Section 2.3 Lesson 3: Drawing the Circle
In this lesson, we will transition from theoretical Star Compass construction to practical implementation. We’ll discuss the challenges of moving from paper to reality, exploring strategies to overcome these challenges. The class will engage in drawing the actual Star Compass circle at the designated site, such as a flagpole.
- Materials for Classroom - Compass (Math Instrument)
- Materials for Outside - Kaula (Rope), Chalk, Paint/Paint Brush
Subsection 2.3.1 Classroom: What is a Circle
We will begin inside the classroom.
What is the main shape of the Star Compass? Ans: Circle
What is a circle? How do we draw a circle?
Ans: A circle is a shape that is round. To draw a circle, imagine drawing a line all the way around a point, keeping the same distance from that point. No matter where you look on the circle, the distance to the center is the same. The center is like the middle point of the circle, and the distance from the center to any point on the edge is called the radius. If you draw a line straight through the center and out the other side, that’s called the diameter, and it’s like the longest line you can make inside the circle. The distance around the circle is called the circumference.
Knowing this, have the students draw a circle on their papers. Next have them identify the center, are all points on the circle the same distance to the center?
Have students discuss how they created their circles.
Ask a student to draw a circle on the board. Discuss with the class how the circle was created.
Let students discuss the following for 5 minutes: What is needed to make a perfect circle on paper? Have students create their own perfect circle using supplies found in the classroom (do not use a compass).
Relate what the students used to create their circle to how you would use a compass (the math instrument, not the navigation instrument)? Why is a compass such a great tool to create a perfect circle? What else could we use to achieve this?
Subsection 2.3.2 Outside: Making a Circle
We will now move outside to the location of the Star Compass, in this case, we are constructing it at a flagpole. You will need to bring kaula (rope) and chalk.
How can we create a circle around this flagpole using what is here with us? Ans: We can use the kaula to create a fixed length (or radius) and use chalk to trace the circle.
How would we hold the kaula to the center of the circle (the flagpole)? Let students discuss, keeping in mind that we donʻt want to have someone hold it for very long or else they may get tired and we may need multiple days to actually build this and we donʻt want people staying overnight holding the kaula.
Students should conclude that we can tie the rope to the pole. What type of knot would be best for securing the kaula to the pole? Review knots and their uses (
https://www.kanehunamoku.org/knots.html):- Hīpuʻu Walu (Figure 8 Knot):
- Function: Stopper Knot
- Uses: Ends of lashings; end of jib sheet lines
- Hīpuʻu Palu (Square Knot):
- Function: Tie two lines of the same diamter (size) together
- Uses: Reef in the sail; Close the sail bag
- Kapolina (Bowline):
- Function: Tie a secure loop at the END of a line
- Uses: Secure jib sheet lines to the jib sheet block; secure jib halyard to the head of the sail; secure shower bucket
- Bowline on a bight:
- Function: Tie a secure loop in the MIDDLE of a line
- Uses: Tighten the stays and secure through donuts
- Kūpeʻe Puaʻa (Clove Hitch):
- Function: Secure an item around a pole or post
- Uses: Secure bumpers to the railing or ʻiako; secure a bundle of line to the railings
Now after having reviewed the various knots, ask students which knot they think should be used to secure the kaula to the flagpole. Based on the review, students may think that a clove hitch is the best method. Letʻs test a clove hitch and see what happens.
Ask a student to secure the kaula to the flagpole by tying a clove hitch, you will want to use a smaller kaula so that the loose end is only 5 feet. Then ask another student hold the other end of the kaula and pull it away from the flagpole so that the kaula is tight. Then ask that student to continue holding the kaula so it stays tight and to walk around the flagpole for one revolution. The steps of the student should create the circle is. Ask the class if the student ended up in the same spot, creating a perfect circle. If we were tracing the steps, the student should actually be a little closer to the flagpole than when they began but it might not be noticeable to students since we arenʻt tracing the steps yet. Now have the student walk around the flagpole several more times. The kaula should start to wrap around the flagpole and the working end becomes shorter until the student walking around is almost to the flagpole. Walking around the flagpole several times should make it clear to students the kaula is getting shorter.
Ask students what happened to the kaula. Ans: it got shorter.
Have students discuss with their neighbors why they think the kaula got shorter. Did we still make a circle, even though the kaula got shorter? Why/why not?
With the whole class, ask why did it get shorter? Ans: It got shorter because the kaula started to wrap around the pole instead of going straight to the edge of the circle.
