Math Adventures with Python: An Illustrated Guide to Exploring Math with Code

by Peter Farrell

Overview

Learn math by getting creative with code! Use the Python programming language to transform learning high school-level math topics like algebra, geometry, trigonometry, and calculus!

Math Adventures with Python will show you how to harness the power of programming to keep math relevant and fun. With the aid of the Python programming language, you'll learn how to visualize solutions to a range of math problems as you use code to explore key mathematical concepts like algebra, trigonometry, matrices, and cellular automata.

Once you've learned the programming basics like loops and variables, you'll write your own programs to solve equations quickly, make cool things like an interactive rainbow grid, and automate tedious tasks like factoring numbers and finding square roots. You'll learn how to write functions to draw and manipulate shapes, create oscillating sine waves, and solve equations graphically.

You'll also learn how to:
- Draw and transform 2D and 3D graphics with matrices
- Make colorful designs like the Mandelbrot and Julia sets with complex numbers
- Use recursion to create fractals like the Koch snowflake and the Sierpinski triangle
- Generate virtual sheep that graze on grass and multiply autonomously
- Crack secret codes using genetic algorithms

As you work through the book's numerous examples and increasingly challenging exercises, you'll code your own solutions, create beautiful visualizations, and see just how much more fun math can be!

Product Details

ISBN-13:	9781593278670
Publisher:	No Starch Press
Publication date:	01/08/2019
Pages:	304
Sales rank:	506,739
Product dimensions:	6.90(w) x 9.20(h) x 1.00(d)
Lexile:	1080L (what's this?)
Age Range:	10 Years

About the Author

Peter Farrell is a math and computer science teacher with a passion for customizing ("hacking") math education and learning with technology. He lives in the San Francisco Bay Area with his wife and children.

