# File: tfancybox.py
# program to draw a box with a hat using turtle
# make it fancy
#
# Matt Bishop, MHI 289I, Fall 2024
#
import turtle               # allows us to use turtles
import math                 # need this for the hat :-)

#
# size of the rectangle's sides
#
side = 100

#
# set up the drawing
#
# window stuff first
wn = turtle.Screen()        # draw the window for the picture
wn.bgcolor("red")           # make the background color red
wn.title("A Box With A Hat")# put up a title
# turtle (or pen) stuff next
box = turtle.Turtle()       # create a turtle, called "box"
box.shape("turtle")         # let's make it a real turtle
box.speed(3)                # a turtle is slow (10 fastest, 1 slowest)
box.color("white")          # white contrasts nicely with red
box.pensize(3)              # make the lines 3 pixels

#
# draw the box
#
box.forward(side)             # tell box to move forward some
box.right(90)               # tell box to turn right
box.forward(side)             # tell box to move forward some
box.right(90)               # tell box to turn right
box.forward(side)             # tell box to move forward some
box.right(90)               # tell box to turn right
box.forward(side)             # tell box to move forward some

#
# now let's draw the hat
# the length of each side of the hat is calculated using
# the Pythagorean theorem for a right triangle; the hat
# side lengths x are equal, and form the legs of the triange;
# the box length is the hypotenuse c, so x**2 + x**2 = c**2;
# solving for x gives sqrt((c**2)/2)
#
box.right(45)                       # tell box to turn right half a turn
box.forward(math.sqrt((side**2)/2))   # tell box to move forward some
box. right(90)                      # tell box to turn right
box.forward(math.sqrt((side**2)/2))   # tell box to move forward some

#
# now hide the turtle and just sit there, displaying the result
#
box.hideturtle()            # make the turtle invisible
wn.mainloop()               # wait until the user closes the window