors to determine the direction or trajectory of ball. Also in basketball match, this is the same. For throwing a ball through a netted hoop, again you have to know the direction or trajectory of ball. Golf is also same, but according to golf ball is small, you must consider the vector of wind force, if wind is strong, you must consider the wind force also in football.
- 15. Application of Vectors 4. Wind Vectors Lets say we have plane with constant velocity, and plane move to south, and we have wind force which direction of it is west, so due to plane movement is south and wind movement is west, finally plane move diagonally, or in the south-west. There is kind of win that experienced by an observer in motion and is the relative velocity of the wind in relation to the observer is called Apparent wind. Suppose you are riding a bicycle on a day when there is no wind. Although the wind speed is zero (people sitting still feel no breeze), you will feel a breeze on the bicycle due to the fact that you are moving through the air. This is the apparent wind. On the windless day, the apparent wind will always be directly in front and equal in speed to the speed of the bicycle.
- 16. Application of Vectors. 5. Apparent wind in sailing In sailing, the apparent wind is the actual flow of air acting upon a sail. It is the wind as it appears to the sailor on a moving vessel. It differs in speed and direction from the true wind that is experienced by a stationary observer. In nautical terminology, these properties of the apparent wind are normally expressed in knots and degrees. On boats, apparent wind is measured or "felt on face / skin" if on a dinghy or looking at any telltales or wind indicators on-board. True wind needs to be calculated or stop the boat. Windsurfers and certain types of boats are able to sail faster than the true wind. These include fast multihulls and some planing monohulls. Ice-sailors and land-sailors also usually fall into this category, because of their relatively low amount of drag or friction.
- 17. Application of Vectors 6. Force, Torque, Acceleration, Velocity and etc. For calculating every vectorial unit, you need vector. For example, there is a tire with mass m, and it has initial and final velocity, acceleration, gravitational, reaction, friction forces, and due to rotation it has torque. For getting the result, you need vectors. Maybe it seems like boring problem, but we need it in daily life, for instance finding velocity or acceleration of cars. In construction, every architect have to know their buildings of durability, for this they need forces that max how many force will apply to their building, and of course they need again vectors. So you can see how the vectors are important.
- 18. Application of Vectors 7. Roller Coaster A roller coaster is an amusement ride developed for amusement parks and modern theme parks. Most of the motion in a roller-coaster ride is a response to the Earth's gravitational pull. No engines are mounted on the cars. After the train reaches the top of the first slope the highest point on the ride the train rolls downhill and gains speed under the Earth's gravitational pull. The speed is sufficient for it to climb over the next hill. This process occurs over and over again until all the train's energy has been lost to friction and the train of cars slows to a stop. If no energy were lost to friction, the train would be able to keep running as long as no point on the track was higher than the first peak. Here vectors of forces, acceleration, and velocity are important to make a safety system, if designer consider them accurately then system will be safety.