Table of Contents

About the Author vi

About the Technical Reviewer vi

Acknowledgments xv

Introduction xvii

The Problem with School Math xviii

About This Book xx

Who Should Use This Book xxi

What's in This Book? xxi

Downloading and Installing Python xxii

Starting IDLE xxiii

Installing Processing xxiv

Part 1 Hitchin' Up Your Python Wagon

1 Dmmma Polygons With The Turtle Module 3

Python's turtle Module 4

Importing the turtle Module 4

Moving Your Turtle 5

Changing Directions 6

Repeating Code with Loops 7

Using the for Loop 7

Using a for Loop to Draw a Square 9

Creating Shortcuts with Functions 9

Using Variables to Draw Shapes 11

Using Variables in Functions 11

Variable Errors 12

Equilateral Triangles 13

Writing the triangle() Function 13

Making Variables Vary 14

Summary 17

2 Making Tedious Arithmetic Fun With Lists And Loops 19

Basic Operators 20

Operating on Variables 20

Using Operators to Write the average() Function 21

Mind the Order of Operations! 21

Using Parentheses with Operators 22

Data Types in Python 22

Integers and Floats 22

Strings 23

Booleons 24

Checking Data Types 25

Using Lists to Store Values 25

Adding Items to a List 26

Operating on Lists 26

Removing Items from a List 27

Using Lists in Loops 27

Accessing Individual Items with List Indices 28

Accessing Index and Value with enumerate() 29

Indices Start at Zero 29

Accessing a Range of List Items 30

Finding Out the Index of an Item 30

Strings Use Indices, Too 31

Summation 32

Creating the running_sum Variable 32

Writing the mySum() Function 33

Finding the Average of a List of Numbers 34

Summary 35

3 Guessing And Checking With Conditionals 37

Comparison Operators 38

Making Decisions with if and else Statements 38

Using Conditionals to Find Factors 39

Writing the factors.py Program 40

The Wandering Turtle 41

Creating a Number-Guessing Game 43

Making a Random Number Generator 44

Taking User Input 44

Converting User Input to integers 45

Using Conditionals to Check for a Correct Guess 45

Using a Loop to Guess Again! 46

Tips for Guessing 47

Finding Square Roots 48

Applying the Number-Guessing Game Logic 48

Writing the squareRoot() Function 49

Summary 50

Part 2 Riding Into Math Territory

4 Transforming And Storing Numbers With Algebra 53

Solving First-Degree Equations 54

Finding the Formula for First-Degree Equations 55

Writing the equation() Function 56

Using print() Instead of return 57

Solving Higher-Degree Equations 58

Using quad() to Solve Quadratic Equations 59

Using plug() to Solve a Cubic Equation 60

Solving Equations Graphically 61

Getting Started with Processing 61

Creating Your Own Graphing Tool 63

Graphing on Equation 69

Using Guess and Check to Find the Roots 73

Writing the guess() Function 73

Summary 75

5 Transforming Shapes With Geometry 77

Drawing a Circle 78

Specifying Location Using Coordinates 79

Transformation Functions 80

Translating Objects with translate() 80

Rotating Objects with rotate() 83

Drawing a Circle of Circles 84

Drawing a Circle of Squares 85

Animating Objects 86

Creating the t Variable 86

Rotating the Individual Squares 87

Saving Orientation with pushMatrix() and popMatrix() 88

Rotating Around the Center 89

Creating on Interactive Rainbow Grid 89

Drawing a Grid of Objects 90

Adding the Rainbow Color to Objects 91

Drawing Complex Patterns Using Triangles 93

A 30-60-90 Triangle 94

Drawing an Equilateral Triangle 96

Drawing Multiple Rotating Triangles 98

Phase-Shifting the Rotation 99

Finalizing the Design 100

Summary 102

6 Creating Oscillations With Trigonometry 103

Using Trigonometry for Rotations and Oscillations 105

Writing Functions to Draw Polygons 106

Drawing a Hexagon with Loops 107

Drawing on Equilateral Triangle 109

Making Sine Waves 110

Leaving a Trail 113

Using Python's Built-in enumerated Function 114

Creating 1 Spirograph Program 116

Drawing the Smaller Circle 117

Rotating the Smaller Circle 117

Making Harmonographs 120

Writing the harmonograph Program 121

Filling the List Instantly 123

Two Pendulums Are Better Than One 124

Summary 126

7 Complex Numbers 127

The Complex Coordinate System 128

Adding Complex Numbers 129

Multiplying a Complex Number by i 130

Multiplying Two Complex Numbers 131

Writing the magnitude() Function 132

Creating the Mandelbrot Set 132

Writing the Mandelbrot() Function 135

Adding Color to the Mandelbrot Set 139

Creating the Julio Set 141

Writing the julia() Function 141

Summary 143

8 Using Matrices For Computer Graphics And Systems Of Equations 145

What Is a Matrix? 146

Adding Matrices 146

Multiplying Matrices 147

Order Matters in Matrix Multiplication 151

Drawing 2D Shapes 151

Transforming Matrices 154

Transposing Matrices 156

Rotating Matrices in Real Time 160

Creating 3D Shapes 161

Creating the Rotation Matrix 162

Solving Systems of Equations with Matrices 166

Gaussian Elimination 167

Writing the gauss() Function 168

Summary 172

Part 3 Blazing Your Own Trail

9 Building Objects With Classes 175

Bouncing Ball Program 177

Making the Ball Move 178

Making the Ball Bounce Off the Wall 179

Making Multiple Balls Without Classes 181

Creating Objects Using Classes 182

Grazing Sheep Program 186

Writing the Class for the Sheep 186

Programming Sheep to Move Around 187

Creating the energy Property 189

Creating Grass Using Classes 189

Making the Grass Brown when Eaten 192

Giving Each Sheep a Random Color 194

Programming Sheep to Reproduce 196

Letting the Grass Regrow 197

Providing an Evolutionary Advantage 198

Summary 200

10 Creating Fractals Using Recursion 201

The Length of a Coastline 202

What Is Recursion? 203

Writing the Factorial() Function 203

Building a Fractal Tree 204

Koch Snowflake 209

Writing the segment() Function 210

Sierpinski Triangle 214

Square Fractal 216

Dragon Curve 220

Summary 224

11 Cellular Automata 225

Creating a Cellular Automaton 226

Writing a Cell Class 228

Resizing Each Cell 230

Making a CA Grow 231

Putting the Cells into a Matrix 232

Creating the Cell List 233

Python Lists Are Strange 234

List Index Notation 235

Letting Your CA Grow Automatically 238

Playing the Game of Life 238

The Elementary Cellular Automaton 241

Summary 246

12 Solving Problems Using Genetic Algorithms 247

Using a Genetic Algorithm to Guess Phrases 248

Writing the makeList() Function 248

Testing the makeList() Function 249

Writing the score() Function 250

Writing the mutate() Function 250

Generating a Random Number 251

Solving the Traveling Salesperson Problem (TSP) 254

Using Genetic Algorithms 254

Writing the calcLength() Method 260

Testing the calcLength() Method 261

Random Routes 262

Applying the Phrase-Guessing Mutation idea 265

Mutating Two Numbers in a List 265

Crossing Over to Improve Routes 269

Summary 271

Index 273

Editorial Reviews

"We have entered an era where learning Python is as essential as knowing the analytical skills of mathematics, and so from students to teachers, Math Adventures with Python is an indispensable book for all."
—Gabrielle Birkman, Mathematician and Writer

"Peter Farrell subverts the structure of a traditional math textbook and adopts an approach centered on student creation and discovery. Rather than treating mathematical facts as symbolic formalism to be mindlessly imitated by students, Math Adventures with Python seeks to teach mathematics through guided discovery. "
—Dr. Tien Chih, Professor of Mathematics, Montana State University-Billings

"If you’re a mathy type and want to get into some computer programming, or if you’re a computer person but want to learn what kinds of math you can do with code, Math Adventures with Python will help you achieve those goals."
—Jenny Bristol, GeekDad

From the Publisher