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The Magic of Math: Solving for X and Figuring Out Why
The world's greatest mental mathematical magician takes us on a spellbinding journey through the wonders of numbers (and more)
"Arthur Benjamin ... joyfully shows you how to make nature's numbers dance."--Bill Nye (the science guy)
The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike.
"A positively joyful exploration of mathematics."
- Publishers Weekly , starred review
"Each [trick] is more dazzling than the last."
- Physics World
"Arthur Benjamin ... joyfully shows you how to make nature's numbers dance."--Bill Nye (the science guy)
The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike.
"A positively joyful exploration of mathematics."
- Publishers Weekly , starred review
"Each [trick] is more dazzling than the last."
- Physics World
336 pages, Hardcover
First published September 1, 2015
385 people are currently reading
4624 people want to read
About the author
Arthur T. Benjamin
22 books95 followersArthur Benjamin holds a PhD from Johns Hopkins University and is a professor of mathematics at Harvey Mudd College, where he has taught since 1989. He is a noted “mathemagician,” known for being able to perform complicated computations in his head. He is the author, most recently, of The Secrets of Mental Math, and has appeared on The Today Show and The Colbert Report. Benjamin has been profiled in such publications as the New York Times, the Los Angeles Times, USA Today, Scientific American, Discover, and Wired.
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Displaying 1 - 30 of 56 reviews
September 15, 2016
My star rating is 5 raised to the power of 0 or 1 raised to the power of negative 1.
I generally read nonfiction and my typical goals are to be entertained and to learn something. This book delivered neither. The author's enthusiasm was nice at first but it quickly became annoying ("By becoming more familiar with the beautiful patterns that emerge when numbers dance, we have a better chance of finding a beautiful answer to this question.") and overwhelming. Imagine someone teaching you to play Row, Row, Row Your Boat on the piano and then telling you to play the piano pieces to Rhapsody in Blue. That's what it felt like to read this book. Here's a sample from Chapter 1 (The Magic of Numbers):
"By reversing this rule, we get an even simpler rule for division: An m-digit number divided by an n-digit number has m-n or m-n+1 digits.
"For example, a nine-digit number divided by a five-digit number must have four or five digits. The rule for determining which answer to choose is even easier than the multiplication situation. Instead of multiplying or dividing the leading digits, we simply compare them. If the leading digit of the first number (the number being divided) is smaller than the leading digit of the second number, then it's the smaller choice (m-n). If the leading digit of the first number is larger than the leading digit of the second number, then it's the larger choice (m-n+1). If the leading digits are the same, then we look at the second digits and apply the same rule. For instance 314,159,265 divided by 12,358 will have a five-digit answer, but if we instead divide it by 62,381 the answer will have four digits. Dividing 161,803,398 by 14,142 will result in a five-digit answer since 16 is greater than 14."
This book is utterly filled with this tangle of horse shit. (This is actually a relatively simple example but it nicely represents the convoluted verbal gymnastics you have to fight through to get to something that isn't useful or interesting. It gets far worse as you go on.)
The book does have a decent trick or two (which I will never remember) and I did like the author's discussion of leap years and the Julian and Gregorian calendars but for the most part it brought tedium to an art form.
I generally read nonfiction and my typical goals are to be entertained and to learn something. This book delivered neither. The author's enthusiasm was nice at first but it quickly became annoying ("By becoming more familiar with the beautiful patterns that emerge when numbers dance, we have a better chance of finding a beautiful answer to this question.") and overwhelming. Imagine someone teaching you to play Row, Row, Row Your Boat on the piano and then telling you to play the piano pieces to Rhapsody in Blue. That's what it felt like to read this book. Here's a sample from Chapter 1 (The Magic of Numbers):
"By reversing this rule, we get an even simpler rule for division: An m-digit number divided by an n-digit number has m-n or m-n+1 digits.
"For example, a nine-digit number divided by a five-digit number must have four or five digits. The rule for determining which answer to choose is even easier than the multiplication situation. Instead of multiplying or dividing the leading digits, we simply compare them. If the leading digit of the first number (the number being divided) is smaller than the leading digit of the second number, then it's the smaller choice (m-n). If the leading digit of the first number is larger than the leading digit of the second number, then it's the larger choice (m-n+1). If the leading digits are the same, then we look at the second digits and apply the same rule. For instance 314,159,265 divided by 12,358 will have a five-digit answer, but if we instead divide it by 62,381 the answer will have four digits. Dividing 161,803,398 by 14,142 will result in a five-digit answer since 16 is greater than 14."
This book is utterly filled with this tangle of horse shit. (This is actually a relatively simple example but it nicely represents the convoluted verbal gymnastics you have to fight through to get to something that isn't useful or interesting. It gets far worse as you go on.)
The book does have a decent trick or two (which I will never remember) and I did like the author's discussion of leap years and the Julian and Gregorian calendars but for the most part it brought tedium to an art form.
July 24, 2015
To a not-so-talented amateur who is from a “pre-pocket calculator” generation, it is not a given that you may be an expert or lover of mathematics; one can imagine that things have not improved with successive generations, where everything can be answered at the touch of a button.
As long as you know what buttons to press, that is. Yet something like this book can light a fire in your mind. You can temporarily forget that it may be full of confusing, difficult-looking symbols and theory. There will be lot of “cool tricks” that can amuse and amaze; you might not thoroughly understand them but nevertheless you may try.
The author tries to explain the concepts behind the magical capabilities of mathematics, balancing the needs of the maths nerd and the bewildered beginner at the same time. Treat it well and this book could be the book you wished that you had when you were at school. It has the potential to get you loving mathematics and understanding the reason and meaning behind all of the strange symbols, names and formula.
It won’t spoil the book for the reader by mentioning one of the first little tricks: Think of a number between 20 and 100, add the digits together, subtract the total from your original number, add the digits of the answer together and you are left with… 9!
There are plenty more tricks and little wrinkles in this book. The challenge might be memorising them so that you can “show off” to your friends!
It is an enjoyable book, surprisingly so. There’s not much more to add. Check it out and prepare for it to possibly “come home” with you!
The Magic of Math, written by Arthur Benjamin and published by Basic Books. ISBN 9780465054725. YYYYY
http://autamme.com/the-magic-of-math/
As long as you know what buttons to press, that is. Yet something like this book can light a fire in your mind. You can temporarily forget that it may be full of confusing, difficult-looking symbols and theory. There will be lot of “cool tricks” that can amuse and amaze; you might not thoroughly understand them but nevertheless you may try.
The author tries to explain the concepts behind the magical capabilities of mathematics, balancing the needs of the maths nerd and the bewildered beginner at the same time. Treat it well and this book could be the book you wished that you had when you were at school. It has the potential to get you loving mathematics and understanding the reason and meaning behind all of the strange symbols, names and formula.
It won’t spoil the book for the reader by mentioning one of the first little tricks: Think of a number between 20 and 100, add the digits together, subtract the total from your original number, add the digits of the answer together and you are left with… 9!
There are plenty more tricks and little wrinkles in this book. The challenge might be memorising them so that you can “show off” to your friends!
It is an enjoyable book, surprisingly so. There’s not much more to add. Check it out and prepare for it to possibly “come home” with you!
The Magic of Math, written by Arthur Benjamin and published by Basic Books. ISBN 9780465054725. YYYYY
http://autamme.com/the-magic-of-math/
January 2, 2023
The Magic of Math: Solving for x and Figuring out Why, Arthur Benjamin https://www.hmc.edu/mathematics/peopl... , 2015, 321 pages, Dewey 510, ISBN 9780465054725
This, I think, will be terrific for a middle-school kid. Benjamin expresses enthusiasm for, and enjoyment of, math. Conversational tone, a little humor.
How to do arithmetic easily in your head.
Elementary algebra.
Modular arithmetic.
Combinatorics, poker, Pascal's triangle, Sierpinski triangle.
Fibonacci numbers, Lucas numbers, golden ratio.
Proofs: constructive, combinatorial, by induction, by geometry, by algebra. Rational numbers, repeating decimals, irrational numbers, prime numbers, pseudoprimes, perfect numbers, Goldbach's conjecture.
Geometry (Euclidean plane geometry. Contrast hyperbolic geometry of M.C. Escher.) Triangles. Pythagorean theorem.
