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Riddles in Mathematics
Two fathers and two sons leave town. This reduces the population of the town by three. True? Yes, if the trio consists of a father, son, and grandson. This entertaining collection consists of more than 200 such riddles, drawn from every branch of mathematics. Math enthusiasts of all ages will enjoy sharpening their wits with riddles rooted in areas from arithmetic to calculus, covering a wide range of subjects that includes geometry, trigonometry, algebra, concepts of the infinite, probability, and logic. But only an elementary knowledge of mathematics is needed to find amusement in this imaginative collection, which features complete solutions and more than 100 black-and-white illustrations.
"Mr. Northrop writes well and simply. Every so often he will illuminate his discussion with an amusing example. While reading a discussion of topology, the reviewer learned how to remove his vest from beneath his jacket. It works every time." — The New York Times
"Mr. Northrop writes well and simply. Every so often he will illuminate his discussion with an amusing example. While reading a discussion of topology, the reviewer learned how to remove his vest from beneath his jacket. It works every time." — The New York Times
240 pages, Paperback
First published January 1, 1967
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94 people want to read
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Displaying 1 - 6 of 6 reviews
November 2, 2014
~3.5
A man asks an architect to build a square house with square windows, one on each side, so that each window faces south. How can this be?
Three men go to a hotel and take a suite for which the charge is $30. Each gives the bellhop $10, who takes the cash down to the manager. But the manager realizes that the actual cost of the suite is $25, so he sends the bellhop back with five $1. The bellhop realizes this will be hard to split, so he pockets two of the bills and returns $1 to each man. Now each man payed $9, so the total is $27. The bellhop snuck $2 in his pocket, for a total of $29. But the men originally handed over $30. What happened to the other dollar?
Want to know the answers? These and other puzzles come from Eugene P. Northrup’s book, Riddles in Mathematics.
In the introduction, Daniel Silver discusses the book’s originally proposed titles. Northrop wanted "Two and Two Make Five," but the publishers were horrified by the idea of promoting such sacrilege and instead suggested a title that would never have made it through the gutter minds of today: "Tricks with Figures." Eventually, they settled upon Riddles in Mathematics: A Book of Paradoxes.
To Northrop, a paradox is “Anything which offhand appears to be true, but is actually false; or which is simply self-contradictory.” This form of paradox is merely a misunderstanding, a mistake made by someone who is talking too fast and thinking too superficially. To me, a paradox is not simply a mistake in calculation, but something deeper. A perfect example of a “true” mathematical paradox, to my mind, is the probability of choosing any particular value from a distribution over the real numbers, a topic covered briefly by Northrop. If the distribution is real-valued, then the probability of choosing any particular value is 0, but somehow the integral of all these 0’s is 1.* For Northrop, on the other hand, a paradox is merely a fallacy caused by insufficient thought or insight, a student error that becomes obvious in hindsight.
Even so, the “paradoxes” that Northrup points out are certainly omnipresent. For example, one of the mistakes I find most frustrating is the general assumption that events with unknown probability are uniformly distributed. According to Northrup, this type of assumption actually distinguishes two schools of thought: the “cogent reasonists,” who assume that in absence of additional knowledge, two choices are equally likely, and the “insufficient reasonists,” who require some form of evidence before assuming a distribution. I’m definitely one of the latter. For example, say we don’t know whether or not it will rain tomorrow. To me, if you don’t know the probability, you don’t know it-- either do your best to estimate it or just state that you don’t know anything at all. A cogent reasonist would say that in absence of evidence, the chance is 50-50. Northrup goes on to point out the contradictions that can arise from such beliefs.
Riddles In Mathematics is enjoyable enough, although it’s a little hard to characterize. It starts out with word problems and brain teasers, where confusion is cultivated by simple phrasing. It then continues on to simple arithmetic, geometry, and algebraic fallacies. I must admit, Northrop demonstrates an impressive variety of ways in which people can be tripped up by division by zero. Despite the entertaining writing, all of these “paradoxes” will be painfully obvious to anyone with a basic mathematical background. From that point forward, however, things start getting technical, delving deep into complex geometric fallacies, discussions of infinity, problems with probability, lessons in logic, and conundrums in calculus. Personally, I’ve never been fond of geometry and have little interest in topology, but I thoroughly enjoyed the sections dealing with infinity and fun with contradictions in convergence. Northrup also writes an entertaining introduction to the subject of martingales. Considering the book is over half a century old, it has aged quite gracefully. Overall, I’d concur that while it is unlikely that someone will find all of the sections interesting, Riddles in Mathematics does indeed have something for everyone.
