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Mathletics: A Scientist Explains 100 Amazing Things About the World of Sports
An entertaining, eye-opening guide to what math and physics can reveal about sports. How can sprinter Usain Bolt break his world record without expending any additional effort? Which demands a faster reaction time, tennis or baseball? What dates of birth give rise to the best professional athletes? Is it better to have the inside or outside lane during a race? And how can you improve your balance just by changing your posture? Drawing on vivid, real-life examples, John D. Barrow shows how math and physics can give us surprising, often counterintuitive insights into the world of sports. For example, we learn that left-handed boxers have a statistical advantage over their right-handed opponents and that gymnasts performing the “giant swing” maneuver on the high bar experience stronger g-forces than roller-coaster designers are allowed to create. Thanks to lucid explanations and a healthy dose of humor, Mathletics is the perfect book for sports enthusiasts and math lovers alike. 40 illustrations
- GenresNonfictionSportsScience
298 pages, Hardcover
First published June 18, 2012
14 people are currently reading
171 people want to read
About the author
John D. Barrow
90 books167 followersJohn D. Barrow was a professor of mathematical sciences and director of the Millennium Mathematics Project at Cambridge University and a Fellow of the Royal Society.
He was awarded the 2006 Templeton Prize for "Progress Toward Research or Discoveries about Spiritual Realities" for his "writings about the relationship between life and the universe, and the nature of human understanding [which] have created new perspectives on questions of ultimate concern to science and religion".
He was a member of a United Reformed Church, which he described as teaching "a traditional deistic picture of the universe".
He was awarded the 2006 Templeton Prize for "Progress Toward Research or Discoveries about Spiritual Realities" for his "writings about the relationship between life and the universe, and the nature of human understanding [which] have created new perspectives on questions of ultimate concern to science and religion".
He was a member of a United Reformed Church, which he described as teaching "a traditional deistic picture of the universe".
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Displaying 1 - 25 of 25 reviews
January 2, 2013
Oh, how I wish I’d read this book prior to the London Olympics. The bulk of its chapters focus on Olympic events, or aspects thereof, and in many cases enhance one’s understanding of an event. There is, as the title implies, a great deal of mathematics in the book – not all of it is difficult to grasp, though some is certainly challenging, and the reader will encounter several of the basic principles of physics (drag, lift, gravitational pull, inertia, and so on).
Barrow explains things concisely, so in a few chapters you’d best be paying close attention. As he is a Cambridge professor, there is a skew towards British and European sports and teams, though he occasionally touches on American sports (such as the fascinating 8 year cycling of an NFL team’s fortunes). Many chapters are instructive (wish I’d read 72 before watching water polo this summer), and others are just plain eye-openers (those on wheelchair speeds and points scoring in track and field, to name just two). Bits of Olympic trivia are tossed in throughout that are always interesting and often head-shakingly unbelievable, like the 300 live pigeons killed in the shooting events in Paris in 1900. Many chapters cause you to look at things from a different perspective, such as the one suggesting that sports like basketball, soccer, and tennis might be unworthy of being included in the Olympic games. The diagrams, charts, and photographs accompanying the text are helpful and always pertinent.
The point of mathematics is to teach one how to think critically, to look beyond the obvious to what lies beneath, thereby getting a handle on the world by understanding the forces driving it. Mathletics does a fine job of doing just that for the world of sports.
Barrow explains things concisely, so in a few chapters you’d best be paying close attention. As he is a Cambridge professor, there is a skew towards British and European sports and teams, though he occasionally touches on American sports (such as the fascinating 8 year cycling of an NFL team’s fortunes). Many chapters are instructive (wish I’d read 72 before watching water polo this summer), and others are just plain eye-openers (those on wheelchair speeds and points scoring in track and field, to name just two). Bits of Olympic trivia are tossed in throughout that are always interesting and often head-shakingly unbelievable, like the 300 live pigeons killed in the shooting events in Paris in 1900. Many chapters cause you to look at things from a different perspective, such as the one suggesting that sports like basketball, soccer, and tennis might be unworthy of being included in the Olympic games. The diagrams, charts, and photographs accompanying the text are helpful and always pertinent.
The point of mathematics is to teach one how to think critically, to look beyond the obvious to what lies beneath, thereby getting a handle on the world by understanding the forces driving it. Mathletics does a fine job of doing just that for the world of sports.
