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The Five Sides of Marjorie Rice: How to Discover a Shape
Ablaze with pattern and color, this ebullient picture book biography celebrates the intersection of art and science—through the life and lens of an extraordinary amateur mathematician.
When Marjorie Rice was a little girl in Roseburg, Oregon, in the 1930s, she saw patterns everywhere. Swimming in the river, her body was a shape in the water, the water a shape in the hills, the hills a shape in the sky. Some shapes, fitted into a rectangle or floor tilings, were so beautiful they made her long to be an artist. Marjorie dreamed of studying art and geometry, perhaps even solving the age-old “problem of five” (why pentagons don’t fit together the way shapes with three, four, or six sides do). But when college wasn’t possible, she pondered and explored all through secretarial school, marriage, and parenting five children, until one day, while reading her son’s copy of Scientific American, she learned that a subscriber had discovered a pentagon never seen before. If a reader could do it, couldn’t she? Marjorie studied all the known pentagons, drew a little five-sided house, and kept pondering. She’d done it! And she’d go on to discover more pentagonal tilings and whole new classes of tessellations. In this visually wondrous tribute, Anna Bron’s intricate art teems with patterns, including nods to M. C. Escher, and radiates the thrill of one woman’s discovery, playfully inviting readers to approach geometry through art—and art through geometry. Back matter offers more on the story of five and suggestions on how to discover a shape.
When Marjorie Rice was a little girl in Roseburg, Oregon, in the 1930s, she saw patterns everywhere. Swimming in the river, her body was a shape in the water, the water a shape in the hills, the hills a shape in the sky. Some shapes, fitted into a rectangle or floor tilings, were so beautiful they made her long to be an artist. Marjorie dreamed of studying art and geometry, perhaps even solving the age-old “problem of five” (why pentagons don’t fit together the way shapes with three, four, or six sides do). But when college wasn’t possible, she pondered and explored all through secretarial school, marriage, and parenting five children, until one day, while reading her son’s copy of Scientific American, she learned that a subscriber had discovered a pentagon never seen before. If a reader could do it, couldn’t she? Marjorie studied all the known pentagons, drew a little five-sided house, and kept pondering. She’d done it! And she’d go on to discover more pentagonal tilings and whole new classes of tessellations. In this visually wondrous tribute, Anna Bron’s intricate art teems with patterns, including nods to M. C. Escher, and radiates the thrill of one woman’s discovery, playfully inviting readers to approach geometry through art—and art through geometry. Back matter offers more on the story of five and suggestions on how to discover a shape.
48 pages, Hardcover
First published March 4, 2025
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Displaying 1 - 30 of 39 reviews
September 7, 2025
Sometimes non-fiction is done best by children’s books. Like this story.
October 7, 2025
I came across this book in the wrong way, and it's too embarrassing of a way to attempt to explain. A key embarrassing part includes a podcast I'm part of, which is into Season 5 - and which (as a rule) I generally refuse to promote anywhere. Scour my profile and thousand reviews... This is likely the first mention of it - and even this is too much.
But I did come across the book. And I did read it. And I did love it.
It was a great combination of art, and math, and nature, and Feminism. Of overcoming obstacles, and finding the big things in little things.
Curiosity and intention. Design and intelligence.
I assume I read more picture books than the average adult, so I assume I'm more qualified to judge the good from the bad. And I judge this one good. Especially so if you're an adult who loves picture books. It's probably too wordy for a pre-K class. Maybe even for Kindergarten, depending on where you teach.
But it's worth picking up and snagging if you see it. It invites you to think about things you may not have thought about before.
But I did come across the book. And I did read it. And I did love it.
It was a great combination of art, and math, and nature, and Feminism. Of overcoming obstacles, and finding the big things in little things.
Curiosity and intention. Design and intelligence.
I assume I read more picture books than the average adult, so I assume I'm more qualified to judge the good from the bad. And I judge this one good. Especially so if you're an adult who loves picture books. It's probably too wordy for a pre-K class. Maybe even for Kindergarten, depending on where you teach.
But it's worth picking up and snagging if you see it. It invites you to think about things you may not have thought about before.
February 7, 2025
In spite of the fact that she serves on the mathematics faculty at Northwestern University, there is actually no reason why Amy Alznauer would necessarily limit herself to children’s books that contain math in them. Indeed, in the past she’s written books like Flying Paintings: The Zhou Brothers: A Story of Revolution and Art, which was about as far from numbers and equations as you might possibly get. Still, it was her picture book biography, The Boy Who Dreamed of Infinity: A Tale of the Genius Ramanujan that really caught my eye back in 2020. I’ve a keen appreciation for any book for kids that tries to get them to think of math as something fun rather than something to be feared. That book was good, but it cannot hold a candle to the work Alzauer has put into Marjorie Rice’s tale. Folks who don’t deal with math on a regular basis may forget, on occasion, that mathematics isn’t just numbers and equations. It’s also patterns and puzzles, and the clever way that Alznauer lures the reader into this book is by setting the title up like a mystery. Could this woman, Marjorie Rice, crack a tricky mathematical puzzle? And if she could… why would she?
Born in the 1930s, young Marjorie loved patterns. She had no idea of them as mathematical concepts, of course. They were the shapes you found in the wild and, later, the shapes that would become letters. Art and geometry enthralled her, but at her parents' bidding she studied to be a secretary instead. Much later she was living in a home with five children, reading her son’s Scientific American when she learned about something fascinating. There was still a chance for people to discover new shapes. Which is to say, shapes that could interlock perfectly without any gaps between them. Inspired, Marjorie began to experiment. She puzzled and experimented and suddenly she found a shape that had never been discovered before. And after that, even more! A fascinating deep dive into one woman’s inquiring mind into an all new world.