~~ I received this ebook from the publisher, Dover Publications, in exchange for my honest review. ~~
Excerpted from my review on BookLikes.
A man asks an architect to build a square house with square windows, one on each side, so that each window faces south. How can this be?
Three men go to a hotel and take a suite for which the charge is $30. Each gives the bellhop $10, who takes the cash down to the manager. But the manager realizes that the actual cost of the suite is $25, so he sends the bellhop back with five $1. The bellhop realizes this will be hard to split, so he pockets two of the bills and returns $1 to each man. Now each man payed $9, so the total is $27. The bellhop snuck $2 in his pocket, for a total of $29. But the men originally handed over $30. What happened to the other dollar?
Want to know the answers? These and other puzzles come from Eugene P. Northrup’s book, Riddles in Mathematics.
In the introduction, Daniel Silver discusses the book’s originally proposed titles. Northrop wanted "Two and Two Make Five," but the publishers were horrified by the idea of promoting such sacrilege and instead suggested a title that would never have made it through the gutter minds of today: "Tricks with Figures." Eventually, they settled upon Riddles in Mathematics: A Book of Paradoxes.
To Northrop, a paradox is “Anything which offhand appears to be true, but is actually false; or which is simply self-contradictory.” This form of paradox is merely a misunderstanding, a mistake made by someone who is talking too fast and thinking too superficially. To me, a paradox is not simply a mistake in calculation, but something deeper. A perfect example of a “true” mathematical paradox, to my mind, is the probability of choosing any particular value from a distribution over the real numbers, a topic covered briefly by Northrop. If the distribution is real-valued, then the probability of choosing any particular value is 0, but somehow the integral of all these 0’s is 1.* For Northrop, on the other hand, a paradox is merely a fallacy caused by insufficient thought or insight, a student error that becomes obvious in hindsight.
Even so, the “paradoxes” that Northrup points out are certainly omnipresent. For example, one of the mistakes I find most frustrating is the general assumption that events with unknown probability are uniformly distributed. According to Northrup, this type of assumption actually distinguishes two schools of thought: the “cogent reasonists,” who assume that in absence of additional knowledge, two choices are equally likely, and the “insufficient reasonists,” who require some form of evidence before assuming a distribution. I’m definitely one of the latter. For example, say we don’t know whether or not it will rain tomorrow. To me, if you don’t know the probability, you don’t know it-- either do your best to estimate it or just state that you don’t know anything at all. A cogent reasonist would say that in absence of evidence, the chance is 50-50. Northrup goes on to point out the contradictions that can arise from such beliefs.
Riddles In Mathematics is enjoyable enough, although it’s a little hard to characterize. It starts out with word problems and brain teasers, where confusion is cultivated by simple phrasing. It then continues on to simple arithmetic, geometry, and algebraic fallacies. I must admit, Northrop demonstrates an impressive variety of ways in which people can be tripped up by division by zero. Despite the entertaining writing, all of these “paradoxes” will be painfully obvious to anyone with a basic mathematical background. From that point forward, however, things start getting technical, delving deep into complex geometric fallacies, discussions of infinity, problems with probability, lessons in logic, and conundrums in calculus. Personally, I’ve never been fond of geometry and have little interest in topology, but I thoroughly enjoyed the sections dealing with infinity and fun with contradictions in convergence. Northrup also writes an entertaining introduction to the subject of martingales. Considering the book is over half a century old, it has aged quite gracefully. Overall, I’d concur that while it is unlikely that someone will find all of the sections interesting, Riddles in Mathematics does indeed have something for everyone.
~~ I received this ebook from the publisher, Dover Publications, in exchange for my honest review. ~~
Excerpted from my review on BookLikes.
January 5, 2022
A man once married his widow's sister.
Explain.
Every page is full of these pearls, and the mathematics behind them.
Explain.
Every page is full of these pearls, and the mathematics behind them.
July 29, 2016
~3.5
A man asks an architect to build a square house with square windows, one on each side, so that each window faces south. How can this be?
Three men go to a hotel and take a suite for which the charge is $30. Each gives the bellhop $10, who takes the cash down to the manager. But the manager realizes that the actual cost of the suite is $25, so he sends the bellhop back with five $1. The bellhop realizes this will be hard to split, so he pockets two of the bills and returns $1 to each man. Now each man payed $9, so the total is $27. The bellhop snuck $2 in his pocket, for a total of $29. But the men originally handed over $30. What happened to the other dollar?
Want to know the answers? These and other puzzles come from Eugene P. Northrup’s book, Riddles in Mathematics.
In the introduction, Daniel Silver discusses the book’s originally proposed titles. Northrop wanted "Two and Two Make Five," but the publishers were horrified by the idea of promoting such sacrilege and instead suggested a title that would never have made it through the gutter minds of today: "Tricks with Figures." Eventually, they settled upon Riddles in Mathematics: A Book of Paradoxes.
To Northrop, a paradox is “Anything which offhand appears to be true, but is actually false; or which is simply self-contradictory.” This form of paradox is merely a misunderstanding, a mistake made by someone who is talking too fast and thinking too superficially. To me, a paradox is not simply a mistake in calculation, but something deeper. A perfect example of a “true” mathematical paradox, to my mind, is the probability of choosing any particular value from a distribution over the real numbers, a topic covered briefly by Northrop. If the distribution is real-valued, then the probability of choosing any particular value is 0, but somehow the integral of all these 0’s is 1.* For Northrop, on the other hand, a paradox is merely a fallacy caused by insufficient thought or insight, a student error that becomes obvious in hindsight.
Even so, the “paradoxes” that Northrup points out are certainly omnipresent. For example, one of the mistakes I find most frustrating is the general assumption that events with unknown probability are uniformly distributed. According to Northrup, this type of assumption actually distinguishes two schools of thought: the “cogent reasonists,” who assume that in absence of additional knowledge, two choices are equally likely, and the “insufficient reasonists,” who require some form of evidence before assuming a distribution. I’m definitely one of the latter. For example, say we don’t know whether or not it will rain tomorrow. To me, if you don’t know the probability, you don’t know it-- either do your best to estimate it or just state that you don’t know anything at all. A cogent reasonist would say that in absence of evidence, the chance is 50-50. Northrup goes on to point out the contradictions that can arise from such beliefs.
Riddles In Mathematics is enjoyable enough, although it’s a little hard to characterize. It starts out with word problems and brain teasers, where confusion is cultivated by simple phrasing. It then continues on to simple arithmetic, geometry, and algebraic fallacies. I must admit, Northrop demonstrates an impressive variety of ways in which people can be tripped up by division by zero. Despite the entertaining writing, all of these “paradoxes” will be painfully obvious to anyone with a basic mathematical background. From that point forward, however, things start getting technical, delving deep into complex geometric fallacies, discussions of infinity, problems with probability, lessons in logic, and conundrums in calculus. Personally, I’ve never been fond of geometry and have little interest in topology, but I thoroughly enjoyed the sections dealing with infinity and fun with contradictions in convergence. Northrup also writes an entertaining introduction to the subject of martingales. Considering the book is over half a century old, it has aged quite gracefully. Overall, I’d concur that while it is unlikely that someone will find all of the sections interesting, Riddles in Mathematics does indeed have something for everyone.
~~ I received this ebook from the publisher, Dover Publications, in exchange for my honest review. ~~
Excerpted from my review on BookLikes.
A man asks an architect to build a square house with square windows, one on each side, so that each window faces south. How can this be?
Three men go to a hotel and take a suite for which the charge is $30. Each gives the bellhop $10, who takes the cash down to the manager. But the manager realizes that the actual cost of the suite is $25, so he sends the bellhop back with five $1. The bellhop realizes this will be hard to split, so he pockets two of the bills and returns $1 to each man. Now each man payed $9, so the total is $27. The bellhop snuck $2 in his pocket, for a total of $29. But the men originally handed over $30. What happened to the other dollar?
Want to know the answers? These and other puzzles come from Eugene P. Northrup’s book, Riddles in Mathematics.
In the introduction, Daniel Silver discusses the book’s originally proposed titles. Northrop wanted "Two and Two Make Five," but the publishers were horrified by the idea of promoting such sacrilege and instead suggested a title that would never have made it through the gutter minds of today: "Tricks with Figures." Eventually, they settled upon Riddles in Mathematics: A Book of Paradoxes.
