Equilateral Area
Create a Python program that defines the function
equilateral_area(edge_length: float) -> float that
computes the area of an equilateral triangle. The
parameter edge_length specifies the length of the
triangle's edges. The function should return the area of the
triangle. The area of an equilateral triangle and be computed with
the equation:
a=√34×l2
Where a is the area of the triangle and l is the length of an edge of the triangle.
Test Cases
Create your own! Use this template:
import test
def equilateral_area(edge_length: float) -> float:
# Put your code here
def main() -> None:
test.equal(equilateral_area(?), ?)
# Put more test cases here
return None
main()
Sierpinski
Create a Python program that defines the
function sierpinski_area(edge_length: float) -> float
that computes the area of a Sierpinski triangle of order one. A
Sierpinski Triangle of order one is an equilateral triangle with a
triangular hole. The vertices of the hole triangle are the mid
points of the Sierpinski triangle's edges. For example:
Copy and paste your solution to the previous exercise into this one
and use it to write
the sierpinski_area function.
Test Cases
Create your own! Use this template:
import test
def sierpinski_area(edge_length: float) -> float:
# Put your code here
def main() -> None:
test.equal(sierpinski_area(?), ?)
return None
main()
Trees
When working with functions, abstraction is key. You will soon find yourself in a position where you start thinking about problems in functions. Being able to break a complex problem, like an advanced drawing, into smaller and simpler problems which can be solved with a function can make your code a lot easier to write, and a lot easier to read.
Details
Create a Python program that defines the function draw_tree(x:
float, y: float) -> None that uses the turtle module to draw
a tree. The x and y location specified is the center of the base of
the triangle making up the tree. The tree should look like the tree
in the example below.
Notice that a tree is defined by a brown square, and a filled
green triangle. To simplify the draw_tree
function, also define the function
draw_triangle(x: float, y: float) -> None, which draws
a filled, green isosceles triangle. The triangle can be any height,
but the length of the base should be the same as the height.
Example
- Drawing the trunk of the tree is simple, just draw a filled square.
-
Drawing the tree's canopy is easier if you use
the
turtle.setpositionfunction. To help figure out the coordinates of the triangle corners, make a drawing of the triangle inside of the square. The triangle fits inside of a square since its width is the same as its height.
Challenge
Modify your program so that you can specify the size of the tree. We will define the size of the tree to be the width of the tree. Use this new function to draw yourself a forest of trees where the trees that are farther away are smaller.