Truly great picture book biographies are never truly just about their subjects, though all too often that’s how they’re presented. Such n’ was born, lived, and died. Now plug in a final sentence about their legacy aaaaaand…. we done. Except that formula is relatively useless when it comes to the truly great bios. Alznauer here isn’t really just writing a bio. She is also writing a history of a mathematical puzzle and mystery. But… nope. Nope. That’s still not enough. It’s neat, but where’s the heart? Where’s the human connection? So just to make sure that everything works perfectly, Alznauer adds a third, dicier element. She traces Marjorie’s own personal relationship to mathematics. From her school days to attempting to follow her son’s math homework to finally discovering the concept of inventing shapes, and engaging with that process fully. You have to be invested in her as a person to fully appreciate what it was that she was doing with shapes. And like a juggler, Alznauer keeps all three of these balls in the air, impressing us all.
Now let us, just for a moment, think about the role of the housewife in children’s literature. What’s the first thing that comes to mind? Old timey picture books, no double. The mom in Blueberries for Sal (canning blueberries like there’s no tomorrow while simultaneously watching over a kid who has a tendency to encounter, I dunno, BEARS!). Or maybe the mom in the Lyle Lyle Crocodile books (who at least got to go antique shopping and skating with him, so it’s not all bad). But we all have that image in our mind, right? The mom with the apron tending the home. A lot of the time she’s not even seen (hat tip to you, Max’s mom in Where the Wild Things Are). The wave of picture books in which moms now had jobs came, but while there are still plenty of stay-at-home moms in the real world, they don’t tend to get books of their own. That’s not terribly surprising when you consider that adults in general don’t tend to star in children’s books unless they’re furry animals (there are exceptions but animal adults definitely pop up more than their human equivalents). And in nonfiction picture books? Forgettaboutit! So to see a stay-at-home mom (something familiar to a bunch of kids out there) with not just an interior life but a goal that she strives for, all kept within the boundaries of the life she made (and reported without judgement) in a book that shows just how doggone brilliant she was… that isn’t just rare. It’s unheard of.
Here is a word of advice when selecting an illustrator for you math and shapes book: Find one that isn’t afraid of the topic. I can’t tell you how many math-related picture books I’ve encountered over the years where the artist’s instincts to choose pretty over accurate has thwarted what could otherwise be an interesting title. Anna Bron’s work on Marjorie Rice isn’t like that at all. First and foremost, her style reminded me quite a bit of Barbara McClintock’s when she worked on Nothing Stopped Sophie: The Story of Unshakable Mathematician Sophie Germain. In both cases, math works its way into the very fabric of its subject’s world. Since Marjorie spent so much of her time at home, it’s fascinating to watch Bron turn her very house into a representative combination of different shapes. The shapes serve a variety of different purposes on these pages, acting as both small confines and representative examples of how Marjorie’s world was expanded, thanks to them. This is no easy matter. Even better, the art in this book keeps the eye constantly moving. There is nothing static about this book. One minute you’re looking down at Marjorie as she sprawls on a rug and the next it’s side views in the kitchen. By the way, someone should give Ms. Bron a chunk of change for her depiction of a 50s/60s household. At one point you get a view of Marjorie’s kitchen and the paintings on the side of the pots on the stove were so blooming familiar, I started to have flashbacks. Impressive only begins to scratch the surface.
A lot of children’s picture book biographies will talk about the women that escaped the strictures of working in the home and just in the home. But if ALL the picture book bios you read talk about that, what do you have in comparison? Alzauer and Bron work together to show how a housewife from the past could still have a rich and full interior life, even going so far as to be the first to make mathematical discoveries. “Even if you haven’t studied art or math, even if you’ve never gone to college, you can make shapes yourself and change how the world looks.” There are plenty of biographies out there about folks who went on to do huge things that changed the course of nations. How much more exciting it is, sometimes, to learn about someone who discovered one truly new thing for the very first time. A little book of discovery couched in both the familiar and unfamiliar at once.
Born in the 1930s, young Marjorie loved patterns. She had no idea of them as mathematical concepts, of course. They were the shapes you found in the wild and, later, the shapes that would become letters. Art and geometry enthralled her, but at her parents' bidding she studied to be a secretary instead. Much later she was living in a home with five children, reading her son’s Scientific American when she learned about something fascinating. There was still a chance for people to discover new shapes. Which is to say, shapes that could interlock perfectly without any gaps between them. Inspired, Marjorie began to experiment. She puzzled and experimented and suddenly she found a shape that had never been discovered before. And after that, even more! A fascinating deep dive into one woman’s inquiring mind into an all new world.
Truly great picture book biographies are never truly just about their subjects, though all too often that’s how they’re presented. Such n’ was born, lived, and died. Now plug in a final sentence about their legacy aaaaaand…. we done. Except that formula is relatively useless when it comes to the truly great bios. Alznauer here isn’t really just writing a bio. She is also writing a history of a mathematical puzzle and mystery. But… nope. Nope. That’s still not enough. It’s neat, but where’s the heart? Where’s the human connection? So just to make sure that everything works perfectly, Alznauer adds a third, dicier element. She traces Marjorie’s own personal relationship to mathematics. From her school days to attempting to follow her son’s math homework to finally discovering the concept of inventing shapes, and engaging with that process fully. You have to be invested in her as a person to fully appreciate what it was that she was doing with shapes. And like a juggler, Alznauer keeps all three of these balls in the air, impressing us all.