December 26, 2013
Parts of this book were very interesting. I was fascinated by the bit about the Sarah Hughes win in the 2002 Olympics, and was interested by the track and field bits regarding force, angle of attack, etc.
Here's the biggest problem with the book, though. It's boring. Not all of it, but enough of it. I'm an engineer, and I understand mathematics, but this was drearily dull. If you want to pull out formulas, that's fine. But explain where they come from. This guy yanks out formulas, but doesn't say why this is the right formula to use. They come out of nowhere, and he doesn't bother to explain much. There's a lot of assumption at play. And I get it...I can sit down and try to remember back to my physics classes from 20 years ago and understand why this is the right value to use for this particular variable. But it's too hard.
The next biggest problem is a lack of cohesion. Barrow bounces around from sport to sport. Here's an idea: try to reorganize the book so that all the track and field stuff shows up in the same place, and them maybe all the soccer stuff in the next section, and so on. It might improve the longevity of the book. Obviously, there's a focus on the 2012 London Games, but here is it on the verge of the 2014 Sochi games... A reader might like to just read up on the winter sports, instead of flipping through the whole book just to find the stuff they're interested in.
Here's the biggest problem with the book, though. It's boring. Not all of it, but enough of it. I'm an engineer, and I understand mathematics, but this was drearily dull. If you want to pull out formulas, that's fine. But explain where they come from. This guy yanks out formulas, but doesn't say why this is the right formula to use. They come out of nowhere, and he doesn't bother to explain much. There's a lot of assumption at play. And I get it...I can sit down and try to remember back to my physics classes from 20 years ago and understand why this is the right value to use for this particular variable. But it's too hard.
The next biggest problem is a lack of cohesion. Barrow bounces around from sport to sport. Here's an idea: try to reorganize the book so that all the track and field stuff shows up in the same place, and them maybe all the soccer stuff in the next section, and so on. It might improve the longevity of the book. Obviously, there's a focus on the 2012 London Games, but here is it on the verge of the 2014 Sochi games... A reader might like to just read up on the winter sports, instead of flipping through the whole book just to find the stuff they're interested in.
July 24, 2018
Really disappointing. The math here is sometimes interesting but often not explained in a very accessible way (and I was a math major). The writing is very bad. This is like a poorly written sports physics textbook. I'm honestly not sure how I could be more the target audience for this book and I still skimmed or skipped most of it.
August 9, 2017
Barrow, J. D. (2012). Mathletics: 100 amazing things you didn't know about the world of sports. New York: W. W. Norton.
Baseball & cricket batters and tennis players all have about 0.4s to react; each has pushed the human response close to the limit. - p. 17
Increasing your kayak team by 1 person over a 1km race improves your times by about 8%. - p. 31
For a set of y cards, to calculate how many cards one needs to buy to get all the cards (assuming the possibility of getting duplicates): y x (0.58 + ln y)
To calculate how many accolades you need so that in 4 terms you can possibly award all ur students: 2.6*(0.58+ln(2.6)) = 4
The number of accolades needed is your enrollment divided by 2.6 e.g. 37/2.6 = 14 accolades!
- p. 37
To reduce the mass of a bike, doing so on the wheels is 3-4 more effective than the frame. - p. 39
The proportionality factor describes what fraction of the person's mass you can use to push off a surface without slipping. For rubber shoes on dry grass, you can exert about 0.3 of your mass; any more and you'll slip.
Rain reduces this to 0.2, though studs will increase this. For extremes, Teflon is 0.04, while silicone rubber is more than 1.
- p. 51
In the 1900 Paris Olympics, 300 live pigeons were used in shooting. - p. 55
Water evaporates from a field at about 1.5cm a day. - p. 57
A gymnast on the uneven faces combined centrifugal and gravitational forces of up to 6g. - p. 61
Left-handlers face an advantage in sports, in that they are used to facing right-handers (90%), but right-ganders aren't used to left-handers (10%). - p. 63
It's calculated that a pole vaulter can convert his kinetic energy into only 4.6m of height. If 1.2m comes from his own centre of gravity, the remainder comes from the elasticity of the fiberglass pole. - p. 65
In a rugby lineup, the jumper can reach 5m! - p. 74
If penalty takers and goalkeepers are optimally competent, 80% of the penalties should be scored. - p. 82
The design of the number of points and sets in a game must balance luck versus skill, in that it should be long enough so that more skillful players generally win, but in a small proportion of matches, luck at key points can still reward the underdog. - p. 85
To know the maximum streak r in a series of N random events, N = 2^r
E.g. If you toss a coin 32 times, you'd expect to see heads or tails a maximum of 5 times in a row.
- p. 107
Strength is proportional to ^(2/3) of the thrower's weight. - p. 130
Currently, triathlons are imbalanced - 17% of the time swimming, 28% running, and 54% cycling. This should be equalized. - p. 158
Crowd movement goes through three liquid-like stages - smooth pedestrian flow (one direction), staccato rolling waves (switching lanes), chaotic turbulence (free-for-all) - p. 162
Drag in water is 780 times more than that in air. - p. 163
In modern pentathlon, swimming contributes most significantly to scoring, with fencing the least; shooting, riding, and running are largely neutral - p. 167
Smaller athletes find it easier to stay cool. - p. 170
While average speeds of runners drop by log^-0.1 over distances of 100m to 42.195km, those in wheelchair events are largely equal. - p. 173
Error allowance for courses is most significant for 25m lap pools (3cm), with it being significant after a mere 8.3s, compared to 100s for an athletics track. - p. 176
It's best to attempt a weightlifting record in Mexico City, as g=9.779m/s^2, due to its altitude and proximity to the equator; its worst at polar Oslo or Helsinki, where g=9.819. - p. 179
For a fairer league table, points for wins/draws should be adjusted based on the relative strength of the teams. This can be solved for the first-ranked eigenvector. The same principle is used to rank results in Google searches. - p. 182
Due to aerodynamic lift, drag of >15m/s is actually more advantageous for a discus thrower, although this is overcome if the tailwind is >20m. - p. 189
A sprinter spends about 3% of his effort overcoming drag, given a frontal surface area of 0.45m^2. While hair only accounts for about 7% of this factor, a more effective strategy would be to use bodysuits. Those with 0.5mm ribs create turbulence to halve the drag; however, this is only at speeds of about 10m/s. - p. 198
The NFL draft system has contributed to balancing the playing field by strengthening weaker teams more, resulting in an average 8-year success cycle, preventing an elite from dominating. - p. 208
If a knockout tournament has a number of teams N that is not a power of 2, you'd need to give (2^r)-N of them a bye, where is r is the power of 2 just more than the number of teams. - p. 210
A penalty is easiest to take in hockey, followed by football, handball, and water polo. This takes into account the cross-sectional area of the ball, the area of the goal, and the distance from the spot to the goal. - p. 222
If you keep promoting the most competent person, everyone will move upward till they reach their level of maximum incompetence; however, this assumes no correlation between successive job requirements. This results in a 10% organizational competence. But if the jobs correlate, it increases by 9%. - p. 232
Oscar Pistorius starts races slow, but can then reach greater cadence and maintain it longer. - p. 236
Of the many projectiles, shot put has the least drag, and a shuttlecock the most. - p. 272
Baseball & cricket batters and tennis players all have about 0.4s to react; each has pushed the human response close to the limit. - p. 17
Increasing your kayak team by 1 person over a 1km race improves your times by about 8%. - p. 31
For a set of y cards, to calculate how many cards one needs to buy to get all the cards (assuming the possibility of getting duplicates): y x (0.58 + ln y)
To calculate how many accolades you need so that in 4 terms you can possibly award all ur students: 2.6*(0.58+ln(2.6)) = 4
The number of accolades needed is your enrollment divided by 2.6 e.g. 37/2.6 = 14 accolades!
- p. 37
To reduce the mass of a bike, doing so on the wheels is 3-4 more effective than the frame. - p. 39
The proportionality factor describes what fraction of the person's mass you can use to push off a surface without slipping. For rubber shoes on dry grass, you can exert about 0.3 of your mass; any more and you'll slip.
Rain reduces this to 0.2, though studs will increase this. For extremes, Teflon is 0.04, while silicone rubber is more than 1.
- p. 51
In the 1900 Paris Olympics, 300 live pigeons were used in shooting. - p. 55
Water evaporates from a field at about 1.5cm a day. - p. 57
A gymnast on the uneven faces combined centrifugal and gravitational forces of up to 6g. - p. 61
Left-handlers face an advantage in sports, in that they are used to facing right-handers (90%), but right-ganders aren't used to left-handers (10%). - p. 63
It's calculated that a pole vaulter can convert his kinetic energy into only 4.6m of height. If 1.2m comes from his own centre of gravity, the remainder comes from the elasticity of the fiberglass pole. - p. 65
In a rugby lineup, the jumper can reach 5m! - p. 74
If penalty takers and goalkeepers are optimally competent, 80% of the penalties should be scored. - p. 82
The design of the number of points and sets in a game must balance luck versus skill, in that it should be long enough so that more skillful players generally win, but in a small proportion of matches, luck at key points can still reward the underdog. - p. 85
To know the maximum streak r in a series of N random events, N = 2^r
E.g. If you toss a coin 32 times, you'd expect to see heads or tails a maximum of 5 times in a row.
