LESSON 2.  Equations with no End

MATERIALS:  Ruler, Compass (to make circles), string

1. Pi(B)is a number with no end and does not repeat itself.  Below is pi(B) calculated to what place? (Yes, that means you need to count them!)
   
   3.14159265358979323846264338327950288419716939937510582097494459230781
   6406286208998628034825342117067982148086513282306647093844609550582231
   7253594081284811174502841027019385211055596446229489549303819644288109
   7566593344612847564823378678316527120190914564856692346034861045432664
   8213393607260249141273724587006606315588174881520920962829254091715364
   367892590360011330530548820466521384146951941511609...
    
2. On a piece of paper use a compass to make 2 circles.  Use string to determine the length of the circumference and then measure it with a ruler.  Than make a ratio of circumference to diameter.   Does your number resemble the number in #1.
    
3. Figure the Fibonacci sequence on your own.  Include how you calculated the answer.

4. Why is the first and second Fibonacci numbers, 1?
   
5. What is the 5^th Fibonacci number?
   
6. What is the 12^th Fibonacci number?
   
7. How many Fibonacci numbers are there?
   
8. Let’s prove if the Golden Ratio a real ratio.   From the information in the reader construct a ratio and calculate up to 3 ratio’s.  See  you come up with the golden ratio.  Use only a/b,  b/c, and c/d.  You will need a ruler to measure the segments.  You may use a calculator.