Now let us, just for a moment, think about the role of the housewife in children’s literature. What’s the first thing that comes to mind? Old timey picture books, no double. The mom in Blueberries for Sal (canning blueberries like there’s no tomorrow while simultaneously watching over a kid who has a tendency to encounter, I dunno, BEARS!). Or maybe the mom in the Lyle Lyle Crocodile books (who at least got to go antique shopping and skating with him, so it’s not all bad). But we all have that image in our mind, right? The mom with the apron tending the home. A lot of the time she’s not even seen (hat tip to you, Max’s mom in Where the Wild Things Are). The wave of picture books in which moms now had jobs came, but while there are still plenty of stay-at-home moms in the real world, they don’t tend to get books of their own. That’s not terribly surprising when you consider that adults in general don’t tend to star in children’s books unless they’re furry animals (there are exceptions but animal adults definitely pop up more than their human equivalents). And in nonfiction picture books? Forgettaboutit! So to see a stay-at-home mom (something familiar to a bunch of kids out there) with not just an interior life but a goal that she strives for, all kept within the boundaries of the life she made (and reported without judgement) in a book that shows just how doggone brilliant she was… that isn’t just rare. It’s unheard of.
Here is a word of advice when selecting an illustrator for you math and shapes book: Find one that isn’t afraid of the topic. I can’t tell you how many math-related picture books I’ve encountered over the years where the artist’s instincts to choose pretty over accurate has thwarted what could otherwise be an interesting title. Anna Bron’s work on Marjorie Rice isn’t like that at all. First and foremost, her style reminded me quite a bit of Barbara McClintock’s when she worked on Nothing Stopped Sophie: The Story of Unshakable Mathematician Sophie Germain. In both cases, math works its way into the very fabric of its subject’s world. Since Marjorie spent so much of her time at home, it’s fascinating to watch Bron turn her very house into a representative combination of different shapes. The shapes serve a variety of different purposes on these pages, acting as both small confines and representative examples of how Marjorie’s world was expanded, thanks to them. This is no easy matter. Even better, the art in this book keeps the eye constantly moving. There is nothing static about this book. One minute you’re looking down at Marjorie as she sprawls on a rug and the next it’s side views in the kitchen. By the way, someone should give Ms. Bron a chunk of change for her depiction of a 50s/60s household. At one point you get a view of Marjorie’s kitchen and the paintings on the side of the pots on the stove were so blooming familiar, I started to have flashbacks. Impressive only begins to scratch the surface.
A lot of children’s picture book biographies will talk about the women that escaped the strictures of working in the home and just in the home. But if ALL the picture book bios you read talk about that, what do you have in comparison? Alzauer and Bron work together to show how a housewife from the past could still have a rich and full interior life, even going so far as to be the first to make mathematical discoveries. “Even if you haven’t studied art or math, even if you’ve never gone to college, you can make shapes yourself and change how the world looks.” There are plenty of biographies out there about folks who went on to do huge things that changed the course of nations. How much more exciting it is, sometimes, to learn about someone who discovered one truly new thing for the very first time. A little book of discovery couched in both the familiar and unfamiliar at once.
December 10, 2025
This is the story of an amazing woman who set out to find beautiful patterns that fit the mathematical requirements of tessellations.
Tessellation is the covering of a surface, normally a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps, in an endless pattern. It’s also referred to as “tiling the plane.”
Figuring out patterns that can entirely tessellate a plane is a puzzle that appeals to fans of “recreational mathematics.” [If the appeal sounds “puzzling,” think about Sudoku and KenKen games - these are widely popular and are considered a form of recreational math.]
Marjorie Rice (nee Jeuck), born in 1923 and died in 2017, was a San Diego housewife and mother of five with only a high school education. But even as a child, she loved looking for patterns and shapes and thinking about how they fit together.
One of her sons subscribed to “Scientific American,” and when it arrived in the mail she always rushed to read it first. She took particular pleasure in Martin Gardner’s columns called “Mathematical Games." [You can read Gardner's initial 1956 article here on "How to Make Flexagons" which, as the Editor of Scientific American noted: ". . . proved so popular that it served as the inspiration for Martin Gardner’s legendary Scientific American column Mathematical Games."]
In July, 1975, Marjorie was particularly struck by Gardner’s column - "On Tessellating the Plane with Convex Polygon Tiles."
[A convex polygon is one in which all of the inner angles are less than 180°. As a result, the polygon's vertices will all face outward. A pentagon is an example.]
Gardner reviewed the difficulty of making tessellations using pentagons, and included drawings that showed what beautiful art could result when it was successful. He wrote that he thought the list of possible pentagon tilings was complete. But then one of his readers sent in another design that worked, and Gardner published the news in his December 1975 column.
Inspired by the articles, Rice decided to search for additional pentagonal tilings herself. She scribbled her designs on little scraps of paper she hid in her Bible. [Marjorie's husband was deeply religious, and believed if you wanted to study something, it should be the Scriptures. Nevertheless, as her son wrote in her obituary, she read avidly and used her mind 'actively, deeply and regularly.' She was fascinated with the golden ratio and pyramids, and studied them 'with extensive drawings and calculations.'”]
Marjorie eventually discovered an astounding four additional types of pentagon tessellations, using a notational system she invented herself since she had no formal math training.
[Making a pentagon tile the plane is more difficult than it might sound, especially without the help of a computer. The distinctive shape of a pentagon means that once you start fitting shapes together, you create vertices - points where two or more lines meet or intersect. The odds of getting new pentagons of the same shape to fit into the vertices and also fit up against new pentagon sides and angles without leaving any gaps, is extremely low. Only two more possible tessellations with pentagons were discovered after Marjorie found four. The last, or 15th one, found in 2015, took a team of mathematicians using computers. In 2017 Michaël Rao, a French computer scientist and mathematician, proved (also with a computer) that these are the only 15 that can exist.]