- p. 107
Strength is proportional to ^(2/3) of the thrower's weight. - p. 130
Currently, triathlons are imbalanced - 17% of the time swimming, 28% running, and 54% cycling. This should be equalized. - p. 158
Crowd movement goes through three liquid-like stages - smooth pedestrian flow (one direction), staccato rolling waves (switching lanes), chaotic turbulence (free-for-all) - p. 162
Drag in water is 780 times more than that in air. - p. 163
In modern pentathlon, swimming contributes most significantly to scoring, with fencing the least; shooting, riding, and running are largely neutral - p. 167
Smaller athletes find it easier to stay cool. - p. 170
While average speeds of runners drop by log^-0.1 over distances of 100m to 42.195km, those in wheelchair events are largely equal. - p. 173
Error allowance for courses is most significant for 25m lap pools (3cm), with it being significant after a mere 8.3s, compared to 100s for an athletics track. - p. 176
It's best to attempt a weightlifting record in Mexico City, as g=9.779m/s^2, due to its altitude and proximity to the equator; its worst at polar Oslo or Helsinki, where g=9.819. - p. 179
For a fairer league table, points for wins/draws should be adjusted based on the relative strength of the teams. This can be solved for the first-ranked eigenvector. The same principle is used to rank results in Google searches. - p. 182
Due to aerodynamic lift, drag of >15m/s is actually more advantageous for a discus thrower, although this is overcome if the tailwind is >20m. - p. 189
A sprinter spends about 3% of his effort overcoming drag, given a frontal surface area of 0.45m^2. While hair only accounts for about 7% of this factor, a more effective strategy would be to use bodysuits. Those with 0.5mm ribs create turbulence to halve the drag; however, this is only at speeds of about 10m/s. - p. 198
The NFL draft system has contributed to balancing the playing field by strengthening weaker teams more, resulting in an average 8-year success cycle, preventing an elite from dominating. - p. 208
If a knockout tournament has a number of teams N that is not a power of 2, you'd need to give (2^r)-N of them a bye, where is r is the power of 2 just more than the number of teams. - p. 210
A penalty is easiest to take in hockey, followed by football, handball, and water polo. This takes into account the cross-sectional area of the ball, the area of the goal, and the distance from the spot to the goal. - p. 222
If you keep promoting the most competent person, everyone will move upward till they reach their level of maximum incompetence; however, this assumes no correlation between successive job requirements. This results in a 10% organizational competence. But if the jobs correlate, it increases by 9%. - p. 232
Oscar Pistorius starts races slow, but can then reach greater cadence and maintain it longer. - p. 236
Of the many projectiles, shot put has the least drag, and a shuttlecock the most. - p. 272
June 5, 2023
As someone who loves both math and sports I was really excited to pick this one up. Unfortunately it was a major disappointment and I cannot recommend it. Of the 100 "Amazing things..." I found at least half of them to be "so what..." - Boring. A number of them Barrow makes absurd simplifications and assumptions. Two I found particularly annoying was comparing reaction times across sports or comparing how difficult it is to score a goal in the four goal based Olympic sports. The simplifications make the exercise meaningless unless you're a math or physics teacher looking to source sports related problems.
April 24, 2020
While on the negative side
The book contains too many errors
omissions
erroneous labeling of diagrams
incomplete/misleading diagrams
and some rather unclear descriptions.
Taken together, I found these to be extremely frustrating. Also, I must agree with a prior reviewer who pointed out that some rather British sports - predominantly rugby and cricket - are discussed with the assumption that the reader knows all about them: terminology, rules, etc. For North American readers like me, this is not necessarily the case.
https://pinoyathletics.info/mathletic...
The book contains too many errors
omissions
erroneous labeling of diagrams
incomplete/misleading diagrams
and some rather unclear descriptions.
