1. Computer Science 1
3.14
And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7: 23)
950 BC

2. Dry run program sumthing; function sum (no : integer): integer; begin
if (no = 1) then
sum := 1
else
sum:= no - sum (no - 1);
end;
var
total : integer;
total := sum(5);
writeln(total);
end.
Dry run

3. PI Memorizers

4. How many digits of PI can you recite?

5. Today there are 3 PI themed options
Describe each methods
Give an example on how each works
Online time to generate the code for one or more.
At the end of class. A round bracelet to the person (team) that generates PI the most digits.

6. Write a program to approximate PI
1400 method (Madhana of Sangamagrama, and rediscovered by Leibniz in the 1600s)
Use this method to estimate PI. What value do you get after 500 iterations, 1000, 10000, …?
Push: How could you write a program to use this method to calculate PI to +/- 1/1000

7. Wallis Method (1655)
Use this method to estimate PI. What value do you get after 500 iterations, 1000, 10000, …?
Push: How could you write a program to use this method to calculate PI to +/- 1/1000

8. Random Circle Area Method
Using a 100 pixel x100 pixel square with a circle inscribed with a 50 pixel radius.
Generate random points (x, y) inside the square. ( 0 <=x <=100, 0<=y<=100).
Count how many of these points are inside the circle and use this to estimate the value of PI.
Try with 500 points, 1000 points, points …
Push: Show graphically
Push: Compare with Squares and Circles of different sizes to see if it makes a difference.
(Dots in)/(total Dots) = (Circle Area)/(Total Area)
= (PI*r2)/(2*r)2
= (PI*r2)/(4*r2)
= PI/4
Multiplying both sides by 4
4*(Dots in)/(total Dots) = PI