It is quite simple to make a very beautiful Hawaiian quilt pattern using the Geometer's SketchPad.
Here are some examples of a real Hawaiian quilt. Notice the symmetry of this quilt pattern. What kind of reflection symmetry do you see? What kind of rotation symmetry do you see? Check your answers below.
If you said this quilt has 4 lines of reflection symmetry, you are absolutely right! (You could fold the pattern on a line down the center vertically, and the two halves would match. You could also fold it on a horizontal line through the center, or across either of the two diagonals of the square, and the two halves would match perfectly in each case.)
It also has 90 degrees of rotation symmetry. (If you traced the pattern and placed the tracing on top of the original, and rotated the tracing about the center, the tracing would match up with the original after a rotation of exactly 90 degrees).
Now look at the lovely quilt below:
This quilt has the same kinds of symmetry as the first quilt.
Would you be surprised to know that you can make a Hawaiian quilt pattern using geometry?
You can create your own Hawaiian quilt pattern using a tracing paper, a pencil, compass, ruler, and your knowlege of geometry. In this example, you will construct a quilt pattern with the same type of symmetry as the one shown above. First draw an interesting leaf or flower shape. near the top of your paper. Then trace your shape, place your traced shape underneath the paper with the first shape on it, and rotate the shape 45 degrees about the center of your original page. Then trace the shape that you rotated onto the top sheet with the original shape. If you do this 3 times, rotating your pattern 45 degrees each time, you will be right back where you started, with a symmetrical pattern with the same symmetries as the example above.
In the paragraphs below, you will learn how to create a geometric quilt pattern using geometry software. There is just one new thing you need to know: how to draw a curve in GSP. You already know how to draw a circle, using the circle tool. An arc of a circle is a curved portion, such as the arc drawn in red below. The name of this arc is "arc CE" and the circle is called "circle A, because A is the center.
Constructing an arc is very simple. Just draw 3 points, such as points F, G and H. Then select the 3 points (remember to hold down the shift key to select more than one thing at a time). Then choose Arc Through 3 Points in the Construct menu. You can change the shape of your arc by dragging any point. Try it!
1) Construct a shape that you like, using segments, triangles, and arcs. Most Hawaiian quilts use flower and leaf shapes, and that's why we will need arcs:
2) Select the 2 endpoins (P and Q) and use the Construct menu to draw a segment connecting them. You don't want segment PQ to intersect any of the arcs, segments or points you have created, so if it does interesect or overlap, drag some of the points so the segements and arcs and points are all on one side of segment PQ:
3) Select segment PQ and Mark it Mirror using the Transform menu. Then select everything, (you can do this quickly by clicking in the white space above and to the left of the shape, then dragging the cursor across to the bottom right. Notice that everything will then be selected.) Use the Transform menu to Reflect everything across the Mirror PQ.
4) Now select point P and Mark it Center using the Transform menu. Select everything and rotate it 60 degrees. If parts overlap each other, drag points so that things don't overlap, as I have done and your result should look something like the drawing below. Select all the points and then use the Display menu to Hide Points.
When you have completed the steps shown above, you will have the beginnings of a beautiful Hawaiian quilt! In the above example, I also constructed the Polygon interiors by selecting all the points in consecutive order, then chose Polygon Interior in the Construct Menu. Sketchpad cannot construct the interiors or curved shapes, except full circles. Here are some other helpful tricks: if you want to select all the points at once, to hide them, then choose the point tool in the tools menu. Then chose Edit . . .Select All Points, and you will see that only points (all of them) will be selected. If you want to then "de-select" a point (or points), hold down the shift key and click on the selected point (or points) that you want to "de-select". Similarly, you can choose the segment tool, Select All Segments, and hide them.
Construct a Hawaiian Quilt using a compass and ruler. Make it more complex than this (which is quite simple). Look at the example below for some other ideas.
Then look closely at the beautiful quilts back up at the top of this web page, and think of the other lovely quilts you have seen. Perhaps you can find some photographs of quilts in your school library.
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