When Mathematics Demonstration meets Art

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