Theory like coordinate geometry

In summary, one-to-one correspondence is necessary for theories like coordinate geometry, polar coordinate, and vector analysis to work. These theories represent quantities by using different sets of quantities that behave similarly. Different notations can be used for the same object as long as there are rules for identifying them. For example, 1/2 and 2/4 are different notations for the same rational number, and 0° and 360° are different notations for the same angle. Similarly, in vector analysis, a vector can be represented by a straight directed line, and its properties can be found using this representation. This is because vectors belong to the same class of entities. Similarly, ordered triplets and points are two quantities that represent each
  • #1
sadhu
157
0
is one -one correspondence must for a theory like coordinate geometry , polar coordinate ,vector analysis etc
to work , i.e theories which work by representing a quantity by a different set of quantities
behaving alike
 
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  • #2
It's hard to tell exactly what you're asking... but I think I can answer.

It is fairly common to allow many different notations for the same object; you just have to include rules for identifying when two notations denote the same object.

e.g. 1/2 and 2/4 are two different notations for the same rational number, and 0° and 360° are two different notations for the same angle. (0° and 360° are different angular displacements, of course)
 
  • #3
what i meant was like in vector we represent a vector by a straight directed line and then use its property to find the property of the represented vector .

this is because they belong to same class of entities i.e vectors

similiarly ordered triplets and points are two quantities which represent each other in space
 

1. What is the definition of coordinate geometry?

Coordinate geometry is a branch of mathematics that deals with the study of geometric figures using a coordinate system. It involves using algebraic methods to solve problems related to points, lines, curves, and other geometric shapes.

2. How is coordinate geometry different from traditional geometry?

While traditional geometry focuses on the properties and relationships of geometric figures, coordinate geometry uses a coordinate system to represent those figures and solve problems using algebraic equations and formulas. It also allows for the use of tools such as coordinate planes and graphs to visualize and analyze geometric concepts.

3. What are some common applications of coordinate geometry?

Coordinate geometry has many practical applications in fields such as engineering, physics, computer science, and economics. It is used to model and analyze real-world situations involving motion, distance, and direction, as well as to solve optimization problems and design structures and systems.

4. What are the basic principles of coordinate geometry?

The basic principles of coordinate geometry include the use of a coordinate system to represent points and lines, the use of equations and formulas to describe geometric figures, and the use of geometric transformations such as translation, rotation, and reflection to manipulate and analyze figures.

5. How can I improve my skills in coordinate geometry?

To improve your skills in coordinate geometry, it is important to practice solving problems and working with geometric figures on a coordinate plane. You can also study and understand the underlying concepts and formulas, and use additional resources such as textbooks, online tutorials, and practice exercises to strengthen your understanding and problem-solving abilities.

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