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The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life
The bestselling author of Alex's Adventures in Numberland returns with a dazzling new book that turns even the most complex math into a brilliantly entertaining narrative. From triangles, rotations and power laws, to fractals, cones and curves, bestselling author Alex Bellos takes you on a journey of mathematical discovery with his signature wit, engaging stories and limitless enthusiasm. As he narrates a series of eye-opening encounters with lively personalities all over the world, Alex demonstrates how numbers have come to be our friends, are fascinating and extremely accessible, and how they have changed our world.He turns even the dreaded calculus into an easy-to-grasp mathematical exposition, and sifts through over 30,000 survey submissions to reveal the world's favourite number. In Germany, he meets the engineer who designed the first roller-coaster loop, whilst in India he joins the world's highly numerate community at the International Congress of Mathematicians. He explores the wonders behind the Game of Life program, and explains mathematical logic, growth and negative numbers. Stateside, he hangs out with a private detective in Oregon and meets the mathematician who looks for universes from his garage in Illinois.Read this captivating book, and you won't realise that you're learning about complex concepts. Alex will get you hooked on maths as he delves deep into humankind's turbulent relationship with numbers, and proves just how much fun we can have with them.
414 pages, Kindle Edition
First published June 10, 2014
158 people are currently reading
3641 people want to read
About the author
Alex Bellos
69 books379 followers"I was born in Oxford and grew up in Edinburgh and Southampton. After studying mathematics and philosophy at university I joined the Evening Argus in Brighton as a trainee reporter. I joined the Guardian in 1994 as a reporter and in 1998 moved to Rio de Janeiro, where I spent five years as the paper’s South America correspondent. Since 2003 I have lived in London, as a freelance writer and broadcaster.
[...]
In 2003 I presented a five-part series on Brazil for the BBC, called Inside Out Brazil. My short films about the Amazon have been broadcast on the BBC, More 4 and Al Jazeera International."
[...]
In 2003 I presented a five-part series on Brazil for the BBC, called Inside Out Brazil. My short films about the Amazon have been broadcast on the BBC, More 4 and Al Jazeera International."
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Displaying 1 - 30 of 140 reviews
December 16, 2020
It’s Never Too Late For A Happy Childhood
In my youth Ripley’s Believe It or Not was a monthly (or was it weekly?) publication in comic book format. It was fascinating to a child because it ‘documented’ all sorts of strange events, people, and conditions that were apparently unknown to adults - two-headed snakes, ghostly apparitions, unlikely survivals, and past-life memories were standard fare. It was instructive, if in no other sense than to provoke an attempt to verify the most outlandish of its claims. In addition, one could feel somehow superior to one’s ignorant elders who were entirely unaware of the essentially magical character of the world.
The Grapes of Math is a sort of Ripley’s Believe It or Not of mathematics; it appeals to that same childish sense of the strange, the bizarre, and the occult. To discover, for example, that it is Shakespeare who is responsible for the transformation of the word ‘odd’ from denoting uneven numbers to suggesting strangeness of people or situations is just the sort of revelation I mean. Or that digits always appear in a frequency specified by Benford’s law regardless of their sources in daily newspapers, census reports, or stock market data - and no one understands why!
These and dozens of others are factoids which the young adolescent mind finds fascinating. They also constitute an enjoyable introduction to the otherwise abstruse and often rather intimidating topics of number theory, algebraic geometry, and infinitesimal calculus, among many others. I’m not sure that Alex Bellos’s breezy survey will appeal to all those young folk who find maths difficult but it certainly does much to bridge the arts/science divide. And if you’re a bit older, the book might even provide some fodder to fill the odd gaps in cocktail party chat.
In my youth Ripley’s Believe It or Not was a monthly (or was it weekly?) publication in comic book format. It was fascinating to a child because it ‘documented’ all sorts of strange events, people, and conditions that were apparently unknown to adults - two-headed snakes, ghostly apparitions, unlikely survivals, and past-life memories were standard fare. It was instructive, if in no other sense than to provoke an attempt to verify the most outlandish of its claims. In addition, one could feel somehow superior to one’s ignorant elders who were entirely unaware of the essentially magical character of the world.
The Grapes of Math is a sort of Ripley’s Believe It or Not of mathematics; it appeals to that same childish sense of the strange, the bizarre, and the occult. To discover, for example, that it is Shakespeare who is responsible for the transformation of the word ‘odd’ from denoting uneven numbers to suggesting strangeness of people or situations is just the sort of revelation I mean. Or that digits always appear in a frequency specified by Benford’s law regardless of their sources in daily newspapers, census reports, or stock market data - and no one understands why!
These and dozens of others are factoids which the young adolescent mind finds fascinating. They also constitute an enjoyable introduction to the otherwise abstruse and often rather intimidating topics of number theory, algebraic geometry, and infinitesimal calculus, among many others. I’m not sure that Alex Bellos’s breezy survey will appeal to all those young folk who find maths difficult but it certainly does much to bridge the arts/science divide. And if you’re a bit older, the book might even provide some fodder to fill the odd gaps in cocktail party chat.
July 26, 2014
*I received this book thanks to Goodreads First Read program and I am giving it a fair review*
Once in a great while I run into a book that I want to savor like fine chocolate. Usually I am very much so a speed reader and just zoom through a book, The Grapes of Math was an entirely different thing. I found myself pausing frequently after sections lost in thought about the material presenting, absorbing the concepts and ideas. I loved it!
Math and I have a very love/hate relationship, to me it is very much so a beautiful language that I only half understand. It has never come easy to me...blame me being an impatient learner, poor teaching, having an 'abnormal' way of looking at the world and needing things explained differently...whatever...it has been a source of wonder and intense frustration my whole life. As an adult I find myself more and more irked that I did not work harder to master the art of numbers, so of course I was more than thrilled to read this book.
It is exactly the kind of reading material I would suggest to someone who has the same 'learning disability' (not that it really is, it is more a learning hiccup) as me. This book takes at times very advanced concepts and explains them in ways that actually make sense. It uses history, real life, art, and some awesome illustrations to make things like calculus and trigonometry approachable.
True this book is not a textbook, I did not walk away from it knowing how to do calculus, but I did walk away from it knowing how to approach it, how to think mathematically.
I am going to go out on a limb and say this is the best book I have read this year, possibly the best book I have read in years. I am most certainly going to read Here's Looking At Euclid now.
