All the Right Angles: From Gear Ratios to Calculating Odds: Mathematics in the World of Sports

All the Right Angles: From Gear Ratios to Calculating Odds: Mathematics in the World of Sports

by Joel Levy


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A visual reference to the mathematics of sports.

Any definition of sport begins with the term "physical". Motion, power, energy and momentum are the driving forces of physics, and numbers govern all sports. People and objects move in lines and curves, geometry determines progress, times are recorded, points counted, scores calculated. Without understanding numbers, it is impossible to understand sport. Athletes should be interested in the mathematics of sport for the simple reason that it can help them win. For fans, it brings greater enjoyment from their favorite sport.

All the Right Angles is a fun, fascinating and highly visual book that explains the mathematical and scientific principles in sports. With a clear infographics approach, the book never burdens readers with too many numbers and formulas or slows them down with jargon. Instead,
dynamic layouts, bold and colorful diagrams and minimal text promote easy comprehension.

There are four parts with self-contained spreads that cover 89 topics in all. They include:

  • Power and Motion: Basketball and Conservation of Energy; Ball Games and the Magnus Effect; Football and Newtonian Physics of Collision; Squash and Gas Pressure; Cycling and Gyroscopes
  • Angles, Trajectories and Geometry: Mathematics of a Golf Shot; Pool and Tangent Lines; Auto Racing and Distance; Baseball and Trajectories; Cycling and Gradients
  • Numbers and Statistics: Statistics in Baseball; Mathematics and Fantasy Football; Game Theory and Fencing; The Statistics of Home Advantage
  • Mathematics, Biology and Environment: Effects of Tennis Court Surfaces; Horsepower; Skydiving and Terminal Velocity; Fencing, Tennis and Reaction
    Speeds; Hydration and Performance.

Eight "Sports by Numbers" feature spreads cover baseball, football, rugby, golf, cricket, soccer, tennis and Formula 1. Throughout the book are facts, statistics, trivia and little-known anecdotes that will entertain all sport fans and athletes.

Sports offer a unique and engaging way into an intimidating topic that many people have written off as "too hard." The games we love have an unrivalled power to turn us on to the beauty of numbers. All the Right Angles is a highly entertaining introduction to that power for the mathematically-minded, the science buff and the curious reader alike.

Product Details

ISBN-13: 9781770851962
Publisher: Firefly Books, Limited
Publication date: 08/18/2013
Pages: 224
Product dimensions: 8.90(w) x 8.90(h) x 0.90(d)

About the Author

Joel Levy is a writer, journalist and the author of more than a dozen books on science and history, including A Bee in a Cathedral. He has written features and articles for the British press, and appeared on numerous television and radio shows. Joel has a BSc in Biological Sciences and an MA in Psychology and lives in London, England.

Table of Contents

Table of Contents


1 Power and Motion

    Bouncing Back to You: Basketball and Conservation of Energy
    Turn Up the Heat: Baseball and Momentum
    Relatively Heavy: Baseball and Relativity
    Throwinng a Curve: Ball Games and the Magnus Effect
    The Hardest Task in Sports: Timeline of a Baseball Swing
    Sport by Numbers: Baseball
    High Impact: Football and Newtonian Physics of Collision
    The Perfect Pass: Football and Aerodynamics
    Sport by Numbers: Football
    Spares and Strikes: Bowling and Algebra
    Weight Watchers: Tour de France and Human Power Output
    Cheating: Cycling and Statistics
    Takedown: Judo and Levers
    The Harder They Come: Rugby and Levers
    Sport by Numbers: Rugby Union
    Spin the Wheel: Cycling and
    The Sweet Spot: Tennis, Baseball and Elastic Collisions
    Club Speed: Golf, Levers and the Coriolis Effect
    Hit the Ball: Golf and Conservation of Momentum
    Sport by Numbers: Golf
    Left, Right, Left: The Power of the Punch
    Faster Than a Speeding Bullet: Pelota, Badminton and Velocity
    Gait Theory: Walking and Pendulums
    Foot Fall: Running and Load
    Degrees of Freedom: Racket Sports and Biomechanics
    On Board: Surfing and the Coefficient of Friction
    Heavy Lifting: Weightlifting and Gravity
    Fast as Lightning: Sprinting and Stride Rates
    Jump to It: Pole Vaulting and Conservation of Energy
    Hot Balls: Squash and Gas Pressure
    Hop, Step and Spring: Hooke's Law and the Triple Jump
    Less is More: Physiology, Biomechanics and Training
    Two Wheels Good: Cycling and Energy

2 Angles, Trajectories and Geometry

    The Sweetest Swing: Mathematics of a Golf Shot
    Take It to the Bank: Billiards and Geometry of Reflections
    Eight Ball: Pool and Tangent Lines
    Spiked: Mathematics of Volleyball
    The Racing Line: Auto Sports and Distance
    Swinging for the Fences: Baseball and Trajectories
    Tale of the Tape: Baseball, Wind Resistance and Distance
    Swing Time: Cricket and Aerodynamics
    Spin Class: Rotation and Bouncing in Cricket
    Sports by Numbers: Cricket
    The Wall of Death: Lean, Tilt, Gravity and Friction in Running
    Launch Trajectory: Shot-Putting, Javelin-Throwing and Angles
    Grade School: Cycling and Gradients

