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, meaning 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 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, and 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, experiences, 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), designs on Rarotongan tivaevae, 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 patterns are throughout the world.
Te reo Māori vocabulary terms such as hangarite (symmetry, symmetrical), hangarite hurihanga (rotational symmetry), whakaata (reflect, reflection), huri (rotate, rotation), and neke (translate, translation) could be introduced in this unit and used throughout other mathematical learning.
Dear family and whānau,
This week we are looking at symmetry and at company logos. We appreciate your help by working with your child to find examples of logos in magazines, television commercials or on websites. For homework your child is asked to sketch two logos in their book and describe their symmetries. Ask your student to explain what reflective and rotational symmetries are, using the logos as examples.
Printed from https://nzmaths.co.nz/resource/logo-licenses at 6:21pm on the 8th May 2024