## Wednesday, March 29, 2017

### Math with Mandalas: Perpendicular Bisector

We learned about bisecting angles and perpendicular bisectors through creating Mandalas.

Creating Mandalas with children is a fun way to teach math concepts that doesn't feel like work. Kids can learn about degrees, angles, bisecting, radius, diameter, circumference, perpendicular, parallel among other geometry concepts.

To begin, all that's needed is a good quality compass, paper and a straight edge (like a ruler). There is an endless possibility of mandalas that can be created. We have a book of simple geometric mandalas and find it very educational to try to recreate them. Interestingly enough, there usually ends up being more than one way each mandala can be created. In other words, sometimes steps can proceed in different orders, or alternative steps can be used which arrive at the same result. After walking kids step-by-step through the creation of several mandalas, I like to give them a challenge mandala and see if they can create one on their own.

Each mandala created requires some construction lines which end up being erased in the final version. Therefore, it's best to draw them lightly. Here are the steps we used to create the above mandala.

1. Draw a horizontal line on your paper with a straight edge. The line should be approximately the diameter of the outside circle. Set the compass radius to slightly greater than on half of the line. Place the pointer on the end of the line and create an arc above the line. Create another arc below the line. Repeat placing the compass point on the other end of the line.

2. Create a perpendicular bisector by using a straight edge to connect the two crossing arc points.

3. Set the compass radius to the desired radius for the center circle. Draw the center circle placing the compass point on the point where the two lines cross.

4. Bisect the perpendicular angles. Place the compass point on one point where the circle and straight line cross. Create an arc just outside the center circle. Repeat the process placing the compass point on the adjacent point where the circle and other straight line cross. The two small arcs should cross.

5. Bisect the angle connecting the center point of the circle and the crossing arc point with a straight edge.

6. Repeat the process to bisect the other 90 degree angle.

7. Find the center point for one of the eight surrounding circles. Referring back to the first picture, you can see that the center is difficult to locate, but a tangent point on the edge of each of the eight surrounding circles lies on the point where the 45 degree angle line and center circle cross. Therefore, set the compass radius to the same radius as the center circle. Place the compass point on the point where the 45 degree line and center circle cross. Create an arc to mark the center of the circle crossing the vertical line.

8. Create one of the eight surrounding circles. Place the compass point on the point where the vertical line and arc meet. Draw the circle.

9. Repeat the process creating three more circles.

10.  Using the same method, repeat the process to create the four arcs which are not quite complete circles.

11. Draw the outer circle. Open the compass so the radius is set for the size of the outer circle measuring the point with the sketched geometry.

12. Erase all construction and undesired lines.

13. Use a sharpie or black marker to define the desired lines.

14. Color the mandala any way you choose.