This unit examines the use of reflective and rotational symmetry in the design of plates. Traditionally, designers often used symmetry to make plates aesthetically pleasing, however, more modern designs are often asymmetric.
This unit focuses on symmetry, particularly reflective and rotational symmetry. A shape has symmetry if it has spatial pattern, that is, it maps onto itself either by reflection about a line, or rotation about a point.
Consider the pattern on this plate. The whole figure is circular. Circles have infinite symmetry, so it is the arrangement of triangles within the circle that determines the symmetry of the whole design. There are eight lines where a mirror could be placed and the whole figure could be seen, with the image in the mirror forming the hidden half.
Four lines bisect opposite triangles:
Four lines bisect the space between opposite triangles:
This pattern also has rotational symmetry about a point, with the point being the centre of the plate. In a full turn, the plate design maps onto itself eight times. Therefore, the design has rotational symmetry of order eight. Each turn of 45⁰ (one eighth of 360⁰, one full rotation) maps the design onto itself. This angle is referred to as the angle of rotation.
The mathematics of symmetry is found in decorative design, like kōwhaiwhai in wharenui, and wallpaper patterns, and motifs such as logos. Human beings are naturally appreciative of symmetry, possibly because it is prevalent in the natural world. Creatures are approximately symmetrical, and reflections in water are a common example of mirror symmetry.
The learning opportunities in this unit can be differentiated by providing or removing support to students, by varying the task requirements. Ways to support students include:
Tasks can be varied in many ways including:
The contexts for this unit can be adapted to suit the interests and cultural backgrounds of your students. Capitalise on the interests of your students. Symmetry is common across all cultures of the world. Kowhaiwhai patterns on the rafters of wharenui (meeting houses), and designs on Fijian tapa or Samoan siapo cloth usually involve symmetries. Look for examples of symmetrical design in the local community. Encourage students to capture symmetric patterns they see and use the internet as a tool for finding images. An internet search for symmetry reveals how prevalent geometric pattern is throughout the world.
Te reo Māori kupu such as hangarite whakaata (line symmetry, reflective symmetry), rārangi hangarite (axis of symmetry, line of symmetry), tau hangarite (order of symmetry), hangarite hurihanga (rotational symmetry), and hangarite (symmetry, symmetrical) could be introduced in this unit and used throughout other mathematical learning
Dear family and whānau,
This week we are looking at symmetry using the context of dinner plates. We appreciate your help by working with your child to find examples of plate designs at home and on websites. Your child is asked to create two original plate designs and describe their symmetries. Ask your child to explain what reflective and rotational symmetries are, using the designs as examples.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/symmetry-crown-lynn at 10:49pm on the 26th February 2024