Real life applications of Analytical Geometry

 Application of Mathematics in Real Life

Definition

        The study of geometry using coordinate points is known as coordinate geometry (or analytic geometry). It is a portion of geometry in which the position of a point is determined by coordinates. A series of values called coordinates is used to show the exact location of a point in the coordinate plane.

It’s always better to understand how information benefits us in the real world. Let’s look at how the co-ordinate geometry can be applied in practice.

Coordinate geometry applications

A few examples of coordinate geometry applications are shown below.

• It’s used to figure out how far two points are apart.
• It is used to calculate the dividing line ratio in the m:n ratio.
• It is used to find the line’s midpoint.
• It’s used to figure out how big a triangle in the Cartesian plane is.
• It’s used in physics, GPS, maps, and a variety of other fields under various names. The underlying principle is the same in every situation: you choose an origin, assign a measure of unit distance, and define two or three directions, and bingo, you can now locate any point! After a couple more points are fixed, do a few extra amazing things.
• Even a computer monitor employs some basic coordinate geometry concepts. Complex curves, conics, and shapes can be mathematically specified using algebraic equations, which would be impossible to analyze using pure geometry.

Some of the detailed applications are shown below.

The Digital Use

The text file or PDF file is an example of coordinate plane usage. The words or graphics in these files are written or edited using coordinate geometry. A 2-dimensional coordinate (x, y) system is used to read any PDF file that comprises text and graphics. Coordinate geometry is also used by scanners and photocopying machines to generate a perfect copy of the original image.

Use in GPS

The Global Positioning System (GPS) is a satellite navigation system that delivers position and timing information in all weather circumstances.

Nature, which surrounds mankind, is the most essential example of geometry in everyday life. Different geometrical shapes and patterns can be found in leaves, flowers, stems, roots, bark, and so on if one looks closely. Geometry is also important in the human digestive system since it is organised like a tube within a tube. Tree leaves come in a variety of forms, sizes, and symmetries. Different geometrical shapes are found in different fruits and vegetables; for example, an orange is a sphere, and after peeling it, one can see how the individual slices make a perfect spherical shape.

Determining Latitude and Longitude

A coordinate framework is required for defining the precise location of a place in the actual world. To assign geographic locations, a particular coordinate system known as the geographical coordinate system is utilised. When weather forecasters watch storms in real life, they note the absolute position on a regular basis to see the storm’s route and try to anticipate the storm’s future path based in part on these discoveries.

Locating Air Transport

Coordinate geometry is used to manage and regulate air traffic. The coordinates of the flight are used to describe the aircraft’s current location. Even if an aircraft moves a tiny distance (up, down, forward, or backward), the system updates the coordinates of flight for every small change in its position.

Defining the location of any object

A coordinate system can be used to determine the position of any item from its starting point (known as the origin) to its current location.

For example, we can measure the distance between the watch and the television from the other side of the room. Allow a horizontal gap of 10 metre between the television and the corner, and a vertical distance of 5 metre between the watch and the ground. If the room is 5 metres wide, we can easily locate the watch’s coordinates and use the distance calculation to calculate its real distance.

Projection of Maps

Map Any 3D curved object can be projected onto a flat 2D surface via projection. This approach can be used to portray the curved surface of the earth on a flat map, for example. A unique sort of coordinate system known as a projected coordinate system is utilised for these purposes. These are primarily used to display maps on a computer screen.

Technology

Technology is the most widespread use of geometry in everyday life. Geometry is used in almost all basic principles in robotics, computers, and video games. Computer programmers can work because they have access to geometric principles at all times. Geometric computations aid in the production of sophisticated graphics in video games, which is how the virtual world of video games is generated. Raycasting is a shooting technique that uses a 2-D map to stimulate the 3-D environment of video games. Raycasting aids in processing speed by performing computations for the vertical lines on the screen.

Art

What exactly does art entail? The formation of figures and shapes, a fundamental comprehension of 2-D and 3-D, knowledge of spatial concepts, and the contribution of estimating, patterns, and measurement are all included in art. From the foregoing, it is clear that art and geometry have a close link. Geometrical forms such as the circle, triangle, square, mandala, and octagon are used to create shapes. Furthermore, the design and shape of frames have a significant impact on the content of paintings or sculptures. Not to mention that the principles of projective geometry are the foundation for most painting perspectives.

Conclusion

In this article, we have understood the application of coordinate geometry in our day-to-day life. We have discussed how coordinate geometry is useful in our life and have discussed various examples of coordinate geometry which will help us to visualise the concept and ultimately help in a deeper understanding of the topic.