Question 3
Having explored the use of a compass, go ahead and recreate the images in Fig. 8.1. Can you make the figures look as good as the figures shown there? Try again if you want to!
Also, has the use of instruments made the construction easier?
- A compass is used to draw perfect circles and arcs by fixing a center point and rotating the pencil with a constant radius.
- Using geometric instruments such as a compass and a ruler ensures precise measurements, symmetry, and smooth curves, making complex geometric patterns and drawings much easier and neater than freehand sketching.
Step 1 · Draw Two Touching or Overlapping Circles
- Draw a circle with a chosen radius.
- Place the compass needle on the circumference of the first circle without changing the radius.
- Draw a second circle of the same radius.
Step 2 · Draw Concentric Circles
- Choose a center point and draw the outer circle.
- Keep the compass needle on the exact same center point, reduce the compass opening (radius), and draw the inner circle.
Step 3 · Draw Three Overlapping Circles
- Draw the first circle.
- Place the compass needle on its edge and draw a second circle.
- Place the compass needle on the edge of the second circle and draw a third circle.
Step 4 · Draw the Cartoon Face Pattern
- Draw a large circle for the face.
- Place the compass needle at two symmetric points on the top edge to draw two smaller circles for ears.
- Add two small circles inside for eyes, a tiny circle for the nose, and a curved line for the mouth.
Step 5 · Draw Crossed Lines with Circles at the Ends
- Use a ruler to draw two straight lines intersecting each other.
- Place the compass needle at the endpoints of the lines and draw small circles at each end.
Yes, using geometric instruments makes the construction significantly easier, neater, and allows us to draw perfect circles and straight lines with accuracy.
- Compass Slipping: The metal point of the compass can slip off the paper if pressed too lightly, resulting in distorted circles.
- Radius Shift: Accidentally squeezing or expanding the compass arms while rotating alters the radius mid-circle.
- Losing the Center Point: When drawing concentric circles, moving the needle away from the original center point ruins the concentric alignment.
More questions in A
Observe the following figures and try drawing them freehand.
Mark a point in your notebook. Then, mark as many points as possible, in different directions, that are away from .
Think: Imagine marking all the points of distance from the point . How would they look?
Try to draw it and verify if it is correct by taking some points on the curve and checking if their distances from are indeed . Explore, if you have not already done so, and see if a compass can be used for this purpose.
You can start by marking a few points of distance from using the compass. How can this be done?
Having explored the use of a compass, go ahead and recreate the images in Fig. 8.1. Can you make the figures look as good as the figures shown there? Try again if you want to!
Also, has the use of instruments made the construction easier?
Construct
1. A Person
How will you draw this?
2. Wavy Wave
Construct this.
Make other artwork of your choice with a ruler and a compass.
Explore
How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?
How will you record your observations? First, identify the parameters that need to be tracked. They are the sides of the rectangle and the 8 angles formed by the two diagonals. Are there any other measurements that you would want to keep track of?
In your experimentation, did you consider the case when all four sides of the rectangle are equal? That is, did you consider the case of a square? See what happens in this special case!
Math Talk
What general laws did you observe with respect to the angles and sides? Try to frame and discuss them with your classmates.
How can one be sure if the laws that you have observed will always be true?