Highhill Homeschool: Spider Web Math-Art

We used geometry to create a math-art spider web design.

Math often exist within art to levels not detected by the viewer. Learning about the connections not only makes art more interesting, but serves as a very enjoyable way of learning about mathematics.

We have often selected geometric mandalas and used a compass and straight edge to recreate them. The challenge is a math puzzle and an exciting problem solving exercise.

This mandala which looks a bit like a spider web, from the book Das große Mandala-Malbuch für Vorschulkinder was redrawn using only a compass and ruler. Here are the steps.

1. Draw a circle with a 2" radius.

2. Use a ruler to draw a line through the center of the circle.

3. Draw a perpendicular line passing through the center of the circle. Increase compass radius (3 inches or so), place the point of the compass on the line where the circle and straight line intersect and draw tick marks just outside the circle on both sides. Move the compass point to the opposite side and repeat.

Place a ruler to line up with the tick marks and draw the perpendicular line passing through the center.

4. Bisect the perpendicular lines. Place the point of the compass where the circle and line cross. Make a tick mark outside the circle about half way between the perpendicular lines. Repeat on the opposite side of the line. Repeat placing the compass at the other three points where the circle and lines cross.

Place a ruler so that the tick marks are lined up and draw two angle bisectors passing through the center of the circle. (The circle should be divided into eight pieces.)

5. Bisect the eight angles within the circle following the procedure detailed in step 4. Note the bisecting lines are not needed within the circle and are only drawn lightly outside the circle.

6. Draw the outer web arches. Set the compass to the initial radius of 2". Place the pencil part of the compass on the line where the circumference and line passing through the center meet. Place the point on the adjacent line outside the circle. Sketch an arc as shown above. Repeat until the outer web of eight arcs is complete.

7. Draw the second web arc. Increase the compass radius to 2 1/4". Place the point in the same location as in step 6. Draw an arc. Repeat around the entire circle.

8. Increase the compass radius to 2 1/2", then 2 3/4" respectively and repeat step 7 drawing the remaining two web arcs.

9. Draw a small circle in the center.