Once in a great while I run into a book that I want to savor like fine chocolate. Usually I am very much so a speed reader and just zoom through a book, The Grapes of Math was an entirely different thing. I found myself pausing frequently after sections lost in thought about the material presenting, absorbing the concepts and ideas. I loved it!
Math and I have a very love/hate relationship, to me it is very much so a beautiful language that I only half understand. It has never come easy to me...blame me being an impatient learner, poor teaching, having an 'abnormal' way of looking at the world and needing things explained differently...whatever...it has been a source of wonder and intense frustration my whole life. As an adult I find myself more and more irked that I did not work harder to master the art of numbers, so of course I was more than thrilled to read this book.
It is exactly the kind of reading material I would suggest to someone who has the same 'learning disability' (not that it really is, it is more a learning hiccup) as me. This book takes at times very advanced concepts and explains them in ways that actually make sense. It uses history, real life, art, and some awesome illustrations to make things like calculus and trigonometry approachable.
True this book is not a textbook, I did not walk away from it knowing how to do calculus, but I did walk away from it knowing how to approach it, how to think mathematically.
I am going to go out on a limb and say this is the best book I have read this year, possibly the best book I have read in years. I am most certainly going to read Here's Looking At Euclid now.
March 5, 2022
Ich hätte nicht gedacht dass ich das Buch so gut finden werde bin ich ehrlich. Eigentlich hätte ich nicht mal gedacht, dass ich es zu ende lese.
- Der Autor war mir sehr sympathisch wegen so einem Kapitel am Anfang
- es ist ne gute mischung aus so fun facts (zb dass es einfach 6 generationen Bernoullis gab, die alle erfolgreiche Mathematiker waren) und Mathe
- hätte glaube nur halb so lange für das Buch gebraucht wenn dieser Teil mit Kegeln nicht da wäre. das waren so 40 seiten vielleicht aber ixh hab locker 2 wochen damit verbracht weil das so langweilig war haha
- manchmal wurden so richtige basics erklärt, also Fakultät oder so und das find ich eigentlich sympathisch dass das buch so accessible sein soll
netter autor, bekommt er direkt n Stern gratis dazu
- Der Autor war mir sehr sympathisch wegen so einem Kapitel am Anfang
- es ist ne gute mischung aus so fun facts (zb dass es einfach 6 generationen Bernoullis gab, die alle erfolgreiche Mathematiker waren) und Mathe
- hätte glaube nur halb so lange für das Buch gebraucht wenn dieser Teil mit Kegeln nicht da wäre. das waren so 40 seiten vielleicht aber ixh hab locker 2 wochen damit verbracht weil das so langweilig war haha
- manchmal wurden so richtige basics erklärt, also Fakultät oder so und das find ich eigentlich sympathisch dass das buch so accessible sein soll
netter autor, bekommt er direkt n Stern gratis dazu
August 10, 2016
A really enjoyable, readable exploration of some higher math that I haven't thought about since the dark days of high school trig and calc. There is a lot of cool stuff for the math curious in here (Benford's Law, Conway's Game of Life, how to fairly divide a cake between three people) presented in a lively manner that I wish I'd seen in my math textbooks. Still, if you never want to see an equation again, this book may not be for you. A notation-heavy dive into calculus about two-thirds of the way through nearly lost me, but Bellos bounces back with a fascinating look at arcane math theory and computing.
December 16, 2020
I never thought I'd choose to read a math book for pleasure but I did. While searching for a puzzle book on the web, the name Alex Bellos came up a lot, so I thought I should explore further. He explains math and his love of numbers with great passion and enthusiasm. Even the Table of Contents is clever, for example:
Chapter One
Every Number Tells a Story
In which the author examines the feelings we have for numbers. He discovers why 11 is more interesting than 10, why 24 is more hygienic than 31, and why 7 is so lucky.
Chapter Two
Love Triangles
In which the author looks at triangles. The shadowy world of Greek geometry leads him down a well, and up the highest mountain in the world.
Each chapter starts out simply and gets more complicated near the end where he lost me but, I learned that:
The number 1 is a male and the number 2 is a female. I love his adorable cartoon that illustrates this! In fact each chapter is introduced with a cute cartoon by The Surreal McCoy.
The number 73 , known to fans of The Big Bank Theory as the "Chuck Norris of numbers," because the main character, Sheldon Cooper, points out that it is the 21st prime number, and its mirror 37 is the 12th. p. 14
The Gateway Arch in Saint Louis, Missouri is a catenary.
It is believed by Allan W. Snyder that all humans have the mental machinery to perform savant-like calculations, but that this machinery cannot normally be accessed because of the way the brain is wired. p. 304
I've put his other books on my TR list.
Chapter One
Every Number Tells a Story
In which the author examines the feelings we have for numbers. He discovers why 11 is more interesting than 10, why 24 is more hygienic than 31, and why 7 is so lucky.
Chapter Two
Love Triangles
In which the author looks at triangles. The shadowy world of Greek geometry leads him down a well, and up the highest mountain in the world.
Each chapter starts out simply and gets more complicated near the end where he lost me but, I learned that:
The number 1 is a male and the number 2 is a female. I love his adorable cartoon that illustrates this! In fact each chapter is introduced with a cute cartoon by The Surreal McCoy.
The number 73 , known to fans of The Big Bank Theory as the "Chuck Norris of numbers," because the main character, Sheldon Cooper, points out that it is the 21st prime number, and its mirror 37 is the 12th. p. 14
The Gateway Arch in Saint Louis, Missouri is a catenary.
It is believed by Allan W. Snyder that all humans have the mental machinery to perform savant-like calculations, but that this machinery cannot normally be accessed because of the way the brain is wired. p. 304
I've put his other books on my TR list.
April 20, 2018
This was a nice book. It's a bit high-level at times... I'm definitely in the upper tail of "people who understand mathematics" and some of this went over my head. But it wasn't a huge hinderance to my own enjoyment of the book, though I will say that if you're math-phobic there are a couple better choices out there than this one.
Most of it was pretty standard. Stuff I've read and thought about before. However, this was honestly my first exposure to the Game of Life. It's the last chapter and I was completely fascinated by it! I don't usually read about math things and wish that I'd been there (hexaflexagons, YES), but this one really got me. I could feel the desire to tinker with something so simple, but so fascinating. Another thing that's great about it is how it stretches your idea of what "math" even is. There aren't any numbers or variables to be found, just tetris-like shapes that morph into different patterns before your eyes. I dunno, I just couldn't stop thinking of Boxes and Chips Challenge and how a game built on a simple square grid can yield so many hours of interest.
The parabola multiplication also caught me off-guard. It's something I may try to work into my future algebra classes, just because it feels so surprising... though there is a proof included in the appendix which was helpful to me for making sense out of it. Maybe I'll give extra credit to any of my students who can generate the proof?
Anyway, solid read, despite the chapter on conic sections (one of my least favorite units in my own math education and which I am loathe to teach to my juniors... so it gets the brunt of my disdain in my curriculum).
Most of it was pretty standard. Stuff I've read and thought about before. However, this was honestly my first exposure to the Game of Life. It's the last chapter and I was completely fascinated by it! I don't usually read about math things and wish that I'd been there (hexaflexagons, YES), but this one really got me. I could feel the desire to tinker with something so simple, but so fascinating. Another thing that's great about it is how it stretches your idea of what "math" even is. There aren't any numbers or variables to be found, just tetris-like shapes that morph into different patterns before your eyes. I dunno, I just couldn't stop thinking of Boxes and Chips Challenge and how a game built on a simple square grid can yield so many hours of interest.
The parabola multiplication also caught me off-guard. It's something I may try to work into my future algebra classes, just because it feels so surprising... though there is a proof included in the appendix which was helpful to me for making sense out of it. Maybe I'll give extra credit to any of my students who can generate the proof?
Anyway, solid read, despite the chapter on conic sections (one of my least favorite units in my own math education and which I am loathe to teach to my juniors... so it gets the brunt of my disdain in my curriculum).
July 25, 2016
Really enjoyed this author's previous book, Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math, which was a lot of fun to read and very accessible to the math-challenged. This book has about the same amount of humor but dives a little deeper into complicated math.
Really enjoyed the sections on triangles, e, and i, the latter including the Mandelbrot set. I believe the author went a little too far into cones, and the chapter topics as a whole feel more scattered than the previous book. Good, but not great.
Really enjoyed the sections on triangles, e, and i, the latter including the Mandelbrot set. I believe the author went a little too far into cones, and the chapter topics as a whole feel more scattered than the previous book. Good, but not great.
August 2, 2014
I read a bunch of these pop math survey books, and this one is somehow better. Great e examples, and playful language. I haven't read his first, Here's Looking at Euclid, but look forward to it as the title is a five-star pun.
February 28, 2015
Not unlike many people, I have not the fondness for math. I also have this unfortunate tendency to explore things I don't like to test my level of discomfort. Thankfully, there's writers like Alex Bellos whose sheer enthusiasm for a topic compels them to create books for the casual reader and engage them in a fun, interesting, and excited manner.
Sure, my eyes go out of focus when reading 2x + 2i = *&%^&** or what have you, but Alex provides not only the numbers but the history of the people and the times where our concepts come from.
The title bears no relation to anything in the book, though, but I think it is a warning about how much he loves bad puns.
Sure, my eyes go out of focus when reading 2x + 2i = *&%^&** or what have you, but Alex provides not only the numbers but the history of the people and the times where our concepts come from.
The title bears no relation to anything in the book, though, but I think it is a warning about how much he loves bad puns.
July 23, 2014
A great Math primer that discusses the role that mathematics plays in western civilization and how we got to where we are. A lot of the topics here are covered in the excellent youtube channel "Numberphile". While those videos are superb, the additional coverage here is a great expansion on the ideas. Not a very formula or computation heavy book, this book deals most with mathematical concepts and how the wonder of math fills our lives.
Highly recommended.
Highly recommended.
Read
July 30, 2016Reasonably easy access to a dozen or so great mathematical concepts: Benford's law of leading digits, conic sections, cycloid, Zipf's law of ranking, Game of life, catenary, the Mandelbrot set, clothoid, cardioid and nephroid, Lissajous' figures, Euler's identity...
We also learn why we studied Venn diagrams but our children don't.
We also learn why we studied Venn diagrams but our children don't.
This entire review has been hidden because of spoilers.
physical_to-read_stack
June 24, 2015I received my copy free from the publisher through Goodreads Firstreads.
July 3, 2014
What a wonderful historical commentary intermixed with delightful anecdotes. I fell in love at the chapter "All About e," and continued to grow more fascinated the more I read.
July 8, 2017
this was so, so much fun. it was challenging, but not so challenging I gave up. I learned so much. I wish I'd been taking notes.
May 10, 2023
You're bound to get idears if you go thinkin' about stuff math
Math is often seen as dry and boring, but Bellos manages to make it fun and entertaining.
The book is filled with interesting stories and fascinating examples that show how math is an integral part of our daily lives.
While not as whimsical as some similar math works - namely Things to Make and Do in the Fourth Dimension, Math with Bad Drawings, Beyond Infinity: An Expedition to the Outer Limits of Mathematics, or Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity - Bellos's writing is still engaging and accessible to both math enthusiasts and novices.
Readers can explore everything from the history of numbers to the intricacies of geometry in a way that is both informative and enjoyable.
Overall, "The Grapes of Math" is a great addition to any math lover's library.
3.7/5
Math is often seen as dry and boring, but Bellos manages to make it fun and entertaining.
The book is filled with interesting stories and fascinating examples that show how math is an integral part of our daily lives.
While not as whimsical as some similar math works - namely Things to Make and Do in the Fourth Dimension, Math with Bad Drawings, Beyond Infinity: An Expedition to the Outer Limits of Mathematics, or Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity - Bellos's writing is still engaging and accessible to both math enthusiasts and novices.
Readers can explore everything from the history of numbers to the intricacies of geometry in a way that is both informative and enjoyable.
Overall, "The Grapes of Math" is a great addition to any math lover's library.
3.7/5
October 19, 2016
Pirms pieciem gadiem pirmoreiz iepazinos ar šī autora daiļradi, viņam ir patiesi labs talants izskaidrot sarežģītas lietas vienkārši. Matemātikas grāmatas vēl nav nolaidušās līdz līmenim, kurā autori mūk no formulām kā velns no krusta. Te vēl mierīgi var sastapties ar kaut ko trigonometrisku vai pat ar nenoteiktu integrāli. Es vairs neatminos, kad šo grāmatu nopirku, tas noteikti nebija dikti sen, bet ne agrāk kā pirms gada.
Ja esi no tiem cilvēkiem, kuri, skolā mācoties, piemēram, trigonometriju vai kombinatoriku, īsti nav sapratuši, kā to visu dzīvē tālāk pielietot, tad šī grāmata ir tieši Tev. Kādos pakšķos šie sinusi un kosinusi ir nolīduši, ka viņus neredz nekur ārpus mācību grāmatām? Skaitļi un matemātiskās formulas mums ir visapkārt un, ja esi praktisks cilvēks, tad pamatskolas kursam pielietojumu atradīsi ātri vien, jo visu tak var izrēķināt. Lai izskaitļotu ēkas vai koka augstumu, nemaz nav jālien viņā augšā ar metramēru. Lai uzbūvētu visstabilāko arku pasaulē, skaitlis e nemaz nav jāzina no galvas, to Tev priekšā var pateikt gravitācija.
Pirmajā nodaļā autors nolēmis pastāstīt par skaitļiem un cilvēku psiholoģiju. Cilvēkiem dikti patīkot pāra skaitļi, taču, ja runa ejot par interesantiem skaitļiem, tad topā paceļas pirmskaitļi. Vispopulārākais skaitlis pasaulē ir 7, bet 110 nevienam neizraisīs nekādu interesi. Un galvenais -ēdienkartē nevajag cenas rindot smuki kolonnā, tas motivē cilvēku izvēlēties vislētāko, nevis pamēģināt ko jaunu.
Otrajā nodaļā var uzzināt visu par Benforda likumu. Tas noder datu analīzē un palīdz nošķirt izdomātus datus no dabiskiem. Dabiskos procesos, grāmatvedību un finanses ieskaitot, skaitļu pirmais cipars pārsvarā ir 1 – 30% un tad pārējie uz leju. Ja gadās kāds datu masīvs, kurā šis likums netiek ievērots, tad ir vērts papētīt sīkāk. Mūsdienās šādi tiek analizēti daudzi finanšu dati, lai saprastu, kurš šmaucas, kurš nē. Tiem, kuri mikroekonomikā visu laiku bija nomodā, noteikti atmiņā nāks Hal Varians, kurš viens no pirmajiem ierosināja šo likumu izmantot analīzēm.
Trešā nodaļa veltīta trijstūriem. Ja tev ciempadome uzticētu uzmērīt dzimto pagastu, ko tu darīsi? Neskriesi jau ar lineālu pa visu pagastu. Izmērīsi viena trijstūra bāzi dikti precīzi, sadalīsi pagastu trijstūros un pēc pārdesmit gadiem paziņosi rezultātu. Īsumā, ja esi skolā aguvis trijstūra pamatformulas, tu vari izmērīt visu uz pasaules, gan standarta, gan pašizdomātās mērvienībās.
Ceturtā nodaļa ir veltīta konusa šķēlumiem – elipsei, parabolai un hiperbolai. No sākuma tiek aplikta sistēma, kuras centrā atrodas Zeme un lēnām ilustrēta pāreja uz heliocentrisko. Pie reizes arī tiek parādīts, kā, ja nav slinkums un ir labs dators, var izdomāt jebkuru debīlu sistēmu, kas vien ienāk prātā, galvenais ir liels korekciju apjoms, un tad arī viss izskatīsies vislabākajā kārtība, lai ar neatbildīs realitātei. Vēl ir daudz par augstceltnēm un komētu orbītām.
Piektā nodaļa ir par skaitli pi, un kādēļ tas nav īsti korekts, jo smukāk būtu divi pi, bet tam vairs nav cerības izsist iesīkstējušo matemātisko notāciju. Daudz cikloīdu un Furjē analīzes pamati iesācējam. Ja hobijs ir domāt par velosipēdu un vilcienu riteņiem, tad dikti aizraujoša lasāmviela.
Sestā nodaļa ir veltīta Eilera skaitlim – e. Tas ir ielīdis praktiski jebkurā vienādojumā, kur runa ir par bezgalībām. Ja redzi kādu dabas fenomenu, tad vari būt drošs – e arī ir tepat blakus un dara savu melno darbu no baku procentu aprēķināšanas līdz superizturīgu arku projektēšanai.
Septītā nodaļa pilnībā mēģina uz pirkstiem izskaidrot imagināros skaitļu, runa ir par mīnus āboliem un ķermeņu rotācijai komplekso skaitļu telpā. Tas viss ir saistīts ar trigonometriju, un beigu beigās sanāk diezgan smuka kopaina. Var jau teikt, ka dabā kvadrātsaknei no mīnus viens nav nekādas jēgas, bet dabai uz to ir uzspļaut, un tā to pielieto riņķī apkārt gan tiešā, gan pārnestā nozīmē.
Astotā nodaļa stāsta par vareno Ņūtona un Lebnica klopi, kuras rezultātā mēģināja noskaidrot diferenciālrēķinu izgudrotāja titulu. Ņūtons izgudroja un noslēpa atvilktnē, Leibnics savukārt publiskoja. Rūgtums abiem palika, bet mums, parastiem cilvēkiem, fizika kļuva daudz aizraujošāka, un matemātikas kurss – pāris reizes garāks. Daudz smuku piemēru par bezgalīgi daudz bezgalīgi mazu lielumu skaitīšanu, atvasināšanu un integrēšanu.
Devītā nodaļa ir veltīta matemātikas teorēmu pierādījumiem. Tā lieta mūsdienās vairs nemaz nav tik vienkārša kā Eiklīda laikos. Ja kāds publicē pierādījumu šauri specializētā matemātikas nozarē uz divsimts lapaspusēm, tad nav nemaz tik daudz cilvēku, kas to spētu pārbaudīt. Savukārt, ja pierādījumu publicē dators uz pārtūkstots lapaspusēm, tad var “žāvēt airus” – tur būs nepieciešams vesels profesora darba mūžs, lai to pārbaudītu.
Desmitā nodaļa ir celluāro automātu pasaule. Pēc būtības tiek aprakstīta vecā labā spēle life. Kurš programmētājs – iesācējs nav ar to niekojies! Taču izrādās šis pasākums vēl nav miris, ir pietiekoši daudz cilvēku, kas ne tikai ar aizrautību skatās rūtiņu miršanā, ir tādi, kas, balstoties uz šīs vienkāršās spēles likumiem, uzbūvējuši pat reālus virtuālos datoru stimulatorus.
Grāmatai lieku 10 no 10 ballēm, autors par katru no tematiem ir izracis kaut ko interesantu, vēl nedzirdētu. Sarežģītās lietas viņš joprojām spēj izskaidrot vienkāršā valodā, un pēc pāris lapaspusēm lasītājs ir ieguvis visu nepieciešamo bagāžu, lai saprastu integrāļus. Ja matemātika un tās vēsture patīk, noteikti iesaku izlasīt. Nez cik daudz no mums bērnībā lasot Alises Piedzīvojumi Brīnumzemē nodaļu Dullais Pēcpusdienas Tējas Laiks saprata, ka te patiesībā slēpjas smalka ironija par tā laika jaunievedumiem imaginārajiem skaitļiem un manipulācijām ar tiem koordinātu telpā?
Ja esi no tiem cilvēkiem, kuri, skolā mācoties, piemēram, trigonometriju vai kombinatoriku, īsti nav sapratuši, kā to visu dzīvē tālāk pielietot, tad šī grāmata ir tieši Tev. Kādos pakšķos šie sinusi un kosinusi ir nolīduši, ka viņus neredz nekur ārpus mācību grāmatām? Skaitļi un matemātiskās formulas mums ir visapkārt un, ja esi praktisks cilvēks, tad pamatskolas kursam pielietojumu atradīsi ātri vien, jo visu tak var izrēķināt. Lai izskaitļotu ēkas vai koka augstumu, nemaz nav jālien viņā augšā ar metramēru. Lai uzbūvētu visstabilāko arku pasaulē, skaitlis e nemaz nav jāzina no galvas, to Tev priekšā var pateikt gravitācija.
Pirmajā nodaļā autors nolēmis pastāstīt par skaitļiem un cilvēku psiholoģiju. Cilvēkiem dikti patīkot pāra skaitļi, taču, ja runa ejot par interesantiem skaitļiem, tad topā paceļas pirmskaitļi. Vispopulārākais skaitlis pasaulē ir 7, bet 110 nevienam neizraisīs nekādu interesi. Un galvenais -ēdienkartē nevajag cenas rindot smuki kolonnā, tas motivē cilvēku izvēlēties vislētāko, nevis pamēģināt ko jaunu.
Otrajā nodaļā var uzzināt visu par Benforda likumu. Tas noder datu analīzē un palīdz nošķirt izdomātus datus no dabiskiem. Dabiskos procesos, grāmatvedību un finanses ieskaitot, skaitļu pirmais cipars pārsvarā ir 1 – 30% un tad pārējie uz leju. Ja gadās kāds datu masīvs, kurā šis likums netiek ievērots, tad ir vērts papētīt sīkāk. Mūsdienās šādi tiek analizēti daudzi finanšu dati, lai saprastu, kurš šmaucas, kurš nē. Tiem, kuri mikroekonomikā visu laiku bija nomodā, noteikti atmiņā nāks Hal Varians, kurš viens no pirmajiem ierosināja šo likumu izmantot analīzēm.
Trešā nodaļa veltīta trijstūriem. Ja tev ciempadome uzticētu uzmērīt dzimto pagastu, ko tu darīsi? Neskriesi jau ar lineālu pa visu pagastu. Izmērīsi viena trijstūra bāzi dikti precīzi, sadalīsi pagastu trijstūros un pēc pārdesmit gadiem paziņosi rezultātu. Īsumā, ja esi skolā aguvis trijstūra pamatformulas, tu vari izmērīt visu uz pasaules, gan standarta, gan pašizdomātās mērvienībās.
Ceturtā nodaļa ir veltīta konusa šķēlumiem – elipsei, parabolai un hiperbolai. No sākuma tiek aplikta sistēma, kuras centrā atrodas Zeme un lēnām ilustrēta pāreja uz heliocentrisko. Pie reizes arī tiek parādīts, kā, ja nav slinkums un ir labs dators, var izdomāt jebkuru debīlu sistēmu, kas vien ienāk prātā, galvenais ir liels korekciju apjoms, un tad arī viss izskatīsies vislabākajā kārtība, lai ar neatbildīs realitātei. Vēl ir daudz par augstceltnēm un komētu orbītām.
Piektā nodaļa ir par skaitli pi, un kādēļ tas nav īsti korekts, jo smukāk būtu divi pi, bet tam vairs nav cerības izsist iesīkstējušo matemātisko notāciju. Daudz cikloīdu un Furjē analīzes pamati iesācējam. Ja hobijs ir domāt par velosipēdu un vilcienu riteņiem, tad dikti aizraujoša lasāmviela.
Sestā nodaļa ir veltīta Eilera skaitlim – e. Tas ir ielīdis praktiski jebkurā vienādojumā, kur runa ir par bezgalībām. Ja redzi kādu dabas fenomenu, tad vari būt drošs – e arī ir tepat blakus un dara savu melno darbu no baku procentu aprēķināšanas līdz superizturīgu arku projektēšanai.
Septītā nodaļa pilnībā mēģina uz pirkstiem izskaidrot imagināros skaitļu, runa ir par mīnus āboliem un ķermeņu rotācijai komplekso skaitļu telpā. Tas viss ir saistīts ar trigonometriju, un beigu beigās sanāk diezgan smuka kopaina. Var jau teikt, ka dabā kvadrātsaknei no mīnus viens nav nekādas jēgas, bet dabai uz to ir uzspļaut, un tā to pielieto riņķī apkārt gan tiešā, gan pārnestā nozīmē.
Astotā nodaļa stāsta par vareno Ņūtona un Lebnica klopi, kuras rezultātā mēģināja noskaidrot diferenciālrēķinu izgudrotāja titulu. Ņūtons izgudroja un noslēpa atvilktnē, Leibnics savukārt publiskoja. Rūgtums abiem palika, bet mums, parastiem cilvēkiem, fizika kļuva daudz aizraujošāka, un matemātikas kurss – pāris reizes garāks. Daudz smuku piemēru par bezgalīgi daudz bezgalīgi mazu lielumu skaitīšanu, atvasināšanu un integrēšanu.
Devītā nodaļa ir veltīta matemātikas teorēmu pierādījumiem. Tā lieta mūsdienās vairs nemaz nav tik vienkārša kā Eiklīda laikos. Ja kāds publicē pierādījumu šauri specializētā matemātikas nozarē uz divsimts lapaspusēm, tad nav nemaz tik daudz cilvēku, kas to spētu pārbaudīt. Savukārt, ja pierādījumu publicē dators uz pārtūkstots lapaspusēm, tad var “žāvēt airus” – tur būs nepieciešams vesels profesora darba mūžs, lai to pārbaudītu.
Desmitā nodaļa ir celluāro automātu pasaule. Pēc būtības tiek aprakstīta vecā labā spēle life. Kurš programmētājs – iesācējs nav ar to niekojies! Taču izrādās šis pasākums vēl nav miris, ir pietiekoši daudz cilvēku, kas ne tikai ar aizrautību skatās rūtiņu miršanā, ir tādi, kas, balstoties uz šīs vienkāršās spēles likumiem, uzbūvējuši pat reālus virtuālos datoru stimulatorus.
Grāmatai lieku 10 no 10 ballēm, autors par katru no tematiem ir izracis kaut ko interesantu, vēl nedzirdētu. Sarežģītās lietas viņš joprojām spēj izskaidrot vienkāršā valodā, un pēc pāris lapaspusēm lasītājs ir ieguvis visu nepieciešamo bagāžu, lai saprastu integrāļus. Ja matemātika un tās vēsture patīk, noteikti iesaku izlasīt. Nez cik daudz no mums bērnībā lasot Alises Piedzīvojumi Brīnumzemē nodaļu Dullais Pēcpusdienas Tējas Laiks saprata, ka te patiesībā slēpjas smalka ironija par tā laika jaunievedumiem imaginārajiem skaitļiem un manipulācijām ar tiem koordinātu telpā?
August 5, 2024
A review of the math vaguely recalled, often with a new, and I’m going to say a more mature understanding.
Then add in the myriad advancements discoveries and applications of math since my school days and package that with adroit explanations, helpful illustrations and a bit of wacky humor, and we have a wonderful book about a subject that I now believe we should revisit now and again. Outstanding! I now have a new GR bookshelf: “Math.”
Then add in the myriad advancements discoveries and applications of math since my school days and package that with adroit explanations, helpful illustrations and a bit of wacky humor, and we have a wonderful book about a subject that I now believe we should revisit now and again. Outstanding! I now have a new GR bookshelf: “Math.”
April 16, 2025
This took me a long time to read mainly because this was my metro book. I pretty much read it when I was on the metro if I felt like reading. Sometimes you just gotta put in headphones and stare out the window.
I learned a lot!! It is crazy how much mathematics is in everyday life, especially nature. I got lost on occasion, but after a couple rereads I could get back into it. I hope to read more from the author and to read more books on mathematics!!
I learned a lot!! It is crazy how much mathematics is in everyday life, especially nature. I got lost on occasion, but after a couple rereads I could get back into it. I hope to read more from the author and to read more books on mathematics!!
July 28, 2025
the best book about mathematics i’ve ever read, so interesting and engaging with lots of photos to illustrate concepts and the author had interviewed so many of the mathematicians he talked about would highly recommend even for non math-centred people because it has such cool concepts that are made easy to understand
December 4, 2022
this was really interesting. my favorite parts were the part about the mandelbrot set & mandelbulb (such a cool fractal) and the last chapter about the Game of Life and the Gemini pattern. the part about how people have tried to model logic gates and computers using the Game of Life reminded me of how in Three-Body Problem, they use people holding flags to model a computer. the concepts are super similar and it's cool to learn about the math context that probably inspired parts of sci-fi I love
November 4, 2024
Definitely more of a history book than a textbook.
This book makes you want to axiomatize your favorite game. Reading complete, time to stare at cellular automata in 4k.
This book makes you want to axiomatize your favorite game. Reading complete, time to stare at cellular automata in 4k.
Want to read
March 16, 2021I haven't read this book yet-- please note the words to-read [sic] above.
If you go to Samantha's comment, do not click on the "....more" because it takes you to an advertisement of some sort
If you go to Samantha's comment, do not click on the "....more" because it takes you to an advertisement of some sort
July 11, 2020
Alex Bellos does it again with The Grapes of Math. Throughout ten chapters Bellos goes through interesting and practical mathematical ideas. For example, people develop emotional attachments to numbers. Perhaps that is not the correct way to phrase it, but people have preferences when they choose random numbers. Cultural differences pop up as well. The floor numbers for buildings is an excellent example. In the United States, the number thirteen is considered unlucky, and due to this fact, the thirteenth floor is often omitted from skyscrapers or tall buildings. If you go to some Asian countries the number four sounds similar to their word for death so they omit the fourth floor. On the opposite end of the spectrum is the number seven in the United States which is considered a ‘lucky’ number. The number eight is lucky in China for a reason similar to that of four being unlucky.
The book explores Benford’s Law to some extent, talking about how it was discovered and why it matters. The idea is that in any random sampling of numbers you will tend to find the numeral one in the leftmost position more often than not. You will find it almost twice as often as you will find the number two. He doesn’t go into the formal proof of this since the reason relies on Ergodic processes and is beyond the scope of the book, but he does provide a good starting point.
Continuing, we find out about trigs, which are posts that were used to make maps back in the olden days. Before the advent of satellites and lasers and other modern surveying equipment, maps were woefully inaccurate. You had people that went out and had to survey the land. I believe George Washington did that for a while back before the French and Indian War, but please correct me if I am wrong. With accurate maps, it was possible to do a lot of things related to areas and land deeds. Trigonometry also made it possible to measure the size of the Earth. The first somewhat accurate measurement was approximated by Eratosthenes who used the information available to him to great effect. Trigonometry brings Trig tables, which confounded me when I was younger. How do you calculate a trig table without a calculator or some other device? I always wanted to know that. I already found out a calculating method to find the square root of a number, so a method of finding a trig ratio would be interesting.
