2D Shapes using Python Turtle

Posted on September 19, 2017 by Administrator Posted in Computer Science, Python - Advanced, Python Challenges

In this challenge we will use Python Turtle to draw regular polygons including:

An equilateral triangle
A square
A pentagon
An hexagon
etc.

Did you know?

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be convex or star.

Convex Regular Polygons

Looking at the following three polygons, we can work out a formula to calculate the external angle of a convex regular polygon based on its number of sides.

Exterior Angle = 360 / number of sides

Python Code

Based on this formula we have implanted a function called drawPolygon() which takes one parameter called numberOfSides. This function will draw the corresponding convex regular polygon on screen.

Star Regular Polygons

Your challenge consists of coding a similar function, called drawStar(), used to draw star regular polygons on the screen. This function will take two parameters called numberOfSides and multiplier.

This time we will use a different formula to calculate the exterior angle:

Exterior Angle = multiplier * (360 / number of sides)

You can test your code with the following parameter values:

Star #	Number of Sides	Multiplier
#1	5	2
#2	8	3
#3	9	4
#4	10	3
#5	12	5

Tagged with: Python Turtle

Print Command Quiz

Posted on September 6, 2017 by Administrator Posted in Coding Quiz, Computer Science, Computing Concepts, GCSE Concepts, GCSE Quiz, Quizzes

The first instruction you will most likely learn when using Python is the print() instruction. It is used to display/output a message on screen.

print("Hello World")

Using Variables
The print command can be used to output the content of a variable:

username="admin"
print("You are logged as:")
print(username)

Using String Concatenation
You can join multiple strings together (string concatenation using +) to print them on a single line:

username="admin"
print("You are logged as:" + username)

Casting numbers (e.g integers) into string and vice-versa:
You can convert (cast) a number (e.g integer) into a string using the str() function or convert/cast a string into an integer using the int() function:

score=10
print("Your score:" + str(score))

Take the Quiz! (open full screen)

How Old is Your Cat?

Posted on August 31, 2017 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges, Solved Challenges

In this challenge we are going to create a cat’s age convertor find out how old a cat is in “human years”. This is very useful to understand more about cats and the care they need and to find out at what stage of life a cat is.
To convert the age of a cat in human years you have to do the following:

Year 1 counts for 15 Human Years
Year 2 counts for 9 Human Years
Thereafter each year counts for 4 Human Years

For example:

A 1 year old cat is 15 Human Years old,
A 2 years old cat is 15 + 9 = 24 Human Years old,
A 3 years old cat is 15 + 9 + 4 = 28 Human Years old,
A 4 years old cat is 15 + 9 + 4 + 4 = 32 Human Years old,
A 5 years old cat is 15 + 9 + 4 + 4 + 4= 36 Human Years old,
A 10 years old cat is 15 + 9 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 56 Human Years old.

You can check the full cat’s age conversion chart at the bottom of this post.

Your Challenge

Complete the following code to ask the user to input the age of a cat in years and return the equivalent in human years.

Extension #1

Amend your code so that it also works for cats under 1 year old. In this case you will have to ask for the cat’s age in months and use the conversion chart below (At the bottom of this post) to return the cat’s age in human years.

Extension #2

The stages of life of a cat are as follows:

Kitten – from birth to 6 months,
Junior – from 7 months to 2 years,
Prime – from 3 years to 6 years,
Mature – from 7 years to 10 years,
Senior – from 11 years to 14 years,
Geriatic – from 15 years above.

Extend your code to tell the end-user what stage of life their cat’s age is corresponding to.

Extension #3

Create another program where the user enters their age in human years and the program tells the user how old they would be if they were a cat!

Cat’s age conversion chart:

Life Stage	Cat years	Human years
Kitten	2 months	9 to 10 months
	3 months	2 to 3 years
	4 months	5 to 6 years
	5 months	8 to 9 years
	6 months	10 years
Junior	8 months	13 years
	1 year	15 years
	2 years	24 years
Prime	3 years	28 years
	4 years	32 years
	5 years	36 years
	6 years	40 years
Mature	7 years	44 years
	8 years	48 years
	9 years	52 years
	10 years	56 years
Senior	11 years	60 years
	12 years	64 years
	13 years	68 years
	14 years	72 years
Geriatric	15 years	76 years
	16 years	80 years
	17 years	84 years
	18 years	88 years
	19 years	92 years
	20 years	96 years
	21 years and above	100 years

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: Python Challenge, Selection

Infinite Quarter Series

Posted on July 17, 2017 by Administrator Posted in Computer Science, Python - Advanced, Python Challenges, Solved Challenges

The infinite quarter series is a series where each term is a quarter of the previous one:

We can visually represent this series by dividing a canvas (or price of paper) into 4 quadrants and colouring in one quadrant (bottom left). Then we repeat this process by dividing the top right quadrant into 4 and so on.

By doing so infinitely we will colour in a third of the initial canvas. This is because this infinite series converges to the value of ¹/₃.

Visual Demonstration using Python Turtle

Your Challenge

It is possible to visually represent this series using a triangle instead of a square.
Your task is to adapt the above Python script to represent this series using a triangle.

Help?

Check our flowchart to solve this challenge.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: Coordinates, Flowchart, iteration, Python Turtle

Estimating Pi using Buffon’s Needle

Posted on July 17, 2017 by Administrator Posted in Computer Science, Python - Advanced, Python Challenges, Solved Challenges

Painting by François-Hubert Drouais – Musée Buffon à Montbard, France

A few hundred years ago people enjoyed betting on coins tossed on to a wooden floor … would they cross a line or not?

