Scribe Post

SCRIBE POST

In today’s Pre- Calculus lesson, we started off with our daily P.O.D. Throughout the class period we worked on a new subject; constants and on limits which we have been working on for a few days now.

P.O.D:
- Today’s P.O.D was divided into four parts:

a. List the first 10 terms of the Fibonacci sequence.
F1= 1 F2= 1 Fn= Fn-1 + Fn-2 - Recursive definition

Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

b. Complete the table of values accurate to 4 decimals.
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c. Describe in words how the value ratio behaved as you completed the table. Be precise.

-As the nth term gets bigger the decimal place moves one place more.
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d. Approximate lim Fn , accurate to 3 decimals.
n-∞ Fn-1



- If we look at the table we did in part B for the later terms like:
tn 1.6190 1.6176 1.6181 1.6179

n 9 10 11 12

Once you round them to the thousands place, they all round up to 1.618 therefore


lim Fn = 1.618
nà∞ Fn-1



The ratio Fn oscillates above and below a constant and the constant approaches
Fn-1
as n approaches infinity.

-this constant is called Phi = Φ = 1.61803
-Φ is an irrational number just like π and е.


During class we tried to prove one of the constants that appeared in the movie the Da Vinci code. Allegedly the ratio of the length from your hip to the ground is the same to that of your total height. This is supposed to be 5.

-Pier volunteered for this activity
-Pier’s measurements: from hip to floor : 98 cm
Total height: 1”75 cm


1”75cm/ 98cm = 1.78 ratio
The next activity we did was a group exercise we had to:
On you index finger:
a. measure the length of the 3rd bone (knuckle to knuckle)
b. Measure the 2nd bone
c. Divide the longer by the shorter
d. Find the average on the board
e. Find Class Average.






My Group’s measurements:
Susy’s: 4cm,/2.5cm =1.6cm

Gaby’s: 4.8cm/2.8= 1.714 cm

Sofi’s: 4cm/2.5cm=1.8cm

group average: 1.703 cm


Class Average
-1.767
cm-1.6305
-1.6422
-1.6666
-1.6666
-1.703

Ans: 1.675 cm


Exercises:
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