The Objective
The projects in this course give you an opportunity to work on larger
problems.
Experience working on a larger problem using good design practices
including:
- top-down design
- top-down implementation using stubs
- incremental programming with individual function testing
- use of meaningfully named constants
For this project, you'll be required to use the design shown in this
description.
For project 2, you will have to develop your own design.
The Background
A REGULAR POLYGON is defined as a
convex polygon with all sides congruent and all angles congruent.
The labeled drawings below show what is meant by the terms: exterior
angle, interior (or vertex angle), central angle,
and diagonal.
Realize that any regular polygon, not just the regular hexagon shown, can
be divided into the same number of triangles as it has sides, with the
base of each triangle being a side of the polygon and that the "tips" of
the triangles join in the center of the polygon.
All formulae shown in the drawings and also those for perimeter and area
shown later are courtesy of
mathwords.com
For all formulae shown:
n - number of sides
s - length of a side
A - area of the polygon
P - perimeter of the polygon
P = n * s
A = 1/4 * n * s2 * cot(180° / n)
Names of Regular Polygons
| Number of Sides | Name |
|---|
| 3 | Equilateral Triangle |
| 4 | Square |
| 5 | Regular Pentagon |
| 6 | Regular Hexagon |
| 7 | Regular Heptagon |
| 8 | Regular Octagon |
| 9 | Regular Nonagon |
| 10 | Regular Decagon |
The Task
Write a program that after printing a greeting to the user which contains
information about regular polygons, presents the user with a nicely-aligned
table that shows :
- the name of the polygon (printed using "%20s")
- the number of sides (an integer)
- the exterior angle in degrees (to 3 decimal places)
- the sum of the interior angles (an integer)
- the interior angle in degrees (to 3 decimal places)
- the number of diagonals (an integer)
for all n-gons from 3 to 10, inclusive. The values in this table may NOT
be hard coded. All of the values in the table
MUST be calculated by
the modular functions described in the design.
After presenting the table, your program must direct the user to input the
number of sides of a polygon and the length of the sides. Use this
information to calculate the perimeter and area of that polygon. Display
the name of the polygon with its perimeter and area to the user. Restrict
the user to regular polygons with n of 3 - 10, inclusive. The user should
be allowed to continue to enter polygons as long as s/he wants and should
signal the end by entering the sentinel 0 for n.
You are required to use Python's dictionary type to hold the polygon's
names with the number of sides as the key.
Your program must be robust checking user input for validity and
reprompt for a new value when the user is in error. This should be
accomplished in the functions getValidNumSides() and getPositiveValue(),
both of which should use post-test loops. See the sample output for
examples of testing these functions.
The Design
The function headers given below must be used and may NOT be altered in anyway.
# printGreeting() provides information to the user about the program
# Inputs: None
# Outputs: None
def printGreeting():
# generateTable() prints a table of data for regular polygons
# whose number of sides are from MIN to MAX
# Inputs: min, the minimum number of sides
# max, the maximum number of sides
# Outputs: None
def generateTable(min, max):
# printInstructions() explains that the user can now enter information
# about specific polygons (# of sides and length of the sides), so that
# the perimeter and area can be calculated.
# Inputs: None
# Outputs: None
def printInstructions():
# getValidNumSides() gets a valid number of sides from the user or the
# sentinel to quit.
# Inputs: sentinel, the value to enter to quit
# min, the minimum allowable number of sides
# max, the maximum allowable number of sides
# Outputs: a valid numSides (either the sentinel or a number between
# min and max, inclusive
def getValidNumSides(sentinel, min, max):
# getPositiveValue() gets a value greater than 0 from the user
# Inputs: None
# Outputs: a positive real number
def getPositiveValue():
# findExteriorAngles() calculates and returns the exterior angles
# of this polygon.
# Input: numSides, the number of sides of this polygon
# Output: the exterior angle of the polygon in degrees
def findExteriorAngles(numSides):
# findAngleSum() calculates the sum of the interior angles
# of this polygon.
# Input: numSides, the number of sides of this polygon
# Output: the sum of the interior angles
def findAngleSum(numSides):
# findInteriorAngles() calculates and returns the size of the interior
# or vertex angles of the polygon.
# Inputs: angleSum, the sum of the interior angles
# numSides, the number of sides of this polygon
# Output: the interior (or vertex angle) in degrees
def findInteriorAngles(angleSum, numSides):