Marjorie wrote Gardner after her first discovery and he in turn submitted it to mathematician and tiling pattern expert Doris Schattschneider for verification. Professor Schattschneider not only confirmed the accuracy of that work as well as Marjorie’s subsequent submissions, but she wrote articles and gave lectures about Marjorie, who was too shy to promote her findings herself. She made sure Marjorie got proper recognition, because, as Amy Alznauer wrote, “she hadn’t done all this work to get a better job or money or fame. For decades, Marjorie Rice had pursued the problem of fitting and forever out of love.” Professor Schattschneider emphasized: “The dauntless curiosity and ingenious methods of amateurs make them the true mathematicians.”
Alznauer added that Marjorie’s pentagon patterns are featured on the lobby floor of the Mathematical Association of America in Washington, D.C. and the entrance to the National Museum of Science and Technology in Stockholm, Sweden.
The book concludes with an Author’s Note, a postscript about shapes and tessellations, and a list of sources.
Illustrator Anna Bron did a wonderful job adding movement, detail, and passion into Marjorie’s life story. She also included examples of tessellating pentagons, and showed the ways in which Marjorie turned her tilings into art by filling the pentagons with plants, flowers, and animals.
Evaluation: The recommended age group of 7 and over will be encouraged by the fact that someone with not much education and no higher level training could still rock the world with her discoveries. As Amy Alznauer said in an interview:
"I hope that my book may encourage you (the kid who is reading my book) to take seriously what your mind likes to think about. The things you care about when you’re six or eight or ten, the things that really excite you, are going to matter to you for the rest of your life. So, pay attention to what you are right now. Write about or sketch your interests in a notebook. Ask questions and read books about what fascinates you. Bravely experiment in the direction of what you love!”
Parents and teachers will also be inspired: a busy housewife and mother with five kids, and yet she managed to do so much more!
Tessellation is the covering of a surface, normally a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps, in an endless pattern. It’s also referred to as “tiling the plane.”
Figuring out patterns that can entirely tessellate a plane is a puzzle that appeals to fans of “recreational mathematics.” [If the appeal sounds “puzzling,” think about Sudoku and KenKen games - these are widely popular and are considered a form of recreational math.]
Marjorie Rice (nee Jeuck), born in 1923 and died in 2017, was a San Diego housewife and mother of five with only a high school education. But even as a child, she loved looking for patterns and shapes and thinking about how they fit together.
One of her sons subscribed to “Scientific American,” and when it arrived in the mail she always rushed to read it first. She took particular pleasure in Martin Gardner’s columns called “Mathematical Games." [You can read Gardner's initial 1956 article here on "How to Make Flexagons" which, as the Editor of Scientific American noted: ". . . proved so popular that it served as the inspiration for Martin Gardner’s legendary Scientific American column Mathematical Games."]
In July, 1975, Marjorie was particularly struck by Gardner’s column - "On Tessellating the Plane with Convex Polygon Tiles."
[A convex polygon is one in which all of the inner angles are less than 180°. As a result, the polygon's vertices will all face outward. A pentagon is an example.]
Gardner reviewed the difficulty of making tessellations using pentagons, and included drawings that showed what beautiful art could result when it was successful. He wrote that he thought the list of possible pentagon tilings was complete. But then one of his readers sent in another design that worked, and Gardner published the news in his December 1975 column.
Inspired by the articles, Rice decided to search for additional pentagonal tilings herself. She scribbled her designs on little scraps of paper she hid in her Bible. [Marjorie's husband was deeply religious, and believed if you wanted to study something, it should be the Scriptures. Nevertheless, as her son wrote in her obituary, she read avidly and used her mind 'actively, deeply and regularly.' She was fascinated with the golden ratio and pyramids, and studied them 'with extensive drawings and calculations.'”]
Marjorie eventually discovered an astounding four additional types of pentagon tessellations, using a notational system she invented herself since she had no formal math training.
[Making a pentagon tile the plane is more difficult than it might sound, especially without the help of a computer. The distinctive shape of a pentagon means that once you start fitting shapes together, you create vertices - points where two or more lines meet or intersect. The odds of getting new pentagons of the same shape to fit into the vertices and also fit up against new pentagon sides and angles without leaving any gaps, is extremely low. Only two more possible tessellations with pentagons were discovered after Marjorie found four. The last, or 15th one, found in 2015, took a team of mathematicians using computers. In 2017 Michaël Rao, a French computer scientist and mathematician, proved (also with a computer) that these are the only 15 that can exist.]
Marjorie wrote Gardner after her first discovery and he in turn submitted it to mathematician and tiling pattern expert Doris Schattschneider for verification. Professor Schattschneider not only confirmed the accuracy of that work as well as Marjorie’s subsequent submissions, but she wrote articles and gave lectures about Marjorie, who was too shy to promote her findings herself. She made sure Marjorie got proper recognition, because, as Amy Alznauer wrote, “she hadn’t done all this work to get a better job or money or fame. For decades, Marjorie Rice had pursued the problem of fitting and forever out of love.” Professor Schattschneider emphasized: “The dauntless curiosity and ingenious methods of amateurs make them the true mathematicians.”
Alznauer added that Marjorie’s pentagon patterns are featured on the lobby floor of the Mathematical Association of America in Washington, D.C. and the entrance to the National Museum of Science and Technology in Stockholm, Sweden.
The book concludes with an Author’s Note, a postscript about shapes and tessellations, and a list of sources.
