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

Chapter problem temperature around the globe.., predict whether there is a ...

predict whether there is a relationship between the mean January temperatures of a city in North America and the city''s position west of the prime meridian.

Find the value of delta, Consider the given graph G below. Find δ( G )=__...

Consider the given graph G below. Find δ( G )=_____ , λ( G )= _____ , κ( G )= _____, number of edge-disjoint AF -paths=_____ , and number of vertex-disjoint AF -paths= ______

how large a sample is necessary to have a standard error, If the populatio...

If the population standard deviation is o=8, how large a sample is necessary to have a standard error that is: a.  less than 4 points? b.  less than 2 points? c.  less than 1 poin

Geometry, Determine the coordinates of the point equidistant from Salt Lake...

Determine the coordinates of the point equidistant from Salt Lake City and Helena

The alternative hypothesis, The alternative hypothesis When formulatin...

The alternative hypothesis When formulating a null hypothesis we also consider the fact that the belief may be found to be untrue thus we will refuse it.  Therefore we formula

Probability, an insurance salesman sells policies to 5 men, all of identica...

an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p

Mdm4uc, The number of hours spent studying and achievement on an exam

The number of hours spent studying and achievement on an exam

Logarithmic function:solve for x: 4 log x2, Solve for x: 4 log x = log (15 ...

Solve for x: 4 log x = log (15 x 2 + 16) Solution:              x 4 - 15 x 2 - 16 = 0                (x 2 + 1)(x 2 - 16) = 0                x = ± 4   But log x is

What is the cost per ounce of detergent, A 64-ounce bottle of detergent cos...

A 64-ounce bottle of detergent costs $3.20. What is the cost per ounce of detergent? To ?nd out the cost per ounce, divide the cost through the number of ounces; $3.20 ÷ 64 =

Question, If X = {a, e, i, o, u} and Y = {a, b, c, d, e}, then what is Y - ...

If X = {a, e, i, o, u} and Y = {a, b, c, d, e}, then what is Y - X ?

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