paper patterns. 3. with circles

Paper Patterns. 3. With CirclesAuthor(s): William GibbsSource: Mathematics in School, Vol. 19, No. 4 (Sep., 1990), pp. 2-8Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30214698 .

Accessed: 10/04/2014 04:44

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access toMathematics in School.

http://www.jstor.org

This content downloaded from 158.37.155.128 on Thu, 10 Apr 2014 04:44:59 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=mathas

http://www.jstor.org/stable/30214698?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


paper

patter 3

with ircle by William Gibbs, School of Education,

Leeds University

There are a delightful variety of patterns that can be created from paper circles either by overlapping and interleaving them or by folding and colouring.

Use paper circles of about 8 to 10 cm diameter cut from coloured paper. Draw around a tin to give the circle and cut out with scissors or if you want circles with clean edges use a circle cutter which can be bought at most good stationers.

i

Fig. 1 Circle cutter

Overlapping Circles Overlapping the circles in rows creates a striking tessellation. To position the circles in the correct position it helps to draw lines which are the radius of the circles apart.

Fig. 2(a) Pattern with overlappng circles.

2

Folding a circle in half will help here.

Fig. 2(b) How to arrange the circles.

Fig. 2(c)

Variations on this basic pattern can be created by grouping circles of the same colour. For example, grouping together four circles of the same colour will create a new tiling unit;

Mathematics in School, September 1990



Fig. 3(a) Overlapping circles.

Fig. 3(b)

Interleaving Circles Four at a Point The basic unit for patterns of this type is created by interleaving four circles so that they meet at a point. To help in the positioning of the four circles, fold one of them in half and in half again to give diameters that intersect at right angles. Place the circle that overlaps this so that the creases are tangential.

Fig. 4(a)

Once the first four circles have been placed accurately further circles can be added to create a tessellation;

Fig. 4(b)

Arranging circles in different ways or by grouping circles of the same colour together will generate other patterns;

Four circles of the same colour can be grouped to give two new tessellations;

Fig. 5(a)

Fig. 5(b)

If four circles, two of each colour, are interleaved and glued to give this basic unit then by combining several units tessellation patterns based on each of the following shapes can be created;

Fig. 6

Mathematics in School, September 1990 3



Here is a pattern created using circles grouped in threes. You will need circles of three different colours.

Fig. 7(a)

Fig. 7(b)

This pattern is created using just two colours and a slight modification of the original interleaving pattern;

Fig. 8

Starting with these three different basic units of four circles each;

Fig. 9

and interleaving this tessellation can be created;

Fig. 10

Circles at a Point If the circles are arranged so that three circles meet at a point then this tessellation can be created;

Fig.11

Fig. 12

4 Mathematics in School, September 1990



Fig. 12(a)

Six Circles at a Point To arrange six circles at a point the centre of each circle needs to be marked. Fold in the edge of each circle so that it lies on the centre of the circle.

Fig. 13

Then each circle is placed on top of the last so that its circumference lies on the centre of the circle below and

the folded edges meet.

Fig. 14

Using three different colours creates a basic pattern like this;

Fig.15

and combining many such units creates this tessellation;

Fig. 16(a)

Fig. 16(b)

Folding Circles Folding the edge of the circle in twice creates a new shape with interesting possibilities. For example work with circles of three different colours and combine pairs of folded circles to create rhombi.

Fig. 17




Then combine the three rhombi to make a hexagon which when tessellated creates a new and striking pattern.

Fig. 18

Folding and Colouring Folding the edge of the circle into the centre three times will create an equilateral triangle.

Fig. 19(a)

These folds can be coloured and interleaved in a variety of ways and a wide range of patterns created. Here are a couple of examples;

Fold the triangle so that just one segment is folded forward and colour to give an equal number of triangles like these;

Fig. 19(b)

Here are two of the many patterns that can be created fro-m these triangles;

Fig. 20(a)

Fig. 20(b)




Fig. 20(c) Single flaps coloured.

Fold and colour pairs of triangles like these;

Fig. 21

Combine them to make this unit which can then be tessellated;

Fig. 22(a)

Fig. 22(b)

If the folds are each of a different colour and interleaved then a triangle like this is created;

Fig. 23

These triangles can be combined to make this tessellation;

Fig. 24(a)

Fig. 24(b)

Fig. 24(c)




Interleave the folds when making the triangle and colour to give two sets of triangles like these;

Fig. 25

then combine the triangles;

Fig. 26(a)

Fig. 26(b)

Folding Thin Paper As a variation, cut the circles from very thin coloured paper. Fold them into triangles and create patterns. Then fix the final pattern to a window. Very delicate and attrac- tive patterns emerge.

The circle can also be folded into other shapes; a hexagon, a square, a kite and a rhombus.

Fig. 27

To make the rhombus, for example, the edge is folded to the centre twice as for the equilateral triangle but then on the next two folds the ends of the chords are folded to the centre;

Fig. 28

These shapes provide further starting points for investi- gation in terms of the tessellations and patterns they can create.

Fig. 29 Tessellation of interleaved rhombi.




paper patterns. 3. with circles

Documents