Explain what is symmetry in maths, Mathematics

Assignment Help:

Symmetry

Definition : A line of symmetry divides a set of points into two halves, each being a reflection of the other. Each image point is also a point of the set.

Definition : A set of points has line symmetry if a line can be drawn through it so that every image point on one side of the line is also a point of the set.
One way to test if a figure has line symmetry is to fold it in half along the supposed line of symmetry and see if the two sides are mirror images of each other. The following have one or more lines of symmetry. The number of symmetry lines is labeled.

Notice that while polygons have a limited number of symmetry lines, a circle has an infinite amount. Any line that passes through the center of the circle is a line of symmetry. The following do not have lines of symmetry.

A line of symmetry through a line segment is its perpendicular bisector.

Similarly, a line of symmetry of an angle is the line which bisects the angle.

Regular polygons have the same number of symmetry lines as their sides.

Definition : A reflection point is the midpoint of a line segment joining any point to its image point.

A set of points has point symmetry if there exists a point P, and every reflection of a point of the set through point P coincides with another point of the set.

In point symmetry, there is one point through which every other point is reflected. That point is also its own reflection. One way to test if a figure has point symmetry is to turn it upside-down and see if it looks the same. To understand the difference between line symmetry and point symmetry, compare the following examples:

A set of points has rotational symmetry, if it can be rotated with reference to a fixed point with a rotation less than 360; so that it coincides or overlaps with the same set of points.

Point symmetry is just one type of rotational symmetry where the figure coincides with itself when rotated 180. The following are examples of rotational symmetry where the figure is rotated at angles other than 180. They have rotational symmetry, but not point symmetry.


Related Discussions:- Explain what is symmetry in maths

rules for solving linear in-equations - linear algebra, Explain what are t...

Explain what are the Rules for solving linear in-equations?

Multiplication of binomials, To understand the multiplication of binomials,...

To understand the multiplication of binomials, we should know what is meant by Distributive Law of Multiplication. Suppose that we are to multiply (a + b) and m. We

Green function, greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t...

greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s

Compute steady state value of capital - solow growth model, Consider the So...

Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function Y t = AK 1-α t L α t a) Set up the underlying nonlinear differen

Chain rule, Chain Rule :   If f(x) and g(x) are both differentiable func...

Chain Rule :   If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x).  Proof We will s

Example of factoring quadratic polynomials, Factor following polynomials. ...

Factor following polynomials.                               x 2 + 2x -15 Solution x 2 +2x -15 Okay since the first term is x 2 we know that the factoring has to ta

Compound interest, you have RM5O,OOO to invest,and two fund that you''d li...

you have RM5O,OOO to invest,and two fund that you''d like to invest in.The You-Risk-It Fund yields 14% interest.The Extra-Dull Fund yields 6% interest.Besause of college financial-

Explain histogramsin details, Explain Histogramsin details? Another way...

Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:

Simplification, how do we answer questions with fraction mixed. what are th...

how do we answer questions with fraction mixed. what are the easier ways to do it

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd