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A Million Dots
Double the numbers to go from 1 to 1,000,000 in 40 pages. A stunning visualization of numbers big and small.
We start with a single tree; 1. As we turn the page, we are presented with a sum doubling the number on the page before it: 1+1 = 2; 2+2 = 4; 4+4 = 8. In this way, we reach a million (actually 1,048,576) within 40 pages. Each sum is brought to life with a simple graphic illustration in the distinctive style of Sven Völker. The dots form the back of a ladybird, the bubbles in a cup of soda and the water in a swimming pool. The final page opens up to a magnificent 8 page gatefold to accomodate the final two big numbers. Gloriously simple in its concept and execution, this is a book that will bring mathematics alive to parents as well as children and will also make a stunning gift book.
We start with a single tree; 1. As we turn the page, we are presented with a sum doubling the number on the page before it: 1+1 = 2; 2+2 = 4; 4+4 = 8. In this way, we reach a million (actually 1,048,576) within 40 pages. Each sum is brought to life with a simple graphic illustration in the distinctive style of Sven Völker. The dots form the back of a ladybird, the bubbles in a cup of soda and the water in a swimming pool. The final page opens up to a magnificent 8 page gatefold to accomodate the final two big numbers. Gloriously simple in its concept and execution, this is a book that will bring mathematics alive to parents as well as children and will also make a stunning gift book.
32 pages, Hardcover
First published September 3, 2019
3 people are currently reading
71 people want to read
About the author
Sven Volker
3 books2 followersSven Völker (*1974) is a designer, author and artist based in Berlin, he is professor for graphic design and editor of Some Magazine.
Together with composer and singer Sting, Völker has released his first picture book at NordSüd Publishers. In „There is a little black spot on the sun today”, his bright illustrations transform Sting’s evocative lyrics from The Police's song "King of Pain" into a minimalistic children’s book that explores pain's sadness, beauty and wonder.
His new picture book „A Million Dots" starts with a single tree and by doubling the number on each page reaches (more than) a million within 44 pages. A book about the magic and poetry of math.
. .
Sven Völker is currently teaching typography at the University of Applied Sciences Potsdam. He studied at the University of Art in Bremen and received an MA from Middlesex University in London. In 2004 he was appointed professor at the University of Arts and Design (HfG/ZKM) in Karlsruhe and since 2010 at Burg Giebichenstein University of Art in Halle.
He designed the award winning corporate identity for the japanese Suzuki Motor Corporation. Völker combines graphic symbols, colour, form and typography in a playful, modular way and allows them to evolve in ever new combinations. With his small and unconventional Berlin based studio he also worked for clients such as Volkswagen and BMW.
In his cultural projects he transfers his visual approach into the world of art, books and lately even onto the stage. For the Opera in Halle/Saale, he created the stage design for the novel symphony „The Trumpet of the Swan” by E.B. White. His large scale art installations, consisting of coloured light and printed posters, traveled to exhibitions in Norway, Prague, Basel and Bern in 2012.
Since 2010 he is Editor-in-chief of Some Magazine and frequently publishes books about design and art: „Some Book” at Lars Müller Publishers and „Go Faster”, a book about the graphic design of racing cars at Gestalten Publishers. „Der Welt über die Straße helfen” was written and edited together with german philosopher Peter Sloterdijk in 2010.
Together with composer and singer Sting, Völker has released his first picture book at NordSüd Publishers. In „There is a little black spot on the sun today”, his bright illustrations transform Sting’s evocative lyrics from The Police's song "King of Pain" into a minimalistic children’s book that explores pain's sadness, beauty and wonder.
His new picture book „A Million Dots" starts with a single tree and by doubling the number on each page reaches (more than) a million within 44 pages. A book about the magic and poetry of math.
. .
Sven Völker is currently teaching typography at the University of Applied Sciences Potsdam. He studied at the University of Art in Bremen and received an MA from Middlesex University in London. In 2004 he was appointed professor at the University of Arts and Design (HfG/ZKM) in Karlsruhe and since 2010 at Burg Giebichenstein University of Art in Halle.
He designed the award winning corporate identity for the japanese Suzuki Motor Corporation. Völker combines graphic symbols, colour, form and typography in a playful, modular way and allows them to evolve in ever new combinations. With his small and unconventional Berlin based studio he also worked for clients such as Volkswagen and BMW.
In his cultural projects he transfers his visual approach into the world of art, books and lately even onto the stage. For the Opera in Halle/Saale, he created the stage design for the novel symphony „The Trumpet of the Swan” by E.B. White. His large scale art installations, consisting of coloured light and printed posters, traveled to exhibitions in Norway, Prague, Basel and Bern in 2012.
Since 2010 he is Editor-in-chief of Some Magazine and frequently publishes books about design and art: „Some Book” at Lars Müller Publishers and „Go Faster”, a book about the graphic design of racing cars at Gestalten Publishers. „Der Welt über die Straße helfen” was written and edited together with german philosopher Peter Sloterdijk in 2010.
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Displaying 1 - 23 of 23 reviews
April 4, 2020
Never have I seen exponential numbers so cleverly depicted as in these stylized illustrations. I loved the fold-out pages at the end, which were necessary to show 524,288 and 1,048,576 dots. One dot is a large green circle, representing the top of a tree. 256 is represented by freckles on a face. A train engine with smoke and a couple of train cars are made up of 524,288 miniscule dots. A cityscape of skyscrapers is made up of 1,048,576 even more miniscule dots. Wonderful math book!
August 10, 2022
This is not marketed as a story, so it shouldn’t be punished for not being one.
I have always had a terribly difficult time estimating.
Visualizing vast counted quantities of items is fascinating to me. It is something I would never be able to guess, something I would certainly never take the time to count.
But estimating is a valuable skill. And this is a great tool towards building it: by visualization.
Instead of a random growing pile of dots, each image ingeniously incorporates that many dots.
Brilliant. Not one for our shelves, but one I am thrilled to have in our library.
I have always had a terribly difficult time estimating.
Visualizing vast counted quantities of items is fascinating to me. It is something I would never be able to guess, something I would certainly never take the time to count.
But estimating is a valuable skill. And this is a great tool towards building it: by visualization.
Instead of a random growing pile of dots, each image ingeniously incorporates that many dots.
Brilliant. Not one for our shelves, but one I am thrilled to have in our library.
June 16, 2020
Note: I accessed a digital review copy of this book through Edelweiss.
January 15, 2020
Excellent visualizations of doubling numbers.
August 21, 2020
Brilliant! An informative and fun way to show addition and numbers. Pictures are clear and unencumbered. Numbers are represented both as a number and written out so those reading can say them out loud.
February 5, 2022
I love the powers of two, so I really want to like this book.
In the beginning, I'm a fan of how easy it is to see that the illustration matches the equation.
It begins to get difficult at 32+32=64 as the dots are rather randomly arranged and it's hard to keep track of what's been counted.
64+64=128 is easier to count as the dots are organized in lines, but they don't seem to show the 64+64, just 128 total dots.
128+128=256 is another one that's hard to count because they're freckles on a face and vey random.
It's hard to read 256+256 because it's black text on a black page (the 512 is white text on a black page).
The dots are blue on black and are lines of rain, so easy to count. But, again, they seem to represent the total more than the equation itself.
The back fold-out pages are a bit difficult to navigate.
In general, I think it's better to view as an indicator of the size of a number and how quickly doubling changes something, rather than helping to intuitively represent the equations.
In the beginning, I'm a fan of how easy it is to see that the illustration matches the equation.
It begins to get difficult at 32+32=64 as the dots are rather randomly arranged and it's hard to keep track of what's been counted.
64+64=128 is easier to count as the dots are organized in lines, but they don't seem to show the 64+64, just 128 total dots.
128+128=256 is another one that's hard to count because they're freckles on a face and vey random.
It's hard to read 256+256 because it's black text on a black page (the 512 is white text on a black page).
The dots are blue on black and are lines of rain, so easy to count. But, again, they seem to represent the total more than the equation itself.
The back fold-out pages are a bit difficult to navigate.
In general, I think it's better to view as an indicator of the size of a number and how quickly doubling changes something, rather than helping to intuitively represent the equations.
October 6, 2023
A math concept book of what you get ~~ a million ~~ in 40 pages when you double the number from each previous page, starting with one. Young children will not understand the math much past the first few pages, and older readers may not engage with the simplicity of the concept, but the clean simple lines of each illustrations may interest those trying to "interpret" what the number represents. Some are simple: freckles on a face, bubbles in a cup. But as the numbers progress the illustration becomes more difficult to interpret.
This import from German illustrator Sven Volker shows the universality of numbers: no translation necessary.
This import from German illustrator Sven Volker shows the universality of numbers: no translation necessary.
September 25, 2020
I am six years old and I think anyone 5 or 6 or 7 or 8 would like this book too. I like how this book keeps showing how numbers grow when you double them! It is amazing how many dots appear in the pictures when the numbers get higher. My mom and I wondered if the illustrator had to use a computer to make sooooo many dots in the last pictures. I like when the book pages open up and pull out to show the numbers that go over a million! This helped me think about how big numbers get just by taking 1+1=2 and then 2+2=4 and then 4+4=8 and keep doing that for a long time. This is a great book.
This entire review has been hidden because of spoilers.
January 22, 2020
Beautiful, stylish, graphic visualization of exponential increase. I appreciate the ambiguity of some of the images - how one has to look carefully to see the word peas or notice the reflection of the moon and ship in the water or recognize the mower’s path. A couple of the images eluded me however - 128 and 8,192, so that I wish there was an answer key at the back. I’ll see if reading the book with younger readers provides any answers.
February 12, 2020
I love the concept, and the beginning spreads, but I believe once you get into the larger numbers, it becomes difficult to conceptualize. The book, HOW MUCH IS A MILLION, by David Schwartz, is the book I'd use to share with children to show what higher numbers actually look like and stand for.
August 31, 2020
LOVED IT! I didn't think numbers and math could be somewhat exciting, but this was a small adventure. I was continuously curious to see how the author would represent the exponentially greater numbers of dots. It was an enjoyable journey. My favorite was 4,096.
November 4, 2021
All of my children enjoyed this visual representation of the enormity of big numbers. We say numbers like a million this and a million that all the time but actually seeing a million dots on a page is fascinating.
March 10, 2020
Just Wow!
March 12, 2020
This is a fun book. I can see the attraction for children.
Read
April 20, 2023Good illustration of doubling.
October 31, 2023
Awesome kids book, helping my 3yr old learn to read numbers from 100-1,000,000. And was so excited to see what 1 million looks like!
January 2, 2026
Not bad. Pretty straightforward execution of its concept, and the illustrations were ok. Lots of dots.
December 16, 2019
Stunning illustrations, and remarkable imagination.
fun to a read and contemplate, but I am not sure that it merits placement on one's bookshelf (a great book to borrow from the library, however). a few times through and one captures all that the author/illustrator has to tell the reader.
fun to a read and contemplate, but I am not sure that it merits placement on one's bookshelf (a great book to borrow from the library, however). a few times through and one captures all that the author/illustrator has to tell the reader.
December 5, 2019
This is a really intriguing conceptual book!
March 15, 2022
Shows how fast numbers grow with dots, similarly to part of Anno's Mysterious Multiplying Jar, but this is an exponential function (powers of two) instead of factorials. It also doesn't have as much of a story or ways to count things/see the relationship as easily.
July 26, 2019
I wasn't sure how in the world this author/illustrator would be able to fit one million of anything within the book's pages, but he pulled it off quite well here. Starting with the number one and one green tree or lollipop, he doubles the numbers and objects on each page so two becomes four, which becomes eight, sixteen, thirty-two, and so on. As the numbers increase, the accompanying images become smaller and smaller, and the illustrations become even more interesting. For instance, 256 freckles are sprinkled across a face, and 512 rain drops fall from the sky. As the tension and excitement mount upon reaching the impossible number of 524,288, readers encounter a gatefold that stretches out over several pages, allowing 1,048, 576 miniscule dots to be aligned in a cityscape of large buildings. This visual representation of such a large number is impressive and sure to leave readers wondering while also prompting some to count those dots to make sure they're all there. I must confess that I did not count the dots since my eyes started to glaze over from the effort to do so. This book will fascinate youngsters with even the slightest interest in math.
October 15, 2019
My goodness, what a clever book. A Million Dots is a perfect book to support both literacy and numeracy as well as create a sense of wonder. Doubling a number is the focus, but as the numbers grow the illustrations alongside them are perfectly presented to include the appropriate number of dots. I loved the way the numbers are represented visually through the images, numerically through the numbers and linguistically through the words so that A Million Dots helps make concrete what can be a very abstract concept in learning.
I actually gasped aloud with a smile at the end of the book when I found ‘one million. forty-eight thousand, five hundred and seventy six’ dots over a pull out page.
For such a simple concept, A Million Dots is beautifully and effectively presented and although this is a book for children, I think it would be a lovely gift to any adult interested in numbers too.
I actually gasped aloud with a smile at the end of the book when I found ‘one million. forty-eight thousand, five hundred and seventy six’ dots over a pull out page.
For such a simple concept, A Million Dots is beautifully and effectively presented and although this is a book for children, I think it would be a lovely gift to any adult interested in numbers too.
September 30, 2019
An impressive and engaging merging of art and counting.
Displaying 1 - 23 of 23 reviews