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Zebra markings - mathematics activities

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Credits:

With permission of the Australian Association of Mathematics Teachers

Creator:

Toby Spencer, photographer, 2005

TLF ID:

R11193

Source:

Australian Association of Mathematics Teachers, http://www.aamt.edu.au/

Description:

This photograph of zebras shows the natural markings on the animals. The origin and purpose of the zebras' pelt markings may intrigue many students. The scientific explanation (the work of gifted mathematicians, biologists and chemists) is quite sophisticated. These images provide an opportunity to address concepts of symmetry, camouflage and habitat in a cross-discipline approach. The work of mathematician James Murray in the late 1970s first presented a unified (although incomplete) explanation for the varied phenomena of pelt markings in the animal world. Teachers are encouraged to scan all the ideas suggested here as relevant to the various year level groupings, as there is clearly an increasing mathematical complexity in the activities.

Key learning objectives:

Early years - an introduction to symmetry with examples from the natural world.
Middle years - adaptation in the wild; camouflage.
Senior years - a rich context for the interrelationship of mathematical modelling and chemistry.

Educational value:

Line symmetry is prevalent in nature. Many insects display almost perfect line symmetry. The pelt markings on many large animals display 'near' line symmetry. Investigating insects and plants with perfect line symmetry and comparing them to the pelt markings will assist students to formulate a clear idea of the principles of line symmetry.
Although dated, the Kipling fable of 'How the leopard got his spots' from the 'Just So Stories' might be a way to introduce the concepts of camouflage. The outdated language and precepts of this story would need to be discussed, as some of the language is nowadays considered derogatory.
Images of zebra or other animal pelts may raise issues of ethical and moral questions regarding the killing and use of animal pelts.
Line symmetry can be explored in a mathematical context in 2D shapes. This could lead to an investigation of reflection in transformation geometry.
The Kipling fable is an introduction to the intricate realities of pelt markings as revealed by modern mathematics and science. The currently accepted explanation of the different markings in animal pelts is a reaction-diffusion model of two different chemicals' effects on the spread (and isolation) of melanin, a skin pigment by-product of the amino acid tyrosine.
The original construct was proposed by Alan Turing, but developed and elaborated by several biologists and mathematicians, including James Murray. Murray's mathematical model attempts to give a single formulation involving higher-order partial differential equations. At the animals' embryonic level (with variation of just a few of the parameters), Murray's model predicted very precisely the various markings in skins of different thickness and shape in different species.

Keywords:

Axis; Symmetry; Transformation (Geometry); Two-dimensional shapes

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