# findNumDiagonals() caluclates and returns the number of diagonals
# of this polygon.
# Input: numSides, the number of sides of this polygon
# Output: the number of diagonals
def findNumDiagonals(numSides):
# findPerimeter() calculates and returns the perimeter of the polygon
# Inputs: numSides, the number of sides of this polygon
# length, the length of each of the sides
# Output: the perimeter of the polygon.
def findPerimeter(numSides, length):
# findArea() calculates and returns the area of the polygon
# Inputs: numSides, the number of sides of this polygon
# length, the length of each of the sides
# Output: the area of the polygon
def findArea (numSides, length):
The following symbolic constants should be used and they should be placed
at the top of your proj1.py file, just after the imports:
# Symbolic constants
SENTINEL = 0
MIN = 3
MAX = 10
HALF_ROTATION = 180
FULL_ROTATION = 360
PI = 3.14159
The math library
- You must import math
- The math library does not have a cotangent function, but it does
have a tangent function called tan(), which takes a float and
returns a float. You should remember and use the trig identity:
cot(theta) = 1/tan(theta)
- All of the math library trig functions take the angle measurements in
radians, not degrees, so you'll have to make that conversion using the
math.radians(x) function. It converts angle x from degrees to radians.
It shouldn't surprise you to learn that there is also a math.degrees(x)
function which converts the angle x from radians to degrees.
Sample Run
linux1[106] python proj1.py
Your greeting goes here
Table of Regular Polygon Facts
Name # Sides Ext Ang Int Ang Sum Int Ang Diags
Equilateral triangle 3 120.000 180 60.000 0
Square 4 90.000 360 90.000 2
Regular pentagon 5 72.000 540 108.000 5
Regular hexagon 6 60.000 720 120.000 9
Regular heptagon 7 51.429 900 128.571 14
Regular octagon 8 45.000 1080 135.000 20
Regular nonagon 9 40.000 1260 140.000 27
Regular decagon 10 36.000 1440 144.000 35
Your instructions about entering the number of sides
and the length of one side for the calculations of perimeter
and area go here.
Enter number of sides, 0 to quit : 4
Enter the length of one side : 4
Square with sides of 4.000
Perimeter : 16.000
Area : 16.000
Enter number of sides, 0 to quit : 3
Enter the length of one side : 4
Equilateral triangle with sides of 4.000
Perimeter : 12.000
Area : 6.928
Enter number of sides, 0 to quit : 6
Enter the length of one side : 4
Regular hexagon with sides of 4.000
Perimeter : 24.000
Area : 41.569
Enter number of sides, 0 to quit : 2
Sorry 3 - 10 or 0 only
Try again.
Enter number of sides, 0 to quit : 1
Sorry 3 - 10 or 0 only
Try again.
Enter number of sides, 0 to quit : -5
Sorry 3 - 10 or 0 only
Try again.
Enter number of sides, 0 to quit : -1
Sorry 3 - 10 or 0 only
Try again.
Enter number of sides, 0 to quit : 5
Enter the length of one side : 2.5
Regular pentagon with sides of 2.500
Perimeter : 12.500
Area : 10.753
Enter number of sides, 0 to quit : 7
Enter the length of one side : 3.75
Regular heptagon with sides of 3.750
Perimeter : 26.250
Area : 51.102
Enter number of sides, 0 to quit : 8
Enter the length of one side : 25.67
Regular octagon with sides of 25.670
Perimeter : 205.360
Area : 3181.690
Enter number of sides, 0 to quit : 9
Enter the length of one side : 15.29
Regular nonagon with sides of 15.290
Perimeter : 137.610
Area : 1445.214
Enter number of sides, 0 to quit : 10
Enter the length of one side : 17
Regular decagon with sides of 17.000
Perimeter : 170.000
Area : 2223.628
Enter number of sides, 0 to quit : 6
Enter the length of one side : 0
Positive values only! Try again : -3
Positive values only! Try again : 6.2
Regular hexagon with sides of 6.200
Perimeter : 37.200
Area : 99.870
Enter number of sides, 0 to quit : 0
linux1[107]
Although your output need not be identical to the above,
all information (including the greeting) must be present.
Extra Credit
For 5 points of Extra Credit, when the user enters a specific polynomial
for calculation of its perimeter and area, also open a graphics window and
draw that polygon to scale. To prove the polygon is to scale, you'll
need to have a grid shown. Have the user click on the window to close it.
For 5 more points of Extra Credit, make this graphical display fancier in
some fashion. Be as creative as you like. It needs to be significantly
different from the regular extra credit portion described above.
Submitting your work
You must be logged into your account and in the same directory
as the file you are trying to submit.
To submit your project, type the following at the linux prompt:
submit cs201 Proj1 proj1.py
To verify that your project was submitted, you can execute the
following command at the Unix prompt. It will show all files that
you submitted in a format similar to the Unix 'ls' command.
submitls cs201 Proj1