Chapter four discusses Conic Sections; parabolas, ellipses, circles, and hyperbolas. It talks about how to calculate them and how to use them in mechanics. I am quite familiar with the humble parabola being used to describe the motion of a projectile, but going back a few centuries we find that this wasn’t always the case. It took someone with an inquisitive mind like Galileo to come up with an experiment to show that projectiles follow parabolas. Before this, they were merely interesting figures to make. Without Cartesian coordinates and the powers of analytic geometry, it is easy to not know such things. The same idea applies to the ellipse. Before Johannes Kepler was around and came up with the three laws of planetary motion, the ancients assumed that the paths the planets took were circular since the circle is so perfect.
Chapter five brings up oscillations and rotations. The ideas come from things like sine waves that translate themselves into other forms via the Euler Identity. So if you have a wave, any wave at all, you can decompose it into simpler equations. This was first discovered by Fourier and is named after him. It bothered his contemporaries, but it turns out that even square waves can be turned into a series of sinusoidal waves.
Chapter six brings in Euler’s constant. Exponential Growth is on full display in this chapter, showing that there is a limit to how much you can earn through interest. Bellos demonstrates this using the tried and true method of a crazy money lender willing to give you 100% interest. So if you don’t compound it at all, one dollar becomes two dollars at the end of the year. It is quite simple. If you double your money twice in one year, that value is increased to 2.25. This is because you have to halve the rate along with the period to get 0.5 added in the first half and 0.75 added in the second half. As you continue this process of compounding the value more and more often, you reach a limit. This limit is a fundamental constant known as e. It pops up all over the place and is the same kind of number as pi. That is, it is a fundamental constant that is transcendental and irrational. You can’t define it exactly with an equation, but you can come very close.
Chapter seven discusses negative numbers and how their development was hampered by suspicion and superstition. Negative numbers are unusual to the layman. They don’t work the same as positive numbers and the rules used to manipulate them can confuse people. Of course, we find a treasure trove of ideas behind the negative number, but that wasn’t always the case. The same goes for imaginary numbers, the numbers that contain the square root of negative one. So this chapter also explores fractals, mainly the Mandelbrot set. Before the age of computers, this would be written off as nothing more than a little diversion. The calculations to make such a thing are tedious, requiring millions of iterations. Once the 1980s rolled around though, computers were able to do it. It helped that computers were now powerful enough to be of use and ubiquitous enough to not have just a giant mainframe.
Chapter eight introduces us to Calculus, a highly useful tool. It allows us to calculate change. Most people know of Calculus, even if they never took it before. It talks about the development of Calculus as a tool and the various jealousies and arguments that came along with it. The battles over notation for example. It set Great Britain back for 100 years since they stubbornly stuck with Newton’s clumsy notations.
Chapter nine discusses proof. How do you prove that there is an infinite number of primes? You can’t just count all of them, that would take forever. So Euclid or someone devised a method using mathematical induction. He was quite clever in what he did. Now computers are used to aid in proofs, but the first one was not accepted as readily. That was for the four-color theorem back in 1976.
The final chapter mentions Conway’s Game of Life. It was originally played on Go boards, but as computers became more powerful and commonplace it became easier to use computers to plot them out. The Game of Life is really simple, it only follows four rules. However, this simplicity leads to remarkable complexity.
So this book was amazing. I enjoyed reading it and learned a little bit that I did not know before.
The book explores Benford’s Law to some extent, talking about how it was discovered and why it matters. The idea is that in any random sampling of numbers you will tend to find the numeral one in the leftmost position more often than not. You will find it almost twice as often as you will find the number two. He doesn’t go into the formal proof of this since the reason relies on Ergodic processes and is beyond the scope of the book, but he does provide a good starting point.
Continuing, we find out about trigs, which are posts that were used to make maps back in the olden days. Before the advent of satellites and lasers and other modern surveying equipment, maps were woefully inaccurate. You had people that went out and had to survey the land. I believe George Washington did that for a while back before the French and Indian War, but please correct me if I am wrong. With accurate maps, it was possible to do a lot of things related to areas and land deeds. Trigonometry also made it possible to measure the size of the Earth. The first somewhat accurate measurement was approximated by Eratosthenes who used the information available to him to great effect. Trigonometry brings Trig tables, which confounded me when I was younger. How do you calculate a trig table without a calculator or some other device? I always wanted to know that. I already found out a calculating method to find the square root of a number, so a method of finding a trig ratio would be interesting.
Chapter four discusses Conic Sections; parabolas, ellipses, circles, and hyperbolas. It talks about how to calculate them and how to use them in mechanics. I am quite familiar with the humble parabola being used to describe the motion of a projectile, but going back a few centuries we find that this wasn’t always the case. It took someone with an inquisitive mind like Galileo to come up with an experiment to show that projectiles follow parabolas. Before this, they were merely interesting figures to make. Without Cartesian coordinates and the powers of analytic geometry, it is easy to not know such things. The same idea applies to the ellipse. Before Johannes Kepler was around and came up with the three laws of planetary motion, the ancients assumed that the paths the planets took were circular since the circle is so perfect.
Chapter five brings up oscillations and rotations. The ideas come from things like sine waves that translate themselves into other forms via the Euler Identity. So if you have a wave, any wave at all, you can decompose it into simpler equations. This was first discovered by Fourier and is named after him. It bothered his contemporaries, but it turns out that even square waves can be turned into a series of sinusoidal waves.
Chapter six brings in Euler’s constant. Exponential Growth is on full display in this chapter, showing that there is a limit to how much you can earn through interest. Bellos demonstrates this using the tried and true method of a crazy money lender willing to give you 100% interest. So if you don’t compound it at all, one dollar becomes two dollars at the end of the year. It is quite simple. If you double your money twice in one year, that value is increased to 2.25. This is because you have to halve the rate along with the period to get 0.5 added in the first half and 0.75 added in the second half. As you continue this process of compounding the value more and more often, you reach a limit. This limit is a fundamental constant known as e. It pops up all over the place and is the same kind of number as pi. That is, it is a fundamental constant that is transcendental and irrational. You can’t define it exactly with an equation, but you can come very close.
Chapter seven discusses negative numbers and how their development was hampered by suspicion and superstition. Negative numbers are unusual to the layman. They don’t work the same as positive numbers and the rules used to manipulate them can confuse people. Of course, we find a treasure trove of ideas behind the negative number, but that wasn’t always the case. The same goes for imaginary numbers, the numbers that contain the square root of negative one. So this chapter also explores fractals, mainly the Mandelbrot set. Before the age of computers, this would be written off as nothing more than a little diversion. The calculations to make such a thing are tedious, requiring millions of iterations. Once the 1980s rolled around though, computers were able to do it. It helped that computers were now powerful enough to be of use and ubiquitous enough to not have just a giant mainframe.
