Press "space bar" to to clear the stage. This command can also position the arrow to a consistent spot and/or direction.
Note: The instructor will use this command between each of the snowflake test runs.
Provide the commands Koch's snowflake as defined below. Match each level to the appropriate number on the keyboard.
Level 0 - Equilateral triangle with side length of 243.
Level 1 - Remove the inner third of each side of your triangle from level 0. Construct another equilateral triangle at the location where the segment was removed.
Level 2 - Repeat the process above with the level 1 snowflake.
Level 3 - Repeat the process above with the level 2 snowflake.
Export command list for submission.
Special note: Must use fewer than 75 commands for snowflake levels, total! Commands counted include: move, turn, repeat, go to, move to.
Try to create the shortest program you can. Let the software do the work for you. Last semester, the shortest program for level 3 was 12 lines!
[save program] Paper icon > Export Project > (give name) > Save
[save image of snowflakes] Right-click stage > Pic > File > Save as
After the UFO reaches the center, it rotates 180 degrees in place before flying off.
Rotation can be achieved by multiplying by the matrix, \( [[ \cos(\theta), -\sin(\theta) ][ \sin(\theta), \cos(\theta) ]] \). It may also help to know that lists can be stored as a matrices, using LIST>MATR( list1, list2, matrix-name ).
Riemann sums revisited
Use loops to create a better Riemann sum program.
Provide the code for a calculator program that could be used to calculate the Riemann sum based on the following:
Inputs
Function of x
Lower bound of x
Upper bound of x
Number of rectangles (N)
Output
Estimated net area based on N equally spaced rectangles using "midpoints"
Include code on website with annotations that explain how the loop works.
Run for the instructor on the due date.
Radians might be good to include early in the program for trig functions
The number of rectangles will dictate how many times your loop will run.
Possible template:
: Input …
: Input …
: 0 → S
: FOR I, ?, ?, ?
: (compute area of next rectangle) + S → S
: END
: Disp S
Discussion questions
What is the perimeter of the level 3 Koch snowflake? How do the commands help determine the perimeter? Please be specific.
For each activity, identify the mathematics that was involved? (try to list as much as possible)
SUBMISSION
Publish the assignment to your EduBlog by:
posting your solution
using LaTeX for all non-calculator mathematics notation
including any files that you created for the assignment