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

Slope of tangent line, Slope of Tangent Line : It is the next major interp...

Slope of Tangent Line : It is the next major interpretation of the derivative. The slope of the tangent line to f ( x ) at x = a is f ′ ( a ) . Then the tangent line is given by,

Basic statistics, #questio Study A Stu...

#questio Study A Study B Study C x2 = 1.683 F = 7.357 r = .83 df = 4

Determine the volume of the pool, An inground pool is pooring with water. T...

An inground pool is pooring with water. The shallow end is 3 ft deep and gradually slopes to the deepest end, which is 10 ft deep. The width of the pool is 30 ft and the length is

Eometry constructions, construct an isosceles triangle ABC when:base BC is ...

construct an isosceles triangle ABC when:base BC is 6.2 and altitude a.a

find the slope and the y intercept of the line - geometry, 1. Find the slo...

1. Find the slope and the y-intercept of the line whose equation is 5x + 6y = 7. 2. Find the equation of the line that is parallel to 2x + 5y = 7 and passes through the mid poin

Calculate the mean, Calculate the mean, variance & standard deviation of th...

Calculate the mean, variance & standard deviation of the number of heads in a simultaneous toss of three coins.     SOLUTION:    Let X denotes the number of heads in a simu

Definition of relation, Definition of Relation A relation is a set of o...

Definition of Relation A relation is a set of ordered pairs. It seems like an odd definition however we'll require it for the definition of a function though, before actuall

Fractions, what the answer to 1/4+1/3=3/12=?

what the answer to 1/4+1/3=3/12=?

Share and divivdend, i m making a project on share and dividend. will u pls...

i m making a project on share and dividend. will u pls give the all of 10pages information ?

Which expression below is equal to 5, Which expression below is equal to 5?...

Which expression below is equal to 5? The correct order of operations must be used here. PEMDAS tells you in which you should do the operations in the subsequent order: Pare

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