6th
International Science, Social Sciences, Engineering and Energy Conference
17-19 December, 2014, Prajaktra Design Hotel, Udon Thani, Thailand
I-SEEC 2014
http//iseec2014.udru.ac.th
Designing Modulo Art Patterns Using
The Geometer’s Sketchpad (GSP)
N.Wattanasiriponga, N.W. Sangwaranatee b,e1 and C. Noradeeb
a
Applied Mathematics, Faculty of Science and Technology,
Valaya Alongkorn Rajabhat University under Royal Patronage, Pathumthani, 13180, Thailand
b
Informatics Mathematics, Faculty of Science and Technology,
Saun Sunandha Rajabhat University, Bangkok, 10300, Thailand
e1
Nisakorn.su@ssru.ac.th
Abstract
The objective of this research is to design artworks by using Modulo addition table which is created by The
Geometer’s Sketchpad (GSP). Geographic figures are adapted to create the patterns. Modulo addition table can create
beautiful artistic patterns by its geometric transformation: rotation, translation and reflection. In this research, there
are 2 types of grids using as the drawing tools: square grid and Kaleidoscopic grid. The artwork created from this
technique can be used as the prototype pattern for creating artwork on tiles, fabric, walls, etc. Additionally, using
GSP to create artwork can reduce human error, be more convenient and save cost.
the Geometer’s Sketchpad, Modulo Art, Kaleidoscopic Grid
1. Introduction
Mathematics has been part of innovations and human’s potentials development in many areas.
Technology is part of important tool for mathematics courses and lesson plan. GSP is not only for the use
of teaching, it also can be used in art [5-6], such as creating patterns on tiles, pottery, cartoons, jewellery,
etc. In this research, GSP was used to create artistic pattern from Modulo addition table. In order to make
the design process simple and convenient, the knowledge of geometric transformation was adapted in
forms of square grid and Kaleidoscope grid.
2. Related theories and work
GSP [1] is the program made for creating visual media to help learners understand better about
mathematics innovation. GSP [3-4] helps learner to develop their visualizing skill and problem solving
skill. Learners can also have the opportunity to improve their multiple intelligences, such as language
skill, logic, visual spatial intelligence and art.
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In this part, we will study on how to create artistic pattern by geometric transformation.
2.1. Transformation Menu
Geometric Transformation [2] are the command section where we can have the first outline of the
pattern by using translating, rotating and reflecting functions.
 Translating process
1. Select the object
2. Go to transformation menu  translate. After selecting the object to be translated, there will
be 3 sub options (polar, rectangle or custom), depending on the demand.
3. Specify the necessary formula, and click OK.
Figure 1. The display of translating the original pattern into Modulo 4 addition table

Rotating process
1. Creating object, choose the center for rotating and go to transformation menu  specify
center or double click on the center spot.
2. Choose the object for rotating and go to transformation menu  rotate. (Response box will
pop up, and rotating object will be shown in the draft pattern.) Choose the stable corner,
specify the rotation degree, and click rotate.
Figure 2. The display of rotating the original pattern into Modulo 4 addition table
 Reflecting process
1. Choose the straight line that will be the reflect, then go to transformation menu
reflecting line, or double click on the line.
2. Choose the object that has to be the reflection, then go to  reflect.
 specify
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Figure 3. The display of reflecting the original pattern into Modulo 6 addition table
2.2. The Remainder Theorem
 The division Algorithm
If we specify the integer a , b when b  0 , there will be the one and only pair of integer, which are q
and r . Therefore, a  bq  r when 0  r  | b |
3. Designing Modulo Art Patterns Using The GSP
The steps of designing modulo art patterns using the GSP are shown below
1. Select the Modulo and grid to be the draft, then creating grids by the size of Modulo. The n
Modulo will contain the n  n grid while n equals n Modulo.
Figure 4. A square grid in addition table in Modulo 2
(a)
Figure 5. The display of how to create square grid
(b)
(c)
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1.1 The creating of square grid
1) The square grid is created by appointing 1 dot, go to transformation menu  translating
input
1 cm. of constant distance and 90 degree constant angle  translating. Do this action till all 3

points are completed. Then create the grid table. Choose all dots, translate the dots at 1 cm. of constant
distance and 90 degree constant angle for two times.
Figure 6. How to draw square grid
2) To draw the square grid, go to line drawing tool as in figure 6. Draw line from one dot to
another.
Meanwhile, the Kaleidoscopic grid can also be created in the similar with the square grid.
Perform adding process into the table by inputting number into the grid.
1) In the square grids, we can input number for n digits according to the size of modulo.
Inputting numbers has to be done by adding all positions. The number taken from the table comes from
the modulo, as in table 1.
Table 1. showing the addition in Modulo 2
+
0
1
0
0
1
1
1
0
2.2 Kaleidoscopic grid is the grid in diagonal line. Adding number starts from the bottom left of
the grid along the diagonal line until ends at the bottom right. Numbers are input in all position. The
numbers come from the Modulo process.
Figure 7. The input of number added into modulo 2 addition table
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3. Make original pattern and replace them onto numbers in the grid.
n
Modulo can have
n
pattern
(a)
(b)
Figure 8. Creating of original grid pattern
3.1 Create the original frame by specify 1 dot by dot tool, and move the dots by 1 cm. of constant
distance and 90 degree constant angle. Then translate both dots, input 1 cm. of distance at 0 degree as in
figure 8.
(a)
(b)
Figure 9: Creating of original pattern of Modulo 2
3.2 Create pattern and replace it on the number, you will get 2 different types of patterns. The
patterns are creating by dot menu, line menu, curve menu and divider menu. Then colors and line are
adjusted as in figure 9.
Figure 9: Display of original pattern in Modulo 4 addition table
4. Inputting original pattern into the grid can be done by copying the drawing and input them
into the grid by the appointed number in modulo 2 addition table. To create motion button, simply click
the corner of the bottom right of the original pattern and click the bottom right of the grid. Go to edit
 function  motion. The response box will pop up, then choose motion  fast. Choose the sign, and
input the destination (1, 1 for example).  OK. The pattern will be transfer into grid as in figure 10.
Note: Replacing original pattern into Kaleidoscopic grid will be different from square grid
because the grid shape is different. We can put any pattern into square grid, but for Kaleidoscopic grid we
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need to create one float line, and make float square grid. Input the pattern into the float grid and cut off
pattern that doesn’t fit into the grid. Finally you will have a pattern fit into the triangle grid.
5. Now we can play with the work by using geometric transformation to translate, reflect and
rotate into Modula 4 addition table.
4. Results
Creating artwork from modulo addition table is a way to use geometric transformation to make
lines and patterns. This technique can be used as a way to create artwork for tiles and fabric.
Figure 11. Display of pattern in modulo 2 addition table of square grid
Figure 12. Display of how to create pattern in modulo 2 addition table of square grid (reflecting, rotating, translating)
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Figure 13. Display of the finished artwork pattern in the form of modulo 4 addition table
(a)
(b)
(c)
Figure 14. Display of how to create pattern in modulo 4 addition table of Kaleidoscopic grid (reflecting, rotating, translating)
5. Summary
This research presents an alternative way to create artwork by using addition tables in modulo 2 and 4
by GSP program along with the adaptation of geometric transformation (translating, reflecting and
rotating). Square grid and Kaleidoscopic grid are also part of the creation. This technique can be used in
designing beautiful patterns for tiles, fabric, etc. It can also save cost of designing and is simple to use .
Acknowledgements
The author would like to thank Research and Development Institute of Suan Sunandha Rajabhat
University, Thailand for providing a financial fund for this research.
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