Ask the class to remember from the start of class what is a circle. Answer: A line where every part of it always has the same distance from the center.
From what we just did with the kaula, is the distance the same or does it change? Ans: It changes so we cannot use this knot to create a circle.
What other knots could we use? Ans: We can make a bowline on a pole so when we walk around the circle, the loop securing the kaula to the pole moves with us and doesnʻt wrap around the pole.
Have a student secure the kaula to the flagpole using a bowline then ask another student hold the working end of the kaula pull the kaula away from the flagpole so that the kaula is tight and then walk around the circle several times to demonstrate the distance from the flagpole to the end does not change. We have just successfully demonstrate designing a perfect circle.
Now we are ready to draw the circle. Ask students how to draw a circle using the kaula and chalk. Remind them of the problems when the kaula wrapped around the pole so we need to make sure the chalk is on the same spot on the kaula. If we hold the chalk at the end of the kaula, we cannot move how our hand is holding it of risk having a different length. A clove hitch around the chalk is preferred for ease of adjusting the length of the kaula but a bowline is also possible with the chalk placed in the loop. Hold the chalk and pull it away from the flagpole so that the kaula between the chalk and the flagpole is tight, and walk around the flagpole, tracing the outline of the circle with the chalk.
Is this the size of the circle you want? You can adjust the knots of the bowline to make the radius of the circle fit your needs and repeat the process.
Subsection 2.3.3 The Star Compass Circle
We are now ready to make the permanent circle for the Star Compass.
Verify with officials the dimension of the Star Compass that you are to construct, and determine the radius. For example, you may be asked to create a Star Compass within a 10 foot area, this represents the diameter of the circle, so your radius will be 5 feet. Next, adjust the length of the kaula to correspond with the radius.
Now that you have the appropriate length of kaula for your radius, draw another circle with chalk. Do not lose track of this line because you will be painting over it shortly.
Make a second circle, with a radius approximately one foot shorter than the previous circle, repeating the steps we did before. The two circles will be the boundaries of where we will eventually label the names of the houses.
Using the chalk lines, paint the outer and inner circles. Your Star Compass should look like that in the figure below , without the dashed lines which are just to help us visualize the cardinal directions.
Let the paint dry and return to the classroom.
Subsection 2.3.4 Summary
Subsubsection 2.3.4.1 What is a Circle
Inside the classroom, we will begin by discussing the main shape of the Star Compass.
1. Discuss the primary shape of the Star Compass. - Answer: Circle
2. Define a circle and the process of drawing one. - Answer: A circle is a round shape. To draw a circle, envision drawing a line around a point, maintaining the same distance from that point. The center is the midpoint, and the distance from the center to any point on the edge is the radius. The diameter is a line through the center, and the distance around the circle is the circumference.
3. Activity: Have students draw circles, identify the center, and discuss their methods. Display a circle on the board, discussing how it was created.
4. Class Discussion: Encourage students to share their experiences in drawing circles, discussing the tools used and the challenges faced.
Subsubsection 2.3.4.2 Outside: Making a Circle
Move outside to the flagpole and discuss methods to create a circle using available materials.
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Discuss how to create a circle around the flagpole using available materials.Answer: Use kaula (rope) to establish a fixed length (radius) and trace the circle with chalk.
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Considerations: Explore how to secure the kaula to the flagpole without human assistance. Introduce various knots and their uses:
- Hīpuʻu Walu (Figure 8 Knot): Stopper Knot
- Hīpuʻu Palu (Square Knot): Tie two lines of the same diameter together
- Kapolina (Bowline): Tie a secure loop at the end of a line
- Bowline on a bight: Tie a secure loop in the middle of a line
- Kūpeʻe Puaʻa (Clove Hitch): Secure an item around a pole or post
- Knot Experiment: Test a clove hitch and observe the kaula shortening. Discuss why it happened.
- Solution: Introduce the bowline knot and demonstrate its effectiveness in maintaining a consistent length.
- Circle Drawing: Use the chalk and kaula to draw a circle, ensuring the chalk remains at a fixed point on the kaula. Discuss adjustments to the knots for different circle sizes.
Subsubsection 2.3.4.3 The Star Compass Circle
- Determine the required dimensions of the Star Compass, including the radius.
- Adjust Kaula: Modify the kaula’s length to match the radius.
- Draw Circles: Use the adjusted kaula to draw the outer and inner circles with chalk.
- Paint Circles: Paint over the chalk lines, creating the final Star Compass circles.
- Completion: Once the paint dries, the Star Compass circle is ready for further construction.
