## Introduction: Mathematical Shapes

On primary school, students in grades seven and eight need to exam mathematical shapes and there characteristics. They also have to draw structures like basket, box, pyramid, cone, three-sided prism or cube and have to construct them.

## Step 1: Drawing and Construct a Cube With Cardboard

First of all, I made een cube with paper. With the help of this video it is easy to make for children in the age of ten, eleven years old. When they construct the cube with paper, they get a sense of the shape and the ratios of the figure. This is what examing, drawing, constructing mathematical shapes means.

## Step 2: Make a Cube in Adobe Illustrator.

For this project I wanted to learn Adobe Illustrator. I thought I would never succeed. So I downloaded this video "Cool Illustrator - cube and cone" and designed a cube by myself in Illustrator. When I finished it turned out to be impossible to print 3-D shapes with illustrator. Then I found a program to make a laserplan for a cube with fingers. The program is called Makercase and you can find it on www.makercase.com.

## Step 3: Create Your Laserplan for a Cube With Makercase.

On www.makercase.com you can find a laserplan to create a cube. I set the units in millimeters and select the edge joints with vingers. So the edge joints fits into each other and make a real puzzle of the cube. I decided to print the cube on a Trotec lasercutter in the Stadslab in Rotterdam. The Stadslab is a place in Rotterdam where students can explore and experiment, also in the field of ICT. I went looking for a guide to the Trotec lasercutter . I found the following video on You Tube: " Stadslab Rotterdam: Handleiding Trotec Lasersnijder". I watched the video three times and it gave me a good idea of how to use the lasercutter and above all: how to set it up. There are specifications for the lasercutter. In order to vector cutting you need to use the line color # FF000000 and a line width of 0.1 millimeters. When I have done all this , I set my laserplan over to Illustrator.

## Step 4: Making a 3-D Cube

Now I could print my cube. I used Triplex of 300 × 600 mm, with a thickness of 3 mm. When the lasercutter was finished, I first looked if the parts were really cut well before I took them out. Be careful to pick up the pieces of wood from the lasercutter, because it still may be hot. I used a hammer to put the cube together. To avoid to damage my cube with the hammer, I used wood in between.

## Step 5: How to Make a 3 -D Shape in Illustrator.

Now I knew what a laserplan for a cube looks like, I decided to make a laserplan for a pologon in Illustrator. I downloaded a video from YouTube with the title "Hoe maak je een Logo - Polygon" and drew the polygon in Illustrator. This part of the project failed, because I ended up making a 2 -D puzzle in the shape of a polygon and not a 3-D re-presentation.

The most important thing I learned in Illustrator was how to make the cuts (fingers) in the drawing. A polygon consists of all triangles. I made the cuts with smaller triangles , which I signed across the larger triangles. In pathfinder I united a larger triangle with a part of a smaller triangle . Then I took a piece of the adjacent triangle , so that everything would fit together. I did this by subtracting the foremost objects of the object farthest back in Pathfinder or pick up the rear objects from the frontmost object . This command allows you to remove areas of an illustration by adjusting the stacking order. You can also accomplish this by selecting a line and cut away the part of which you want to be a part of a larger part. It also showed that the cuts can better be a square than a triangle otherwise it will not fit together.

I also found out that the pyramid was still hard to draw in Illustrator. In order to make a 3-D re-presentation, the figure had to be drawn in miter or become larger and more convex. Because it was so complex, I decided to draw the cube again, but now in Illustrator.

## Step 6: The Materials

For the paper cube you need:

• paper
• a scissor
• a ruler
• a pencil
• an eraser
• a pencil sharpener
• and an instruction from You Tube, if necessary

For the wooden cube you need:

• Triplex 300 × 600 mm , with a thickness of 3 mm. In the Stadslab in Rotterdam this will costs € 2.00