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 LESSON 2.  Equations with no End MATERIALS:  Ruler, Compass (to make circles), string 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...   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.   Figure the Fibonacci sequence on your own.  Include how you calculated the answer.
 Calculation Fibonacci number Calculation Fibonacci number 1 Starting point 11 2 1 +  0 1 12 3 1 13 4 14 5 15 6 16 7 17 8 18 9 19 10 20
 Why is the first and second Fibonacci numbers, 1? What is the 5th Fibonacci number? What is the 12th Fibonacci number? How many Fibonacci numbers are there? 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.
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