To Northrop, a paradox is “Anything which offhand appears to be true, but is actually false; or which is simply self-contradictory.” This form of paradox is merely a misunderstanding, a mistake made by someone who is talking too fast and thinking too superficially. To me, a paradox is not simply a mistake in calculation, but something deeper. A perfect example of a “true” mathematical paradox, to my mind, is the probability of choosing any particular value from a distribution over the real numbers, a topic covered briefly by Northrop. If the distribution is real-valued, then the probability of choosing any particular value is 0, but somehow the integral of all these 0’s is 1.* For Northrop, on the other hand, a paradox is merely a fallacy caused by insufficient thought or insight, a student error that becomes obvious in hindsight.
Even so, the “paradoxes” that Northrup points out are certainly omnipresent. For example, one of the mistakes I find most frustrating is the general assumption that events with unknown probability are uniformly distributed. According to Northrup, this type of assumption actually distinguishes two schools of thought: the “cogent reasonists,” who assume that in absence of additional knowledge, two choices are equally likely, and the “insufficient reasonists,” who require some form of evidence before assuming a distribution. I’m definitely one of the latter. For example, say we don’t know whether or not it will rain tomorrow. To me, if you don’t know the probability, you don’t know it-- either do your best to estimate it or just state that you don’t know anything at all. A cogent reasonist would say that in absence of evidence, the chance is 50-50. Northrup goes on to point out the contradictions that can arise from such beliefs.
Riddles In Mathematics is enjoyable enough, although it’s a little hard to characterize. It starts out with word problems and brain teasers, where confusion is cultivated by simple phrasing. It then continues on to simple arithmetic, geometry, and algebraic fallacies. I must admit, Northrop demonstrates an impressive variety of ways in which people can be tripped up by division by zero. Despite the entertaining writing, all of these “paradoxes” will be painfully obvious to anyone with a basic mathematical background. From that point forward, however, things start getting technical, delving deep into complex geometric fallacies, discussions of infinity, problems with probability, lessons in logic, and conundrums in calculus. Personally, I’ve never been fond of geometry and have little interest in topology, but I thoroughly enjoyed the sections dealing with infinity and fun with contradictions in convergence. Northrup also writes an entertaining introduction to the subject of martingales. Considering the book is over half a century old, it has aged quite gracefully. Overall, I’d concur that while it is unlikely that someone will find all of the sections interesting, Riddles in Mathematics does indeed have something for everyone.
~~ I received this ebook from the publisher, Dover Publications, in exchange for my honest review. ~~
Excerpted from my review on BookLikes.
September 14, 2014
Riddles in Mathematics is a wonderful book of riddles and their explanations. If you have ever wondered at certain riddles, and never gotten an explanation, this book is for you. You will be able to amaze your friends with your knowledge once you read this book.
I gave this book 4 stars, only because I did not like the way it was formatted. I expected riddles in the front and answers, or explanations in the back. Unfortunately by the time you start thinking about the answer to the problem, the author is already telling you the answer. I just wish that the whole problem was posed as a question first, and then maybe even in a second paragraph, include the explanation. I felt like I was reading an instructional book, not a book of riddles.
I gave this book 4 stars, only because I did not like the way it was formatted. I expected riddles in the front and answers, or explanations in the back. Unfortunately by the time you start thinking about the answer to the problem, the author is already telling you the answer. I just wish that the whole problem was posed as a question first, and then maybe even in a second paragraph, include the explanation. I felt like I was reading an instructional book, not a book of riddles.
October 20, 2014
Given To Me For An Honest Review
Riddles In Mathematics: A Book of Paradoxes (Dover Recreational Math) by Eugene P. Northrop is a must have for your child's book shelf. This book is full of math jokes and riddles. It provides lots of entertainments for children and adults at home, school and travel. It is great in developing mathematical thinking and knowledge having fun while doing so. I gave this book 5 stars and I highly recommend it to all. I look forward to more from Eugene P. Northrop.
Riddles In Mathematics: A Book of Paradoxes (Dover Recreational Math) by Eugene P. Northrop is a must have for your child's book shelf. This book is full of math jokes and riddles. It provides lots of entertainments for children and adults at home, school and travel. It is great in developing mathematical thinking and knowledge having fun while doing so. I gave this book 5 stars and I highly recommend it to all. I look forward to more from Eugene P. Northrop.
September 7, 2012
Packed with wonderful, unbelievable but always thought provoking ideas this 66 year old book (first published in 1944) is by far the best and most inspiring I've read in this genre. I'm already working on turning the small section on the ancient game of 'hex' into a Java applet.
Displaying 1 - 6 of 6 reviews