Chapter eight introduces us to Calculus, a highly useful tool. It allows us to calculate change. Most people know of Calculus, even if they never took it before. It talks about the development of Calculus as a tool and the various jealousies and arguments that came along with it. The battles over notation for example. It set Great Britain back for 100 years since they stubbornly stuck with Newton’s clumsy notations.
Chapter nine discusses proof. How do you prove that there is an infinite number of primes? You can’t just count all of them, that would take forever. So Euclid or someone devised a method using mathematical induction. He was quite clever in what he did. Now computers are used to aid in proofs, but the first one was not accepted as readily. That was for the four-color theorem back in 1976.
The final chapter mentions Conway’s Game of Life. It was originally played on Go boards, but as computers became more powerful and commonplace it became easier to use computers to plot them out. The Game of Life is really simple, it only follows four rules. However, this simplicity leads to remarkable complexity.
So this book was amazing. I enjoyed reading it and learned a little bit that I did not know before.
July 9, 2017
This is a fun book to read for those of us who have some background in math from a long time ago, but don't use it very often. I took a year of high school calculus and a semester of university calculus more than thirty years ago. I work with lots of engineers who are for more intimately acquainted with mathematical concepts. Mr. Bellos explains concepts in mathematics in a historical fashion, but also shows how the concepts were used to solve real world problems and create new applications. Mr. Bellos starts with a fascinating discussion of the psychology of numbers, showing how knowledge of human reaction to certain quantities can be used for marketing, detecting fraud and understanding behavior. He then proceeds to explain how are understanding of triangles, comics and circles grew throughout time and how that growing understanding led to amazing inventions and understanding of our world. He discusses exponential growth, calculus, differential equations, trigonometry and the rise of mathematical models of life and the universe. Along the way, he incorporates interesting biographical details making the book a fun read. Me. Bellos clearly marvels at the coincidences of numbers and the underlying rationality of mathematical systems. His enthusiasm is infectious. Do not skip,the footnote material where Mr. Bellos incorporates a lot of interesting etymology of mathematical terms and other historical facts.
March 7, 2019
I can't get enough of these post-school mathematics books. This one focuses on exactly what the sub-title describes: how we're involved with numbers on a daily basis, how we interact with them, what they mean, how wonderful and elegant all of this is, and how excitingly self-referential the more you explore.
This books goes a bit further than most in exploring the wacky gamesmanship lives of the several personalities who explored numerical phenomena and its manifold depths - and it barely scratched the surface. There's so much more to explore, and to know, and to apply.
I think our school system has this all backwards. Books like *this* should be part of curricula, whetting appetites, and once whetted, a curious ambitious sort could grab a textbook and learn more if he or she wishes, and parlay to discovery and advancement.
Would that it were so.
This books goes a bit further than most in exploring the wacky gamesmanship lives of the several personalities who explored numerical phenomena and its manifold depths - and it barely scratched the surface. There's so much more to explore, and to know, and to apply.
I think our school system has this all backwards. Books like *this* should be part of curricula, whetting appetites, and once whetted, a curious ambitious sort could grab a textbook and learn more if he or she wishes, and parlay to discovery and advancement.
Would that it were so.
November 21, 2017
This title has been tantalizing me since I added it to my To-Read list in May 2014. Having finished it, I now feel a bit like Aesop's Fox ("The Fox and the Grapes"). Here are these beautiful mathematical truths (the "grapes") and I cannot grasp them all. I was familiar with some of them, such as pi, and e, and i (the square root of -1), and Euler's Identity (e^i*pi +1 = 0), but others were totally new or only marginally familiar. Not that the book was BAD, it just seemed to be written for professional mathematicians rather than laypeople.
(What was really discouraging? The fact that, 49 years ago, I graduated from the University of Utah with a BA degree in mathematics. Guess I should have tried to keep up with advances in the field.)
(What was really discouraging? The fact that, 49 years ago, I graduated from the University of Utah with a BA degree in mathematics. Guess I should have tried to keep up with advances in the field.)
June 3, 2018
This is meant to be a fun book about some of the more whimsical parts of mathematics. The problem for me is that it's too trivial. It's enough to look at the chapter on logarithms. Every three paragraphs ends with "isn't this neat!?" like it's a TV show. That doesn't belong in a book. Books are active engagement mediums, I'm already interested, sentences like those interrupt what is being told. It's the equivalent of breaking the fourth wall.
I'm ok with the higher level descriptions and I believe laypeople can pick up the math. I just dislike the presentation and as a result the book.
I'm ok with the higher level descriptions and I believe laypeople can pick up the math. I just dislike the presentation and as a result the book.
March 13, 2020
I never thought I’d say I loved reading about math, but here we are. There are complex ideas in this book, ranging from geometry all the way to derivatives and integrals. With a basic understanding of math through calculus, this is a great book. It’s beautiful and fun and educational and funny all in one. He provides clear concise explanations, with appendices to explain more in depth if math wasn’t to it thing. He provides real life examples and takes you through history from Ancient Greece to computers. It’s amazing and I loved it.
April 21, 2020
A dozen (basically) independent chapters, each on a different math topic. A pretty good description for the layman. Lots of stories about the personalities involved.
I liked how he would start a chapter with a fairly straightforward topic and just sort of let it lead to wherever it led. For example, negative numbers lead to imaginary numbers and eventually to the Mandelbrot set. Trigonometry leads to the measuring of Mount Everest.
I also really liked the chapter on the Game of Life, which one doesn’t often see addressed in these “Math for the Layman” books.
I liked how he would start a chapter with a fairly straightforward topic and just sort of let it lead to wherever it led. For example, negative numbers lead to imaginary numbers and eventually to the Mandelbrot set. Trigonometry leads to the measuring of Mount Everest.
I also really liked the chapter on the Game of Life, which one doesn’t often see addressed in these “Math for the Layman” books.
December 24, 2018
This is s great book if you like anything about science or math. You don’t need to be a savant to understand the concepts. I gave a copy to my sister in law, a math teacher, as I think some of the information might be used as special topics in a high school math class. It may just excite a few young minds to pursue math.
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