Illustrator Anna Bron did a wonderful job adding movement, detail, and passion into Marjorie’s life story. She also included examples of tessellating pentagons, and showed the ways in which Marjorie turned her tilings into art by filling the pentagons with plants, flowers, and animals.
Evaluation: The recommended age group of 7 and over will be encouraged by the fact that someone with not much education and no higher level training could still rock the world with her discoveries. As Amy Alznauer said in an interview:
"I hope that my book may encourage you (the kid who is reading my book) to take seriously what your mind likes to think about. The things you care about when you’re six or eight or ten, the things that really excite you, are going to matter to you for the rest of your life. So, pay attention to what you are right now. Write about or sketch your interests in a notebook. Ask questions and read books about what fascinates you. Bravely experiment in the direction of what you love!”
Parents and teachers will also be inspired: a busy housewife and mother with five kids, and yet she managed to do so much more!
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March 31, 2025An interesting story about a woman in mathematics; the illustrations are SO GOOD.
However...I'm not fully convinced that the mathematical concept itself was explained as clearly as it needed to be for the intended audience to fully grasp it.
Those illustrations though...complete with nature, Fibonacci spirals, and intentional patterns just hidden in plain sight throughout the book, just waiting to be noticed. Loved that.
However...I'm not fully convinced that the mathematical concept itself was explained as clearly as it needed to be for the intended audience to fully grasp it.
Those illustrations though...complete with nature, Fibonacci spirals, and intentional patterns just hidden in plain sight throughout the book, just waiting to be noticed. Loved that.
March 6, 2025
Copy provided by Young Adult Books Central
Marjorie Rice didn't go to college to study math, and wasn't in any way a professional, yet she solved a geometrical puzzle that baffled people in the field. While squares, triangles, and even hexagons can fit together, it's very difficult to find a five side shape that will create an interlocking pattern. People have studied this for years, and found a few shapes that will work, but Marjorie tried to look for more. Entranced by nature and shapes as a child, this continued as she grew up, and she read all that she could about geometry and shapes. She was entranced by an article in Scientific American detailing a shape that worked, and she decided to try to find others. She found a previously unknown tessellating shape, the tenth that people had figured out. She sent her work to Martin Gardner at the magazine, who consulted Doris Schattschneider. Marjorie found three different shapes that would tesselate, and was honored for her work in tiling pentagons in 1995.
Ordinary people who chas etheir passions with amazing results are always fun to read about, and the pictures of Price's ordinary life, washing clothes and taking care of her home and children, are a gret contrast to the intricate patterns that she helped create. I can't imagine the mathematical acuity necessary to figure out these problems; it's just too bad that Price, born in 1923, didn't have opportunities for more formal education; who knows what aelse she might have figured out.
The tesselations in this book are exquisitie, and there are plenty of different examples, from nature to history. I can't say that I fully understood the importance of finding these new five sided shapes, or the work in volved, but they are very interesting.
Add The Five Sides of Marjorie Rice to a list of picture book biographies about women mathematicians that shapes up to include Reid and Jaleel's Maryam's Magic: The Story of Mathematician Maryam Mirzakhani, Mosca and Rieley's The Girl With A Mind For Math: The Story of Raye Montague, Becker and Rust's Emmy Noether: The Most Important Mathematician You've Never Heard Of, and Bardoe and McClintock's Nothing Stopped Sophie: The Story of Unshakable Mathematician Sophie Germain.
Marjorie Rice didn't go to college to study math, and wasn't in any way a professional, yet she solved a geometrical puzzle that baffled people in the field. While squares, triangles, and even hexagons can fit together, it's very difficult to find a five side shape that will create an interlocking pattern. People have studied this for years, and found a few shapes that will work, but Marjorie tried to look for more. Entranced by nature and shapes as a child, this continued as she grew up, and she read all that she could about geometry and shapes. She was entranced by an article in Scientific American detailing a shape that worked, and she decided to try to find others. She found a previously unknown tessellating shape, the tenth that people had figured out. She sent her work to Martin Gardner at the magazine, who consulted Doris Schattschneider. Marjorie found three different shapes that would tesselate, and was honored for her work in tiling pentagons in 1995.
Ordinary people who chas etheir passions with amazing results are always fun to read about, and the pictures of Price's ordinary life, washing clothes and taking care of her home and children, are a gret contrast to the intricate patterns that she helped create. I can't imagine the mathematical acuity necessary to figure out these problems; it's just too bad that Price, born in 1923, didn't have opportunities for more formal education; who knows what aelse she might have figured out.
The tesselations in this book are exquisitie, and there are plenty of different examples, from nature to history. I can't say that I fully understood the importance of finding these new five sided shapes, or the work in volved, but they are very interesting.
Add The Five Sides of Marjorie Rice to a list of picture book biographies about women mathematicians that shapes up to include Reid and Jaleel's Maryam's Magic: The Story of Mathematician Maryam Mirzakhani, Mosca and Rieley's The Girl With A Mind For Math: The Story of Raye Montague, Becker and Rust's Emmy Noether: The Most Important Mathematician You've Never Heard Of, and Bardoe and McClintock's Nothing Stopped Sophie: The Story of Unshakable Mathematician Sophie Germain.
February 25, 2025
This absorbing picture book biography tells the story of a woman, with no special mathematical training, who solves an ages-old mathematical puzzle. It was so interesting how the author explains the problem of tessellating tiles as being at the intersection of art and geometry, and how it is just the work of fitting shapes together without gaps. Marjorie Rice, with five children and very little free time, amused herself by reading Scientific American magazine. In 1975, there was an article about solving the “problem of pentagons,” and Marjorie set to work trying to solve it. When she sent her work off to the article’s author, he couldn’t understand her work. But when mathematician Professor Doris Schattschneider saw it, she saw “a tessellating shape that no human eyes had ever seen before…”
I love that Price’s discovery is an example of women scientists supporting one another, as opposed to stealing another’s work (as in the case of Rosalind Franklin). Beautiful, detailed digital artwork explains the text and brings Marjorie’s work and world to life. Observant readers will notice a ginger cat following Marjorie on all of her geometric quests, and there are many examples of differently shaped tessellating shapes from history shown in the book’s pages. The text excels at explaining a complicated geometric idea in a way that early grade students and interested adults can understand and be inspired by. Why, if Marjorie Price can do it, why can’t I? Budding young mathematicians can get to work. Extensive back matter, including an author’s note, supporting facts about “The Story of Five,” resources, activities and a bibliography, add much to understanding Marjorie Price’s quest to solve a problem in geometry.
Only thing I would have like is that it would have been nice to see the author lend her considerable talents to defining the golden rectangle for the target audience.
I love that Price’s discovery is an example of women scientists supporting one another, as opposed to stealing another’s work (as in the case of Rosalind Franklin). Beautiful, detailed digital artwork explains the text and brings Marjorie’s work and world to life. Observant readers will notice a ginger cat following Marjorie on all of her geometric quests, and there are many examples of differently shaped tessellating shapes from history shown in the book’s pages. The text excels at explaining a complicated geometric idea in a way that early grade students and interested adults can understand and be inspired by. Why, if Marjorie Price can do it, why can’t I? Budding young mathematicians can get to work. Extensive back matter, including an author’s note, supporting facts about “The Story of Five,” resources, activities and a bibliography, add much to understanding Marjorie Price’s quest to solve a problem in geometry.
Only thing I would have like is that it would have been nice to see the author lend her considerable talents to defining the golden rectangle for the target audience.
June 3, 2025
I was charmed by the cover of “The Five Sides of Marjorie Rice” and, like all good books, it only gets better from there. Author Amy Alznauer manages to weave together the story of an ancient geometry problem and the life of a thoughtful woman who made a mathematical discovery that left me feeling inspired to go pursue my own passion project.
Anna Bron knocked it out of the park with her endearing illustrations that are necessary to understand this story of tessellating shapes. I find myself poring over the gorgeous illustrations on every page.
This would be an amazing book to show anyone who is fascinated by M.C. Escher’s tessallating artworks. For some reason, I imagine fans of The Questioneers series (Ada Twist Scientist, etc.) would appreciate this story of dedication to a project that inspires the reader to be problem solvers themselves.
I think everyone is a little fascinated by tiling shapes, so the book would have wide appeal. I’m a quilter and loved the discussion of repeating patterns while my engineer husband picked up the book and wouldn’t put it down until he had read every page (there are no shortage of picture books in my house yet most have not been opened by him). This one is winner for me.
Anna Bron knocked it out of the park with her endearing illustrations that are necessary to understand this story of tessellating shapes. I find myself poring over the gorgeous illustrations on every page.
This would be an amazing book to show anyone who is fascinated by M.C. Escher’s tessallating artworks. For some reason, I imagine fans of The Questioneers series (Ada Twist Scientist, etc.) would appreciate this story of dedication to a project that inspires the reader to be problem solvers themselves.
I think everyone is a little fascinated by tiling shapes, so the book would have wide appeal. I’m a quilter and loved the discussion of repeating patterns while my engineer husband picked up the book and wouldn’t put it down until he had read every page (there are no shortage of picture books in my house yet most have not been opened by him). This one is winner for me.
September 24, 2025
It's nice to find a read aloud picture book about math and history and a woman, no less! I started with a four star, but upped it to a five star, after I thought about all the connections that could be made, across curriculum. I love when cross-discipline ideas are introduced, as I often as a child felt that math/art/history were separate subjects and I love that they intersect here!
While I'm not sure about the initial engagement with students, I believe maybe 3-5th grade would be appropriate and I can see doing a lesson with tangrams and having students try to come up with a new 5 sided shape, like Marjorie.
I'd need to double-check curriculum (what grade do we learn about polygons?)
I've been wanting to teach a lesson with tangrams and pentominoes, and this would be a great intro book. I would also like to read companion as a chapter book Chasing Vermeer.
This book made me think, taught me something new about a person I did not know, and has beautiful and thought-provoking illustrations.
I'm building lessons in case one day I get to be a librarian and I am going to build one on tangrams and pentominoes and use this book and Chasing Vermeer, to tie in math, art, and logic/puzzle-solving.
While I'm not sure about the initial engagement with students, I believe maybe 3-5th grade would be appropriate and I can see doing a lesson with tangrams and having students try to come up with a new 5 sided shape, like Marjorie.
I'd need to double-check curriculum (what grade do we learn about polygons?)
I've been wanting to teach a lesson with tangrams and pentominoes, and this would be a great intro book. I would also like to read companion as a chapter book Chasing Vermeer.
This book made me think, taught me something new about a person I did not know, and has beautiful and thought-provoking illustrations.
I'm building lessons in case one day I get to be a librarian and I am going to build one on tangrams and pentominoes and use this book and Chasing Vermeer, to tie in math, art, and logic/puzzle-solving.
August 7, 2025
Marjorie Rice grew up loving shapes, enchanted by the golden rectangle. She studied art and geometry, but her parents wanted her to be a secretary. Meanwhile, others were discovering five-sided shapes that could fit together, creating a seamless pattern. They each declared they had found them all. Majorie was raising children, doing art, helping with math, and discovered the question of five-sided shapes in her son’s Scientific American magazine. Marjorie started to work on the problem, despite it being declared as solved. Her first discovery was declared the tenth tiling pentagon, but she wasn’t done yet!