3 Number Crunching and Statistics

    Strike it Lucky: Statistics in Baseball
    Fortunate Streak:
    Statistics in Cricket
    Soccer Crazy: Statistics in Soccer
    Sport by Numbers: Football
    The Bell Curve: Statistical Distribution and Performance
    Points Mean Prizes: Ranking Coefficients in Soccer
    Keeping Score: Scoring Systems in Sport
    Fantasy Mathematics: Mathematics and Fantasy Soccer
    Faster, Higher, Stronger: Mathematics of World Records
    Ahead of the Curve: Geometry of World Records
    Battle of the Sexes: Gender and World Records
    The Long and the Short: Running and World Records
    Stick or Twist? Game Theory and Fencing
    What are the Odds? Calculating Odds
    No One Expects: Statistics, Upsets and the Most Interesting Sports
    Playing at Home: The Statistics of Home Advantage
    Best of the Best: How Do You Measure Sporting Perfection?
    One Percent at a Time: Swimming and Performance
    Athletes Uncovered: Unusual Olympic Statistics
    Animal Olympics: Athletic Records in the Animal and Human Worlds
    Money Makes the World Go Round: Sporting Salaries
    A Hard Rain: Duckworth-Lewis
    Spotting a Winner: Tour de France
    Marathon Men: Soccer Players' Exertion

4 Mathematics, Biology and the Environment

    A Man for All Surfaces: Effects of Tennis Court Surfaces
    Sport by Numbers: Tennis
    The Right Tools for the Job: Materials Science and Sports
    Around the Oval: Horsepower
    Slipstreaming: Cycling and Aerodynamics
    In at the Deep End: Mathematics of Swimming
    Get a Grip: Tires in Motorsports
    Juicing the Ball: Baseball, Tennis and Velocity
    Sports by Numbers: Formula 1
    VO2 the Max: The Respiratory System
    Blood and Guts: The
    Circulatory System
    The Speed of Thought: Fencing, Tennis and Reaction Speeds
    The Big Blue: Free Diving and the Diving Reflex
    All Things Ice: Speed Skating and Ice
    Body Heat: Temperature and Performance
    Dry as a Bone: Hydration and Performance
    Sky High: Skydiving and Terminal Velocity
    The Outer Limits: Physiology, Biomechanics and Sports




Did you know that the oldest known soccer ball dates to 1540 C.E., that the British cyclist Bradley Wiggins climbed the equivalent of a 62-mile-high mountain in training for the 2012 Tour de France, or that a pronghorn antelope would finish galloping the 800-meter race while the world record-holding human was only one-third of the way round the running track?

Did you know that a baseball batter has just over one-fifth of a second to decide whether, how hard and at what angle to hit the ball, and that getting the timing wrong by 7 milliseconds will make the difference between a home run, a pop fly or a strike?

Did you know that an average man can hold his breath for over 20 min, that badminton is the fastest racket sport in the world and that, statistically speaking, Australian cricket player Donald Bradman's batting average is the single most impressive record in sports?

Is it all simply fascinating trivia, or do these facts and figures have any greater significance for the world of sports? Sports are all about motion, power, energy and momentum. The people and objects involved move in lines and curves, their progress determined by geometry. Any definition of sports begins with the term "physical," as in "governed by physics." To regulate and score sports, times are recorded, points counted, scores calculated. Every one of these phenomena, processes and events is governed by numbers, from the energy involved in propelling a ball to the calculation of a coefficient that determines tournament seeding. It is not possible to understand sports without numbers, and without understanding it is impossible to improve.

At elite levels, winning is determined by the tiniest of margins and precise analysis is essential to the incremental improvement of performance. Knowing the numbers can give you the edge. This is increasingly recognized in professional sports, where the introduction of statistical recording and analysis systems, such as Sabermetrics in baseball and Prozone in soccer have made major contributions to athletic success and placed mathematics firmly in the heart of the locker room and the manager's office. Athletes should be interested in the mathematics of sports for this simple reason if nothing else: the application of science can help them win.

The traffic between sports and mathematics goes both ways, because sport offers a unique and engaging way into mathematics. Everyone, whether they realize it or not, is a sort of 'folk mathematician,' unconsciously relating quantities and magnitudes, angles and vectors. But too many people switch off as soon as the maths in their life becomes explicit, and sport has an unrivalled power to turn them on to the power and beauty of numbers.

The fascination of numbers, geometry and statistics will hopefully shine through the pages of this book and you will never think the same way about hitting, or watching someone else hitting, a nine iron, swinging at a curveball, winding up for a slap shot or curling in a free kick.

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