# Student Projects/Geometric patterns

A geometric pattern is a kind of pattern formed by geometric shapes that typically repeats like a design. These patterns can be easily observed by using our senses. But to observe certain complicated patterns that are abstract, analysis is necessary, especially in mathematics and science.Factors like the rule, number of turns, number of rotations,direction of rotation, angle of rotation help us identify the pattern.Patterns are generally created by rotational and reflectional symmetry.

### Symmetry[edit | edit source]

Any object is said to be symmetric when it remains unchanged on any transformation like rotation or reflection. There are two types of symmetry, namely reflectional symmetry ( also called as line symmetry or mirror symmetry) and rotational symmetry. If a line going through a object divides it into two parts which are mirror images of each other, then the object is said to possess reflectional symmetry and if a object can be rotated about a fixed point without changing the overall shape, then it is said to possess rotational symmetry.

#### Line symmetry[edit | edit source]

A figure has line symmetry if a line can be drawn dividing the figure into two identical parts and the line dividing them is called as line of symmetry. Both the parts are mirror images of each other. The line of symmetry is also called the mirror line or axis of symmetry. Lines of symmetry can be vertical, horizontal or diagonal.A figure may have no line of symmetry, only one line of symmetry, two lines of symmetry or multiple lines of symmetry. For example, circle has infinite lines of symmetry. Regular polygons have as many line of symmetry as their number of sides.

#### Rotational symmetry[edit | edit source]

If, after a rotation, an object looks exactly the same, then it is said to have a rotational symmetry and the object is rotated about a fixed point.This fixed point is the centre of rotation. The angle by which the object rotates is the angle of rotation. The order of rotational symmetry of a geometric figure is the number of times the geometric figure can be rotated so that its looks exactly the same as the original figure.