A French mathematician called Georges-Louis Leclerc, Comte de Buffon (1707-1788) started thinking about this and worked out the probability.

This probability is called “Buffon’s Needle” in his honor.

Buffon then used the results from his experiment with a needle to estimate the value of π (Pi). He worked out this formula:

π ≈ 2LN / CW

Where

L is the length of the needle
N is the total number of needles
C is the total number of needles crossing a line
W is the line spacing (Width of the wooden boards on the floor)

We have decided to simulate this experiment using a Python script (using Python Turtle).

Task 1

Run the above script and count how many needles (out of 50) are crossing a line. Apply Buffon’s formula to estimate the value of Pi using:
π ≈ 2LN / CW

L is the length of the needle (L = 30 pixels
N is the total number of needles (N = 50 needles)
C is the total number of needles crossing a line
W is the line spacing (Width of the wooden boards on the floor W = 40 pixels)

Task 2

Adapt this Python script to automatically detect if a needle is crossing a line.

Your Python script should then count how many needles are crossing a line and use this to estimate a value of Pi.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: Coordinates

Euler’s Number

Posted on July 17, 2017 by Administrator Posted in Computer Science, Python - Advanced, Python Challenges, Solved Challenges

The number e is a famous irrational number called Euler’s number after Leonhard Euler a Swiss Mathematician (1707 – 1783). Number e is considered to be one of the most important numbers in mathematics.

The first few digits are: 2.7182818284590452353602874713527… It has an infinite number of digits with no recurring pattern. It cannot be written as a simple fraction.

Number e is the limit of (1 + ¹/_n)ⁿ as n approaches infinity:

Number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. Find out more on https://en.wikipedia.org/wiki/E_(mathematical_constant).

In this challenge we will use a Python script to calculate an approximation of e using three different approaches. The first approach as described above as already been implemented in the above Python trinket.

Calculating e using an iterative approach

Euler’s number, e, can also be calculated as the sum of the infinite series:

Complete your Python script to implement this infinite series using an iterative approach. (Method 2)

Calculating e using a continuous fraction (iterative approach)

A less common approach to calculate number e is to use a continued fraction based on the following sequence:

Continued Fraction:
$euler-continued-fraction$

Complete your Python script to implement this continued fraction. (Method 3)

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: iteration, recursion

Golden Angle

Posted on July 14, 2017 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges

In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio.

Golden Angle ≈ 137.5°

The golden angle plays a significant role in the theory of phyllotaxis; for example, the golden angle is the angle separating the florets or branches on some plants or flowers (e.g. sunflower).

Plants have their leaves spread all around the stem to soak up as much sun as possible. Using the golden angle between two consecutive leaves is the most effective approach to spread the leaves around the stem.

Let’s see how this work:
Leaf 1:

Leaf 2: Would be at an angle of around 137.5° (The Golden Angle) from leaf 1

Leaf 3: Would be at an angle of around 137.5° (The Golden Angle) from leaf 2

And so on for all new leaves…

etc…

Python Challenge

For this challenge we will apply the golden angle to position the first 50 branches of a tree using Python Turtle:

Sunflower using Python Turtle and the Golden Angle

Tagged with: Coordinates, iteration, Python Turtle

Graphing Algorithm

Posted on July 14, 2017 by Administrator Posted in Computer Science, Python - Advanced, Python Challenges

In this challenge we will write several procedures to graph different mathematical equations on screen using Python Turtle.

We will focus on:

Linear equations: y = ax + b
Quadratic equations: y = ax² + bx + c
Trigonometric functions: e.g. y = cos(x)

(x,y) coordinates using Python Turtle?

On the Python trinket used below the turtle screen is 400 pixels wide by 400 pixels high.

Look at the canvas below to understand how (x,y) coordinates work:

Linear Equation

y = ax + b

A linear equation produces a straight line when graphed on screen.

Your task:
Change the parameters used when calling the drawLine() procedure to graph the following equations:

y = 2x + 60
y = -x + 10
y = x
y = ¹/₂x

Quadratic Equation

y = ax² + bx + c

Add another procedure called drawQuadraticEquation() that will take three parameters: a, b and c and be used to graph and display the matching quadratic equation.

Use this new procedure to graph the following equations:

y = x² + 2x + 60
y = ¹/₂x² – 3x + 20
y = x²
y = -x² + 100

Trigonometric Functions

You can now add further procedures to draw the main trigonometric functions. To do so you will need to import the math library using an import statement.

import math

Here are the three main functions you will need to implement:

cosine: y = cos(x)
sine: y = sin(x)
tangent: y = tan(x)

Tagged with: Coordinates, iteration, Python Turtle, subroutine

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Did you know?

Convex Regular Polygons

Python Code

Star Regular Polygons

Take the Quiz! (open full screen)

Your Challenge

Extension #1

Extension #2

Extension #3

Cat’s age conversion chart:

Solution...

Solution...

Python Code

Solution...

Visual Demonstration using Python Turtle

Your Challenge

Help?

Solution...

Task 1

Task 2

Solution...

Calculating e using an iterative approach

Calculating e using a continuous fraction (iterative approach)

Solution...

Python Challenge

Sunflower using Python Turtle and the Golden Angle

(x,y) coordinates using Python Turtle?

Linear Equation

Quadratic Equation

Trigonometric Functions

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