Taken together, I found these to be extremely frustrating. Also, I must agree with a prior reviewer who pointed out that some rather British sports - predominantly rugby and cricket - are discussed with the assumption that the reader knows all about them: terminology, rules, etc. For North American readers like me, this is not necessarily the case.
https://pinoyathletics.info/mathletic...
March 1, 2022
Every nerdy cell in my body loved this! Fun little math-factoids related to sports, on everything from physics, fluid dynamics, statistics, and mechanics. I listened to the audio book, so I could tell there were several graphs and figures that I was missing and just had to imagine in my mind.
March 28, 2019
I continually went through liking and disliking the book. It is more math heavy than I ever anticipated.
May 27, 2024
An interesting book. Might have been better if I had read a physical copy because the audio book kept referring to graphs and pictures. It still got it's point across.
September 22, 2016
Kind of boring. Some of the parts were interesting, though. For example, wasn't aware that javelin throwers injure their elbows and shoulders so frequently.
September 24, 2012
Part of the long delay in reading this book is that the library took it from me before I was done and then they wouldn't give it back. "My audience is waiting," I tried to tell them (subconsciously), but they simply ignored that. So I had to wait weeks to get this book back in my hands.
My hope for this book was that I'd learn new and interesting things about a variety of sports, based in the language of mathmatics. When I started reading it, though, only the first amazing thing was really about athletics... the rest seemed to be simply word problems laid over the subject of athletics. That, fortunately, didn't carry through the whole book. Only about 8 or 10 of the articles were of that nature.
Math is a great tool for exploring some of the nuances of athletics... for explaining things that can't be seen as clearly in any other way. I learned much from this book, including things about sports that I haven't know much about until now.
My hope for this book was that I'd learn new and interesting things about a variety of sports, based in the language of mathmatics. When I started reading it, though, only the first amazing thing was really about athletics... the rest seemed to be simply word problems laid over the subject of athletics. That, fortunately, didn't carry through the whole book. Only about 8 or 10 of the articles were of that nature.
Math is a great tool for exploring some of the nuances of athletics... for explaining things that can't be seen as clearly in any other way. I learned much from this book, including things about sports that I haven't know much about until now.
September 5, 2014
Did you ever wonder what whether the inside or outside lane has an advantage? Or what the most extreme sport is? Or what is the best time of day to water a baseball field? This book has the mathematical formulas to explain these and many more burning athletic questions. For those who are allergic to such formulas, though, there are straightforward explanations that do not require any specialized math knowledge.
May 19, 2015
I think that I would have rated this book higher if I were good at math or even enjoyed math. The subject matter was interesting and the writing style was entertaining for the most part, but I couldn't wrap my brain around most of the equations and just had to assume that he was doing things right. Overall, a fun read!
November 18, 2012
Fun book with a lot of interesting facts that was worth my time to skim, but sometimes it felt like he was just trying to see how many different calculus equations he could apply to different throwing sports.
September 5, 2014
100 very short essays about the math underlying various aspects of sports: How to bend it like Beckham and why you cannot hit a bullseye with an arrow by aiming at it. My interest level varied quite a bit, but each chapter was so short that I never considered putting it down or skipping ahead.
March 21, 2016
This was my - ahem - bathroom book for the past several weeks. It was perfect bathroom reading: quick, mildly interesting and entirely forgettable. Two-stars for all of the cool math equations I didn't understand.
June 24, 2012
funny to read, no serious math
This entire review has been hidden because of spoilers.
August 21, 2012
Fun book but I would only recommend it to those who like math/physics. Gives you some interesting things to think about.
January 3, 2013
Oriented toward UK sports (the author is British), but very interesting
January 3, 2013
I was kind of expecting things to go more in depth. 100 chapters but about 2-3 pages per chapter. It makes the reading doable if you are not a math guy, but if you are, it left you wanting.
July 18, 2014
Not great, but contains some very interesting elements. The math was way over my head, but the conclusions were sometimes enlightening.
October 20, 2013
This book was stupid.
January 27, 2014
Amazingly executed book! I agree in that it is targeted at those with a strong math/physics background. I thoroughly enjoyed it and found lots of fascinating food-for-thought!
September 6, 2014
Good read however could have been better. Very big difference from easiest stuff to most challenging solutions
September 30, 2020
55th book of 2017 - (3 stars) ~finished december 10th, 2017~
haven't been on goodreads in forever but i have to finish updating books so
haven't been on goodreads in forever but i have to finish updating books so
Displaying 1 - 25 of 25 reviews