Problem Solving with Python Challenges 2 Scratch to Python

Transcription

1 Problem Solving with Python Challenges 2 Scratch to Python Contents 1 Drawing a triangle Generalising our program to draw regular polygons in Scratch and Python Drawing a square Using variables to remove duplication Drawing other polygons Calculating the angle Removing all code duplication Drawing five triangles while rotating through 360 degrees Generalising the five triangle program to draw spirographs Drawing polygons and spirographs based on user input Switching between colours when drawing a spirograph Drawing a triangle Together we will draw a regular triangle in Scratch and then draw the same triangle in Python. A regular triangle is a triangle with each side the same length and each interior angle the same number of degrees. In the Python shell type: from turtle import * 1

2 The Python shell allows us to enter program code a line at a time in a window and the Python interpreter executes the code line by line. However, the shell does not save the program. We will use IDLE's built- in syntax highlighting text editor to write a program that we can save to a file. The separate document on Writing and Saving a Program in Python explains this process in a little more detail. Our first Python program will be the program to draw a triangle typed into the text editor as follows: from turtle import * 2 Generalising our program to draw regular polygons in Scratch and Python In each of the following exercises we will increasingly generalise our program. We will progress from the specific solution to drawing a regular triangle with a fixed side length to a program to draw regular polygons and spirographs. The process of generalisation abstracts away from specific details to give a more widely applicable solution to the problem of drawing regular polygons. In the following exercises you can refine the program in Scratch and then do equivalent modifications in Python. Alternatively, you can program directly in Python and only use Scratch if you get stuck in Python or to verify the behaviour of certain programming constructs. It can be useful to build up a series of programs in which the constructs in Scratch are mapped to equivalent constructs in Python. The Scratch and Python Programming Constructs document should help with this mapping. See Writing and Saving a Program in Python for how to write and save a program in Python using the IDLE environment. You can do the following exercises by progressively modifying your programs. However, you may find it less confusing to save a program for each exercise and then use a copy of that program as the starting point for the next exercise. If you are writing both Scratch and Python versions, you will have two programs per exercise. 2.1 Drawing a square Using the code in Section 1 as a starting point, draw a square. You can do this by duplicating blocks in Scratch or lines of code in Python. You will also have to change the angle to turn. 2

3 2.2 Using variables to remove duplication There are two fixed values in the programs so far the length of a side triangle and the interior angle. If we want to change a value we have to do it in three places for a triangle. If we are drawing square we have to change it in 4 places. Modify either your triangle or square program to use variables in in place of the fixed values. o Make or declare a variable for each fixed value and use the relevant variable in the move and turn blocks in Scratch and/or in the forward and right lines of code in Python. Experiment with changing the values of the variables in the place that you declare them and see the effect on the program. In Scratch use Make a Variable under the Data tab to create a variable. You will then see blocks to set the value of a variable. In Python declare and assign to a variable using the = assignment operator. For example, the following Python code declares a variable called name and gives it the value 21. age = 21 See Section 5 of Scratch and Python Programming Constructs for a comparison of variables in Scratch, Python and Excel. Example code The following code shows the declaration of variables to draw a regular polygon in Python. side_length = 100 angle = 90 forward(side_length) right(angle) # complete this program Given the value for the angle shown, if you complete the program correctly, which shape will it draw? What is the equivalent program in Scratch? Note: # starts a comment in Python. 3

4 2.3 Drawing other polygons Using the program from Exercise 2.2 as a starting point, duplicate relevant blocks/lines of code to draw a pentagon Duplicate blocks/lines of code to draw a hexagon You will have to the code that draws the shape but you do not have to change the value of the angle for each turn block or forward line. You can simply set your angle variable to a different value to draw a different polygon, provided you have enough move/turn blocks or forward/right lines. 2.4 Calculating the angle What do you notice about the relationship between the number of sides and the interior angle of a regular polygon? Create a new variable that will allow you to calculate the interior angle from the number of sides Hint: The interior angles of regular polygons add up to Removing all code duplication In exercise 2.2, we used variables to remove some duplication of code. This made it easier and less error- prone to create different shapes. In the use of the move/turn blocks in Scratch and forward/right lines in Python, we abstracted away from fixed values and replaced them with variables. However, we still have duplicate code. Use a repeat / for loop to draw a triangle Change your loop to draw a square Change it again to draw a pentagon Change it again to draw a hexagon If you write your repeat block or for loop in terms of the variable you introduced in Section 2.4, you should be able to simply change one value and use the same code to draw polygons with different numbers of sides. See Section 3 of Scratch and Python Programming Constructs for a comparison of a repeat block in Scratch and a for loop in Python. Example code In Python, use the range function to control the number of repetitions. For example: for counter in range(10): # statements indented here repeat 10 times 4

5 2.6 Drawing five triangles while rotating through 360 degrees You should now have a drawing program that uses the following constructs to draw polygons A variable for the length of each side A variable for the number of sides A variable for the interior angle that is calculated from the number of sides A repeat/for loop that draws a polygon with the required number of sides You should be able draw different polygons with different side lengths and different number of sides by simply setting the first two variables to different values. Changing the number of sides should determine the interior angle and the polygon that is drawn. You will now modify your program to draw the following picture: Modify your program to draw five triangles while rotating through 360 degrees. That is: Your starting point can be the program you developed in exercise 2.5. You can then duplicate the repeat block/for loop code so that instead of drawing a single triangle, your program draws five triangles. As shown in the preceding outline program, you will need a turn block/right statement between each loop that draws a triangle. What do you notice about the angle to turn through after drawing each triangle and its relationship to the number of triangles? 5

6 2.7 Generalising the five triangle program to draw spirographs As with the process for drawing a single polygon, improve your program by removing duplication. Replace any fixed values with variables Use the number of polygons (triangles in the case of exercise 2.6) to draw to calculate the angle to turn through after drawing each polygon Use a repeat block/for loop to remove any code duplication in your program You will need two repeat blocks/for loops: 1. To draw a single polygon 2. An outer loop to repeatedly draw polygons Use the following Python turtle function speed(0) to speed up drawing. Using your program You should now have a program that you can use to draw spirographs from polygons with any number of sides. That is, drawing repeated instances of a polygon while rotating through 360 degrees. You should be able to produce different shapes by just changing the value of variables for the length of a polygon's side, the number of sides of the polygon and the number of polygons to repeat to produce a spirograph. Experiment with changing these values and see the different shapes you can draw. 6

7 2.8 Drawing polygons and spirographs based on user input Modify your program to allow the values of variables to be set from user input. In Scratch, you can use the answer to an ask block such as: to set the number of sides for a polygon. The equivalent Python code is: answer = input('how many sides do you want for each polygon? ') See Section 6 of Scratch and Python Programming Constructs for a comparison of user input in Scratch and Python and how to convert an answer to a number in Python. You will need other user input statements to set other variables. It is advisable to progress step by step. Write a user input code to set one variable. Test that it works. Then write subsequent code to set another variable, test it, and so on. 2.9 Switching between colours when drawing a spirograph Modify the program from exercise 2.8 so that the first polygon in a spirograph is red, then the second polygon is green, then the third polygon is blue, then the fourth is red again and so on. The following figure shows the expected result for a spirograph of five triangles: You do this by setting the pen colour before drawing each polygon. You can use if/then blocks/statements to select the pen colour. There is a way to use a data structure called a list to simplify the solution. We will come to that next 7