This picture book tells the story of an amateur mathematician who discovered tiling shapes that others couldn’t. These were questions from the beginning of math and design, solved by a mother of five working out of her home. It is an inspiring story of resilience, tenacity and patience. The illustrations in the book invite readers to look at five-sided shapes themselves, seeing them elongate and shrink and they fit together.
It’s a book that makes mathematics something tangible and beautiful. Appropriate for ages 5-9.
This picture book tells the story of an amateur mathematician who discovered tiling shapes that others couldn’t. These were questions from the beginning of math and design, solved by a mother of five working out of her home. It is an inspiring story of resilience, tenacity and patience. The illustrations in the book invite readers to look at five-sided shapes themselves, seeing them elongate and shrink and they fit together.
It’s a book that makes mathematics something tangible and beautiful. Appropriate for ages 5-9.
March 31, 2025
A picture book biography about the amateur mathematician Marjorie Rice and her lifelong interest in shapes and patterns. Marjorie was especially fascinated by five-sided shapes and how they could be combined to create a repeating pattern. With an accessible text and lovely illustrations which include well designed diagrams, this book does a wonderful job showing how Marjorie went about discovering different kind of pentagons and tessellations. A fascinating topic and Marjorie is an inspiring subject, especially since she didn't do this for fame or fortune but for love of the problem! This will be a useful book to include in units introducing geometry or to inspire art projects using geometric patterns.
"If you can fit them together without gaps or overlaps, you hold in your hand one of the most amazing shapes in all the world.
A shape that tiles, or tessellates, can make an endless puzzle all by itself."
"If you can fit them together without gaps or overlaps, you hold in your hand one of the most amazing shapes in all the world.
A shape that tiles, or tessellates, can make an endless puzzle all by itself."
May 22, 2025
Yes for SLQB.
Good illustrations that depict math stuff along with the story.
Marjorie Rice was born in Oregon in the 1930s. She grew up to be an amateur mathematician who discovered many new "tiling" pentagon shapes. About shapes: "How incredible that all stories were made out of just 26 shapes." Golden rectangle "underneath sunflowers and shells and webs." The overlap between math and art = shapes. Marjorie lived in California as a grownup and had five children, but still pursued art and math around her household and family work. I don't know if it's true, but she is depicted as happy (not frustrated or discouraged). Professor Schattschneider determined that Marjorie had discovered "a tessellating shape that no human eyes had even seen before--the tenth tiling pentagon." This was 1975. She was honored in 1995 at a big math meeting. She discovered 4 new tiling pentagon shapes. She was inspired by nature.
Good illustrations that depict math stuff along with the story.
Marjorie Rice was born in Oregon in the 1930s. She grew up to be an amateur mathematician who discovered many new "tiling" pentagon shapes. About shapes: "How incredible that all stories were made out of just 26 shapes." Golden rectangle "underneath sunflowers and shells and webs." The overlap between math and art = shapes. Marjorie lived in California as a grownup and had five children, but still pursued art and math around her household and family work. I don't know if it's true, but she is depicted as happy (not frustrated or discouraged). Professor Schattschneider determined that Marjorie had discovered "a tessellating shape that no human eyes had even seen before--the tenth tiling pentagon." This was 1975. She was honored in 1995 at a big math meeting. She discovered 4 new tiling pentagon shapes. She was inspired by nature.
July 17, 2025
The beautiful illustrations will encourage children to observe, notice, draw, and think about different repeated shapes, patterns, and geometric designs. It will take multiple readings and slow, quiet time to absorb what this amateur mathematician did, and the detailed, careful illustrations are conducive to that time and attention.
I was a little sorry the author rushed through the concise explanation of WHY it is hard to create this sort of special shape, and what makes it special. Taking a little extra time and space to explain exactly how and why it is different from any other shape would have been worth it. Nevertheless, if someone is as enthralled as I was by the illustrations, they will make time to start over and read the initial framing of the mathematical problem again, and it will become clear.
Very nice non-fiction related to math for families to share.
I was a little sorry the author rushed through the concise explanation of WHY it is hard to create this sort of special shape, and what makes it special. Taking a little extra time and space to explain exactly how and why it is different from any other shape would have been worth it. Nevertheless, if someone is as enthralled as I was by the illustrations, they will make time to start over and read the initial framing of the mathematical problem again, and it will become clear.
Very nice non-fiction related to math for families to share.
This entire review has been hidden because of spoilers.
April 19, 2025
Perhaps it’s the quilter in me, but this incredible story ticks all the boxes. It’s about math and art—say no more! Another nonfiction that can do so much! And I love the illustrations. Marjorie Rice discovers unique types of tiling pentagons just for the love of discovery. Not having gone to college, Marjorie takes it upon herself to solve these intriguing puzzles. What a marvel! And what intriguing shapes. It looks like she discovered the tenth, eleventh, twelfth, and thirteenth 5 sided tillable shapes!
September 2, 2025
Creativity and support of it abound in THE FIVE SIDES OF MARJORIE RICE. Phenomenally intricate illustrations by Anna Byron (including her own tesselating patterns) bring life to Amy Alznauer’s text about mathematics and puzzles surrounding tesselating tiles. Marjorie Rice was a true amateur mathematician who decided that she would create new “versatiles” even though it had been decades since any were discovered. Readers learn about the Goldrn Ratio, M.C. Escher, and more while exploring nature with Marjorie.
December 19, 2025
In beginning: but like a puzzle, a story often takes a long time before all the pieces begin to fit.
