This unit examines the use of reflective, rotational, and translational symmetry in the design of logos. Logos are designs associated with a particular trade name or company and usually involve symmetry to make them aesthetically pleasing as well as functional.
This unit centres on symmetry, particularly reflective and rotational symmetry, although there is some reference to translation 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 Mitsubishi logo. There are three lines where a mirror could be placed and the whole figure could be seen, with the image in the mirror forming the hidden half.
This logo also has rotational symmetry about a point. Each turn of 120⁰ (one third of one full rotation) maps the logo onto itself. Since the logo maps onto itself three times in a full turn of 360⁰, the figure has rotational symmetry of order three.
The mathematics of symmetry is found in decorative design, like kowhaiwhai in wharenui, and wallpaper patterns, and motifs such as logos. Human beings are naturally appreciative of symmetry, possibly 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 in Aotearoa. Search for symmetry to show how common geometric pattern is throughout the world.
Printed from https://nzmaths.co.nz/resource/logo-licenses at 5:43am on the 20th May 2022