Tumbling-Block Design
A tumbling-block design is commonly found in Amish quilt patterns. We can call it an example of "op art" because of its interesting optical effect, which is suggested by its name. A tumbling-block design can be created in Geogebra using [i]translations[/i].
1. Construct a regular hexagon (6-sided polygon) by clicking the [icon]/images/ggb/toolbar/mode_polygon.png[/icon][b]Polygon[/b] menu and choosing [icon]/images/ggb/toolbar/mode_regularpolygon.png[/icon][b]Regular Polygon[/b]. (You can use the [icon]/images/ggb/toolbar/mode_move.png[/icon][b]Move[/b] tool to move points A and B until your polygon looks like the one below.)
Step 1
2. Construct the center of the hexagon by clicking the [icon]/images/ggb/toolbar/mode_point.png[/icon][b]Point[/b] menu, then the [icon]/images/ggb/toolbar/mode_midpoint.png[/icon][b]Midpoint or Center[/b] tool. Click on the interior of the hexagon to construct the center, which should be labeled G.[br][br]3. Choose the [icon]/images/ggb/toolbar/mode_polygon.png[/icon][b]Polygon[/b] tool and click on E, G, A, F, and E again in order to construct quadrilateral EGAF. (A quadrilateral is a 4-sided polygon.) Construct quadrilateral ABCG in the same way.
Step 3
Pro tip: You can change the color of a polygon interior at any time by clicking on it with the [icon]/images/ggb/toolbar/mode_move.png[/icon][b]Move[/b] tool, opening the Styles drawer (triangle, circle, and lines in the upper right corner), and clicking the Set Color and Transparency menu (colored square). Use whatever colors you like, or change the opacity of each interior to 0 and then color your final picture by hand.
4. Click the [icon]/images/ggb/toolbar/mode_join.png[/icon][b]Line[/b] menu, then choose the [icon]/images/ggb/toolbar/mode_vector.png[/icon][b]Vector[/b] tool. Click point E, then point C.[br][br]5. Click the [icon]/images/ggb/toolbar/mode_mirroratline.png[/icon][b]Transformations[/b] menu and choose [icon]/images/ggb/toolbar/mode_vectorfrompoint.png[/icon][b]Translate by Vector[/b]. Click and drag to enclose the entire hexagon in a box (see the video below). Click the vector. This will translate the hexagon by the vector from E to C.
Step 5
6. Control-click each vertex of the new hexagon (the [i]image under translation[/i]) and uncheck "Show object". You may have multiple points on top of each other at some vertices, so you may have to hide the vertex multiple times. When you finish, your sketch should look this.
Step 6
7. Translate the new hexagon by the original vector, then hide the new points. See steps 5 and 6 for detailed instructions. Repeat until you have at least four hexagons.
Step 7
8. Construct a vector from point D to the bottom right vertex of the first hexagon. Translate the entire row of hexagons by the new vector, as shown below.
Step 8
9. Hide the new points as in step 6.[br][br]10. Continue to translate the new row and hide the new points until you have at least four rows of blocks.[br][br]11. Drag the original control points for your first hexagon and observe how the tumbling-block pattern changes.[br][br]12. Experiment with different color patterns to enhance your design (see pro tip in step 3). You can use the [icon]https://www.geogebra.org/images/ggb/toolbar/mode_text.png[/icon][b]Text[/b] tool under the [icon]/images/ggb/toolbar/mode_slider.png[/icon][b]Slider[/b] menu to add your name to your sketch. Hide all the remaining points and vectors. When you have your design the way you want it, click the menu (three horizontal lines in the upper right corner), then click File...Export Image. Upload the resulting file to [url=https://docs.google.com/forms/d/e/1FAIpQLScFtCLVkeRNykvWcJ_3ZM7Xd9ZN0EBjJsYocbvxgizWRO2ubA/viewform?usp=sf_link]this Google form[/url].
[size=85]Adapted from [u]Exploring Geometry with The Geometer's Sketchpad[/u] by Key Curriculum Press.[/size]