Marjorie’s story/bio from childhood on alternating pages and history of math and shapes on other pages, especially the puzzle of 5 sided shapes
Loved/studied math & art
discovered a 10th thru 13th pentagon tessellating shape that hadn’t been seen before
Fascinating back matter includes a website for the now 14 types of tessellating, pentagons, long biography or long bibliography and a photo of young and old Marjorie Rice
Housewife and mother not a professional mathematician
Marjorie’s story/bio from childhood on alternating pages and history of math and shapes on other pages, especially the puzzle of 5 sided shapes
Loved/studied math & art
discovered a 10th thru 13th pentagon tessellating shape that hadn’t been seen before
Fascinating back matter includes a website for the now 14 types of tessellating, pentagons, long biography or long bibliography and a photo of young and old Marjorie Rice
Housewife and mother not a professional mathematician
March 20, 2025
This is exactly what I hope for from a juvenile biography: a chance to inspire my kids with the true story of an ordinary person accomplishing the extraordinary via curiosity, determination, and passion. Marjorie Rice's love of art and math is contagious. With excellent text and superlative illustrations, I plan to buy a copy for the elementary classroom at my kids' school because every child should read it!
April 13, 2025
The detail in the illustrations! Showing all the geometry accurately, including or mimicking some of the real characters added to the tilings, natural and architectural detail that inspired or is inspired by geometry...
And the text really celebrates Marjorie Rice, showing her perseverance and creativity and mathematical work across her life.
The endnotes are about the author's process, the story of tiling pentagons, some ways kids can think about tiling, and a bibliography.
And the text really celebrates Marjorie Rice, showing her perseverance and creativity and mathematical work across her life.
The endnotes are about the author's process, the story of tiling pentagons, some ways kids can think about tiling, and a bibliography.
May 15, 2025
A story of how an amateur mathematician discovered versions of pentagons that could tesselate (create an image with equal-sized shapes that have no gaps or overlaps). It's a neat book for older kids and encourages them to seek out patterns for themselves. The images are beautiful and the story is told in an interesting way. I'd recommend it for girls and boys, since Marjorie's gender is not the focus of the book.
May 31, 2025
The Five Sides of Marjorie Rice explores pentagons and their mathematical weirdness through the life of a woman who spent her life working on them--while raising a family! This would be a great resource for teaching about pentagons, of course, but also for tessellations. The illustrations are fantastic and certain to inspire young minds!
I'm going to need Amy Alznauer to keep doing what she's doing, world without end, amen.
I'm going to need Amy Alznauer to keep doing what she's doing, world without end, amen.
July 12, 2025
3 stars (I liked it)
It's always interesting to read a picture book biography of someone I didn't know about previously. I think the illustrations in this book are beautiful. I'm not sure the whole concept of the tessellations, shapes, etc. were explained in this book in a way that children will understand. I'm pretty math minded (both of my parents were math teachers) but I struggled to understand some parts of this book.
Also, the font is too small.
It's always interesting to read a picture book biography of someone I didn't know about previously. I think the illustrations in this book are beautiful. I'm not sure the whole concept of the tessellations, shapes, etc. were explained in this book in a way that children will understand. I'm pretty math minded (both of my parents were math teachers) but I struggled to understand some parts of this book.
Also, the font is too small.
July 20, 2025
Obviously well researched and written, with gorgeous illustrations. But it didn't make a ton of sense to me. And I really did not like the first part that alternated between one typeface/her life on the left page and another typeface/history on the right. Confusing design.
And honestly, in reading the afterword, how can we really PROVE that there are no other ways to make a tessellating 5-side shape?
And honestly, in reading the afterword, how can we really PROVE that there are no other ways to make a tessellating 5-side shape?
March 7, 2025
I love picture book biographies and this one was so good.
Have you ever hear of Marjorie Rice? Because I sure hadn’t.
It tells the story in a way you can relate and it’s so easy to understand, which is crucial when you are reading it with elementary school age kids.
The illustrations are gorgeous too and it makes you want to star creating patterns.
Have you ever hear of Marjorie Rice? Because I sure hadn’t.
It tells the story in a way you can relate and it’s so easy to understand, which is crucial when you are reading it with elementary school age kids.
The illustrations are gorgeous too and it makes you want to star creating patterns.
April 8, 2025
Story of a woman who discovers a shape. I really liked the illustrations in this book and it was interesting/although kinda confusing how she discovered a new shape. I did like the breakdown of the process and the tessellations. Def for older elementary even middle school because the concept is rather complex.
November 14, 2025
Yes and no did I understand this picture book biography and by my guess is there is a limited audience that will have interest in this title about finding pentagons (five sided object) that will make a pattern/ design which are called tessellations.
Marjorie Rice was fascinated from the time she was a child. While never becoming as a mathematician, Marjorie became fascinated with these shapes b in early childhood a discovered several in her adult life.
Marjorie Rice was fascinated from the time she was a child. While never becoming as a mathematician, Marjorie became fascinated with these shapes b in early childhood a discovered several in her adult life.
October 6, 2025
I loved this beautiful book with its great illustrations, its portrayal of anyone doing math even if they aren't a professional or fancy, and its great backmatter including extra resources to continue to do math yourself, more info about tessellating shapes, references, and a couple of real photos.
June 10, 2024
ARC from Edelweiss.
March 7, 2025
What a spectacular biography and much, much more. I was fascinated by the story and captivated by the illustrations. A must have for every library collection!
April 3, 2025
Loved the art and the story of this amateur math fan turned mathematician. Would be great to pair with an activity about tangrams or tesselations.
April 24, 2025
This is a brilliant, delightful, clever picture book biography of Marjorie Rice, who I'd never heard of before and who should absolutely be a household name. What a remarkable woman.
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