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When Mathematics meets Art
- Is it possible?
Demonstration
Workshop
1. Introduction to STEAM
2.MathArt tessellations
• International trend towards STEAM
• Research shows the positive influence of including Art on the
performance of learners and the development of the STEM
subjects.
• Need to think more creatively
• Need innovators
• Explore mathematics and art in a different manner.
• The responses that we receive from teachers and learners
during the competitions motivate us
Why combine Maths and Art?
• Visual pathways are used when we work on mathematics
• The problem of mathematics in schools is it has been presented, for decades, as a subject of numbers and symbols.
• Mathematicians rarely if ever, solve a problem without visual representations.
• We all need to develop the visual areas of our brains.
“Learners with a more creative way of learning struggle in class,because the way mathematics is being taught is rigid and set in thepast.” Gr 12 Learner from Eastern Cape
“At my school we do not have the opportunity to nurture our skill inthe arts, design or mechanics/engineering……… deprives learners,like myself an opportunity to get a head start, to get the necessaryfoundation …..” Gr 12 Learner from Eastern Cape
Maths
or
Art?
Lines
Curves
Shape
Dimension
Proportion
Scale
Perspective
Size
Parallel
Mirror image
Line of symmetry
Golden Ratio
Pattern
Space
Creative Problem solving
Circle Geometry with Kadinsky
Really make Geometry
F U N
with the parallel lines
of Esther Mahlangu
Workshop objectives
• “Learning can be fun”
• Encourage Maths and Art to work together to improve innovation and creativity
• Inspire participants to see the links between Mathematics and Art.
• Stimulation of participants to start looking differently at the world around them.
• Encouraged participants to experiment with more examples in their own classes.
Transformations
▪ A transformation is a general term for 4 specific ways to manipulate
a point, a line, or shape.
▪ Changing a shape using
• Turn (rotation)• Flip (reflection)• Slide (translation) • Resize (enlargement)
▪ The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation.
Tessellations
Tessellations are arrangements or tiling of shapes
that cover the picture (surface)
without overlapping and
without leaving any gaps.
Not just manmade Look at tessellations in nature
The scales of a lizard’s leg
The patterns on a giraffe
Buildings
▪ Mathematicians, had shown that only the following regular
polygons, could be used for a tessellation.
▪ Why only these regular polygons?
▪ Because their angles are a factor of 360°
triangle, square, and hexagon
▪ Escher used these basic shapes in his tessellations but also
distorted them
60°
90° 120°
Artistic tessellations
Sometimes Escher changed the basic shapes
By “distorting” the basic shapes he
changed them into animals,
birds,
and
other figures.
The effect can be
both startling and beautiful.
Escher Horses
Tessellating hexagons
• https://www.geogebra.org/m/ZXHFvRn2
• The above shows the tessellation of hexagons
Begin with a simple geometric shape
The cardboard square to make a template for the fishes
Get creative – Try this!
Draw a triangle pattern on the cardboard
Cut it out and attach to the left.
Draw triangles at the bottom
Attach the cut-outs to the top
Use the template to cut out the fishes (4 on coloured paper and 4 on plain paper)
Now you have a fish template
Paste your fishesAlternating plain paper and coloured paper
fishesRemember - no gaps!!
Construct a hexagon – demo on webcam
• https://www.geogebra.org/m/b8atzetv
• Which popular sports item contains regular hexagons?
• Where else would you find hexagons?
• What is the shape of the triangles surrounding the midpoint of the regular hexagon?
• How can you determine the area of the hexagon?
• What is the area of the hexagon that you created?
Thank you