1. The document discusses the application of coordinate systems and vectors in real life contexts. It provides several examples, such as using coordinates to describe the location of objects or aircraft, map projections, latitude and longitude coordinates, their use in economics, and by the military. 2. Vectors are also discussed as applied to cannons, sports like baseball and football, wind vectors, and sailing. Calculating forces, torques, acceleration, and velocity also require the use of vectors. 3. Coordinate systems and vectors have many practical applications, from describing positions to applications in transportation, navigation, military targeting, sports, and physics concepts like motion. They underlie many areas of science, engineering, and daily 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.

19. References
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