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what makes a gerrymander work is that your party wins a lot of districts by a little and loses a few districts by a lot. The ultimate reason for teaching kids to write a proof is not that the world is full of proofs. It’s that the world is full of non-proofs, and grown-ups need to know the difference. It’s hard to settle for a non-proof once you’ve really familiarized yourself with the genuine article. He’s approaching the problem just the way a mathematician would – starting from the end of the game. That’s no surprise; we are all mathematicians in the deep strategic parts of our brain, whether it says that on our business cards or not. p. 115 Mathematicians have an imperial tendency - we often see other people's problems as consisting of a true mathematical core surrounded by an irritating amount of domain specific information"
You don’t need to be an expert to support your child with maths! Here are four simple but effective ways to help your child develop their understanding of geometry. Imagine a 2D or 3D shape. Can your child guess which shape you are thinking of by asking questions about its properties? Can they draw or make it from modelling dough just from your description? Can they identify shapes by touch alone? Shape is University of Wisconsin math professor and bestselling author Ellenberg’s far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. This hit my sweet spot for popular science books. High school geometry was the last math course I understood and I don't remember much from that. Did you know Einstein played violin on the street for extra cash? Or that Gauss was often only a few steps ahead of his debts? Or that Wordsworth (the poet) and Lincoln (the politician) were excellent mathematicians? Can you even imagine the last president read Euclid for fun!? Oh and my favorite bit -- Karl Pearson, the correlations guy, apparently looked like a Greek God. He also taught his class the law of large numbers by throwing 10,000 pennies on the floor and making students count the heads. I remember the dreary day I was taught that theorem. Yikes. Maybe this is how we should teach math!
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Math professor Ellenberg ( How Not to Be Wrong) shows how challenging mathematics informs real-world problems in this breezy survey . . . Math-minded readers will be rewarded with a greater understanding of the world around them.” —Publishers Weekly Ellenberg likes to focus on the literary history of his mathematical interests, so we get a number of mathematician/poets. (Usually, they are better at mathematics.) And, in general, he explains well the cultural milieu of the times. I'm somewhat surprised that I first learned that Tolstoy was excommunicated in a popular mathematics book. Ellenberg’s commitment to explanation, his exploration of the humanity of mathematics, and the tour de force of the final chapter in defense of a democracy girded by fairness and science are enough to remind you why he is America’s favorite math professor.”— Daily Beast Containing multitudes as he must, Ellenberg’s eyes grow wider and wider, his prose more and more energetic, as he moves from what geometry means to what geometry does in the modern world.” —The Telegraph I thoroughly enjoy Ellenberg's style (and his hand-drawn pictures/diagrams to aid with explanations), which is friendly and not overly formal. But he is also careful to state things in a way that aren't so simplified they are no longer true. There's a difficult balance and I think Ellenberg manages it quite well. I learn a lot from seeing his presentation of an issue, even if I was already somewhat familiar with it.
What really carried this book for me was the author's ability to explain things clearly and enthusiastically, often with diagrams and concrete examples. The book is quite accessible. It starts off with the author talking about how he thinks geometry should be taught. He also mentions that he initially wasn't good at geometry. It's clear that he wants to students to have fun and understand things, not just memorize them. As someone who's essentially going to be his student reading this book, that was nice to hear. The sections on gerrymandering are excellent. I learned a lot, and Ellenberg did a fantastic job explaining why proportional representation wasn't the ideal metric for dividing up districts and why random walks through the space of possible congressional districts can be a powerful tool. People often complain that no one likes facts and numbers and reason and science anymore, but as someone who talks about those things in public, I can tell you that’s not true. People love numbers, and are impressed by them, sometimes more than they should be. An argument dressed up in math carries with it a certain authority. If you’re the one who outfitted it that way, you have a special responsibility to get it right. From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. There are a few chapters dealing with the COVID pandemic (which was unfolding as he wrote it), and epidemiology more generally, as well. All very interesting to read from inside the pandemic, though I wonder if their topic will retain its interest as the pandemic recedes. (Maybe I should say _if_ it ever recedes!)I loved Jordan Ellenberg's earlier book, How Not to Be Wrong: The Power of Mathematical Thinking, and it was a hard act to follow. But not for Ellenberg, as this book is also great. While the title, "Shape" implies that this book is about geometry--and it is--it is also about so much more. This book shows how mathematics is applicable to just about everything under the sun. And Ellenberg manages to make it all so fascinating! The sheer depth at which he covers an incredibly diverse range of topics is staggering. This is the type of book that I love! Ellenberg is a professor of mathematics, so he certainly knows what he is talking about! If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Jordan Ellenberg] is up to the engaging standard of his prior book . . . almost anyone is likely to enjoy Ellenberg’s prose, and mind.” — Harvard Magazine From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything
Spoiler: this book is about math because everything is about math. And this is a former math-hater saying this.
Geometry activities
Ellenberg can ramble; there are a few times I felt the book was turning into a primer on COVID-19 modelling (which isn't bad, but didn't feel like the book I started reading). At times, the emphasis on geometry works (especially when discussing huge multi-dimensional spaces), but sometimes I felt he was pushing too hard to make something geometrical (e.g., the SIR model for epidemics). Overall, the theme is there to give Ellenberg a focus, but it's not carried out strongly. If you’re like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it’s plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That’s not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. understanding through the sorites paradox (at how many grains of wheat do you get a pile), that even if you don't know when something bad starts, you can tell when it's VERY bad. Draw the line there, might be arbitrary but still useful Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” — The New York Times
Serious mathematics at its intriguing, transporting best . . . [a] humorous, anecdotally rich dive into numerous mathematical theories.” —Kirkus Mathematics is a fundamentally imaginative enterprise, which draws on every cognitive and creative ability we have. p. 110 Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word 'geometry', from the Greek for 'measuring the world'. If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. 'Shape' shows us how." How Many Mice Make An Elephant? and other big questions about size and distance’ will be an invaluable addition to any KS1 or KS2 classroom wishing to engage the students with maths and its uses.Mathematics is not my forte. It was a problem for me in school and for a long time, I was convinced that I just wasn't a math person. Of course, when I grew older, a lot older, some really smart mathematicians online tried to convince me that anyone can become good at math. Not excellent or exceptional, but good is possible. As a humanities major, however, I think I approach the whole problem the wrong way because instead of actually trying to do some maths (Who has time for that?), I prefer to read books about it. "Shape" is one such book.
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