1. Lesson 16: The Most Famous Ratio of All

2. Terms of the Circle Radius (r) – Diameter (d) – Circumference –
Pi (π) –

3. Terms of the Circle
Radius (r) – distance from the mid-point of the circle to the arc of the circle
Diameter (d) –
Circumference –
Pi (π) –

4. Terms of the Circle
Radius (r) – distance from the mid-point of the circle to the arc of the circle
Diameter (d) – the distance across the center of the circle
Circumference –
Pi (π) –

5. Terms of the Circle
Radius (r) – distance from the mid-point of the circle to the arc of the circle
Diameter (d) – the distance across the center of the circle
Circumference – distance around the circle
Pi (π) –

6. Terms of the Circle
Radius (r) – distance from the mid-point of the circle to the arc of the circle
Diameter (d) – the distance across the center of the circle
Circumference – distance around the circle
Pi (π) – Ratio of the circumference to the diameter or 22/7.

7. Draw a Circle Opening Exercise
a. Using a compass, draw a circle like the picture.
C is the center of the circle. The distance between C and B is the radius of the circle.

8. §  Circle: Given a point in the plane and a number , the circle with center C and radius r is the set of all points in the plane that are distances from point .
§   What does the distance between the spike and the pencil on a compass represent in the definition above?   
§   What does the spike of the compass represent in the definition above?
§   What does the image drawn by the pencil represent in the definition above?

9.   Circle: Given a point in the plane and a number , the circle with center C and radius r is the set of all points in the plane that are distances from point .
§   What does the distance between the spike and the pencil on a compass represent in the definition above?
   The radius
§   What does the spike of the compass represent in the definition above?
§   What does the image drawn by the pencil represent in the definition above?

10. Circle: Given a point in the plane and a number , the circle with center C and radius r is the set of all points in the plane that are distances from point .
§   What does the distance between the spike and the pencil on a compass represent in the definition above?
   The radius
§   What does the spike of the compass represent in the definition above?
  The center
§   What does the image drawn by the pencil represent in the definition above?

11. Circle: Given a point in the plane and a number , the circle with center C and radius r is the set of all points in the plane that are distances from point .
§   What does the distance between the spike and the pencil on a compass represent in the definition above?
   The radius
§   What does the spike of the compass represent in the definition above?
  The center
§   What does the image drawn by the pencil represent in the definition above?
  The “set of all points”

12. The Diameter The Diameter
a. Extend segment to a segment , where is also a point on the circle. The length of the segment is called the diameter of the circle.
b. The diameter is twice, or 2 times, as long as radius.

13. Draw three different circles
Draw three different circles. Measure the radius and diameter of each circle. What do you notice?

14. Now, using string and a ruler, let’s measure the circumference of each of the circles you drew. Record the radius, diameter, and circumference of each. What do you notice?

15. Pi
3.14 or 22/7
The circumference of any circle is always the same multiple of the diameter. Mathematicians call this number pi. It is one of the few numbers that is so special it has its own name.

16. Using pi to calculate circumference
The circumference of any circle should be a little more than 3 times its diameter.
Let’s check:
Based on your observations from the comparisons between the diameters and circumferences of your circles, does the value of pi (3.14) seem to be correct?
To calculate circumference, multiply diameter by pi.
Formula C = π x d or 2πr

17. Examples
   The following circles are not drawn to scale. Find the circumference of each circle. Use 22/7 or 3.14 for π.
What about a semi-circle?