Symmetry, Design and Tessellations

Subject: Compulsory Maths

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Overview

This note gives information about tessellation and its types and also it gives information about symmetry.A tessellation is known as tiling .
Symmetry, Design and Tessellations

The dotted line which is the half part of each shape to one side of a dotted line is the mirror image of the other parts is called the line of symmetry . In another word, it is also called the axis of symmetry , so the figure is said to have bilateral symmetry or to be symmetrical by reflection in the dotted line and a line of symmetry shape can be turned so as it exactly into its outline.

Source : math.cmu.edu Fig :Symmetry
Source : math.cmu.edu
Fig :Symmetry

Rotational symmetry

When a shape can be mapped onto itself by a rotation of less than a complete turn (360o) about a point the shape is said to have a rotational symmetry .

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Order of rotational symmetry

order of rotation
order of rotation

When the shape is rotated through a half -turn it can be fitted to the original shape . It means , when it is rotated through 2 times half-turns , it reaches its original position .

\(\therefore\) It has rotational symmetry of order 2.

When the equilateral triangle is rotated through a \(\frac{1}{3}\) of turn 120o, it can fit over the original shape. When it is rotated through3 times \(\frac{1}{3}\) and then it will reach its original place.

\(\therefore\) It has rotational symmetry of order 3.

When the square is rotated through quarter-turn \(\frac{1}{4}\)of the turn 90o. Which can be fitted over the original shape . It means when it is rotated through 4time \(\frac{1}{4}\)of turn , it reaches its original position .

\(\therefore\) It has rotational symmetry of order 4.

Tessellation

 mathworld.wolfram.com

A tessellation is known as tiling . It is covering of the plane with congruent geometrical shape un which a repeating pattern without leaving any gaps and without overlapping each other.The shape is polygons in it . It may be an equilateral triangle , regular hexagon or square . To make a tessellation :

  • We should not leave any gaps.
  • We should not have any overlaps.
  • We should use the sets of congruent figures .

Types of tessellation

  • Irregular tessellation : In this case , we use irregular types of polygons.
  • Semi-regular tessellations:In this case , we use two or more regular polygons . In the adjoining tessellation , regular octagons and squares are used .
  • Regular tesselation : In this case, we use the same types of regular polygons . The polygons that we use may be equilateral triangle, regular hexagon etc.

Things to remember
  • When the shape is rotated through a half -turn it can be fitted to the original shape .
  • To make a tessellation we should use the sets of congruent figures .
  • A tessellation is known as tiling . 
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Videos for Symmetry, Design and Tessellations
Tessellations
GCSE Maths from Scratch 18.05a Lines of Symmetry
Symmetry and Tesselation GCSE Maths Foundation revision
Questions and Answers

When a shape can be mapped onto itself by a rotation of less than a complete turn (360°) about a point, the shape is said to have rotational symmetry.

When the half part of each shape to one side of the dotted line is the mirror image of the other part, the dotted part is called the line of symmetry.

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