Use your string to estimate the length of the circumference of each circle in Math about Circles. Use the grid to measure the string. Remember, the space between bold lines is 1 unit.

  • Small circle circumference: ______
  • Medium circle circumference: _____
  • Large circle circumference: _____

Estimate the relationship between the circumference and the diameter for each of the three circles:

  • The circumference is approximately ______ times the diameter.

Is that true for any circle? _____ Talk about it: Why do you think so?

Answers

There is a special number that always relates the circumference of a circle and its diameter. You estimated it when you measured the circles with string. The number is π (say “pi” with a long i). ​

  • Fill in C (for circumference) and d (for diameter) in the following formula:​ ___= π•___​
Answer

π is an irrational number. That means that its digits to the right of the decimal point never form a repeating pattern. We can use estimates of π when finding the circumference and area of a circle. ​

Two common estimates for π are 3.14 and 22/7. But neither is exactly π.​

This is π with many digits. Notice how they do not form a repeating pattern. (How can you check?)​ There are infinitely many more digits of π. ​

many digits of pi
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