Orchard 16 ­ Block 16 ­ Pi.notebook
October 05, 2012
Bell Work
• Sit at....
Table 2 ­ if you were a club last time
Table 3 ­ if you were a diamond last time
Table 4 ­ if you were a heart last time
Table 5 ­ if you were a spade last time Share the results from your worksheet. Work to form an agreement on the entries we need to add to the table.
ADD THE ENTRIES TO THE TABLE!
1
Orchard 16 ­ Block 16 ­ Pi.notebook
Shape Circle
October 05, 2012
Perimeter
Area
kcr =
kar2 =
8r
4r2
Pentagon
7.27r
3.63r2
Hexagon
6.93r
3.46r2
Septagon
6.74r
3.37r2
Octagon
6.63r
3.31r2
Nonagon
6.55r
3.28r2
Decagon
6.50r
3.25r2
11
6.46r
3.23r2
12
6.43r
3.21r2
Square
15
20
25
30
100
200
300
360
2
Orchard 16 ­ Block 16 ­ Pi.notebook
October 05, 2012
Ridiculous Accuracy
• If you are currently sitting at a seat with a...
Black Card ­ find the entries for a 36,000 sided figure
Red Card ­ find the entries for a 360,000 sided figure 3
Orchard 16 ­ Block 16 ­ Pi.notebook
October 05, 2012
Shape Perimeter
Area
Circle
kcr =
kar2 =
360
6.28r
3.14r2
36000
360000
4
Orchard 16 ­ Block 16 ­ Pi.notebook
October 05, 2012
Polygoning Conclusions
• How are Kc and Ka related?
• Do the approximate values for Ka suggest anything to you?
5
Orchard 16 ­ Block 16 ­ Pi.notebook
October 05, 2012
Pi
The value of Pi is approximately 3.14 as you have seen in our investigation.
Pi is an irrational number – there is no exact decimal or fraction that gives this value.
6
Orchard 16 ­ Block 16 ­ Pi.notebook
October 05, 2012
Pi
• We will define pi as the ratio of the area of a circle to the square of its radius.
Area = • Historically Pi has been defined as the ratio of the circumference of a circle to its diameter.
Circumference = 7
Orchard 16 ­ Block 16 ­ Pi.notebook
October 05, 2012
Homework…
Complete Another Kind of Bisector
Complete Orchard Growth Revisited
8