Is This Equation Symmetric About the Origin?

In summary, the purpose of conducting a test for symmetry is to determine whether an object or system possesses a symmetry or not. This is done by observing and analyzing for symmetrical elements or characteristics using mathematical and physical principles, as well as visual inspection and experimentation. There are three main types of symmetry that can be tested for: reflection symmetry, rotational symmetry, and translational symmetry. A test for symmetry has various real-world applications in fields such as crystallography, physics, architecture, design, and biology. It can also be used to identify asymmetrical objects or systems, providing valuable insights and aiding in problem-solving and decision making.
  • #1
mathdad
1,283
1
Test for symmetry about the x-axis, y-axis and the origin.

|x + y| = 2

About y-axis:

|-x + y| = 2

Not symmetric about y-axis.

About x-axis:

|x + -y| = 2

I say not symmetric about the x-axis.

About the origin:

|-x + -y| = 2

Not symmetric about the origin.

Correct? If not, why?
 
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  • #2
I agree there is no symmetry about the axes, however:

\(\displaystyle |(-x)+(-y)|=|-(x+y)|=|x+y|\)

Hence, this is symmetric about the origin.
 
  • #3
MarkFL said:
I agree there is no symmetry about the axes, however:

\(\displaystyle |(-x)+(-y)|=|-(x+y)|=|x+y|\)

Hence, this is symmetric about the origin.

Nicely done!
 

FAQ: Is This Equation Symmetric About the Origin?

What is the purpose of conducting a test for symmetry?

The purpose of conducting a test for symmetry is to determine whether a particular object or system possesses a symmetry or not. This can help in understanding the underlying properties and patterns of the object or system, and can also aid in making predictions and solving various problems.

How is a test for symmetry conducted?

A test for symmetry is conducted by observing and analyzing the object or system in question for any symmetrical elements or characteristics. This can involve using mathematical and physical principles, as well as visual inspection and experimentation.

What are the different types of symmetry that can be tested for?

There are three main types of symmetry that can be tested for: reflection symmetry, rotational symmetry, and translational symmetry. Reflection symmetry involves a mirror-like reflection of an object or system, rotational symmetry involves a repeated pattern around a central point, and translational symmetry involves a repeated pattern shifted in space.

What are some real-world applications of a test for symmetry?

A test for symmetry has various real-world applications, such as in crystallography to determine the structure of crystals, in physics to understand the behavior of particles and systems, in architecture and design to create aesthetically pleasing structures, and in biology to study the symmetry of organisms and their functions.

Can a test for symmetry be used to identify asymmetrical objects or systems?

Yes, a test for symmetry can also be used to identify objects or systems that do not possess any symmetrical elements. This can help in understanding the unique properties and characteristics of asymmetrical objects and systems, and can also aid in problem-solving and decision making.

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