Pi
Trigonometry, Pythagorean triples, trig functions, finding heights of trees and mountains, law of cosines, law of sines, Hero's formula, trigonometric identities, radians, graphs of trig functions
Imaginary number i, Euler's number e, e^(i theta) notation, polyhedrons, complex arithmetic, compound interest, exponential functions, logarithms
Calculus: optimization, differentiation, derivatives of products of functions, quotients of functions, polynomials, exponentials, trig functions; chain rule; Taylor series
Infinity: infinite series: geometric series, harmonic series. Magic squares.
Read also:
/Proofs that really count: the art of combinatorial proof/, Arthur Benjamin & Jennifer J. Quinn
Biscuits of Number Theory, Arthur Benjamin & Ezra Brown, editors
The Fascinating World of Graph Theory, Arthur Benjamin, Gary Chartrand, and Ping Zhang
books by Martin Gardner
books by Alex Bellos
books by Ivars Peterson
books by Ian Stewart
/The Joy of X: A Guided Tour of Math, from One to Infinity/, Steven Strogatz
/The Art of Problem Solving/ series by Richard Rusczyk
ArtOfProblemSolving.com
www.math.hmc.edu/funfacts
Cut-The-Knot.org
Numberphile.com
The sum of the first n integers:
Sum[i, {i, 1, n}] = n (n + 1)/2 https://www.wolframalpha.com/input?i=... p. 7
The sum of the cubes of the first n integers is the square of the sum of the first n integers:
Sum[i^3, {i, 1, n}] = (Sum[i, {i, 1, n}])^2 = (1/4)(n^2)(n + 1)^2
https://www.wolframalpha.com/input?i=... p. 12
How to find the day of the week for any date. pp. 65-70.
Sum[i i!, {i, 1, n}] = (n + 1)! - 1
https://www.wolframalpha.com/input?i=... p. 73.
Sierpinski triangle: a fractal pattern of the odd (black) and even (white) numbers in Pascal's triangle: https://www.wolframalpha.com/input?i=... pp. 92-94. The larger the triangle, the more nearly white it is.
Wilson's theorem: n is a prime number if and only if (n - 1)! + 1 is a multiple of n. p. 144.
If p is an odd prime number, then 2^( p - 1) - 1 is a multiple of p . (Fermat. p. 145) A number that has this property, but is not prime, is called a pseudoprime.
Goldbach's conjecture: Every even number greater than 2 is the sum of two primes. https://www.wolframalpha.com/input?i=... p. 147.
Connecting the midpoints of any quadrilateral always produces a parallelogram. p. 150.
There are over 300 proofs of the Pythagorean Theorem. p. 174. Benjamin gives us five of them.
Three points on a circle, two of them forming the diameter, are a right triangle. Proof p. 185.
Central angle theorem: For any two points X and Y on a circle centered at O, the angle XPY at /any/ point P on the major (larger) arc of the circle, from X around to Y, will be half of the angle XOY. The angle XQY at any point Q on the minor arc of the circle, from X to Y, will be 180 degrees minus the angle XPY. p. 186.
Area of circle of radius r = pi r^2. Proofs pp. 187-188.
Ellipse, semimajor and semiminor axes a and b:
(x/a)^2 + (y/b)^2 = 1
p. 189.
Drawing an ellipse: p. 190.
Approximate formula for the circumference of an ellipse, semimajor and semiminor axes a and b:
pi( 3a + 3b - sqrt( (3a + b)(3b + a) ) )
Notice that if a = b = r, it's a circle, circumference 2 pi r.
Srinivasa Ramanujan (1887-1920). p. 191.
Volume of sphere = (4/3) pi r^3
Area of sphere = 4 pi r^2
Cone of height h, on a circle of radius r, slant height s (s^2 = r^2 + h^2):
Volume of cone = pi r^2 h/3
Area of cone = pi r s
p. 192.
Volume of a pizza, radius z, thickness a, V = pi z z a
p. 193.
Pi also appears in surprising places:
Stirling's approximation to n! ≅ ( (n/e)^n ) * Sqrt(2 pi n) p. 193.
This is better than Log(n!) ≅ ( n Log[n] - n ) for small n.
Plots: https://www.wolframalpha.com/input?i=...
Theory: https://mathworld.wolfram.com/Stirlin...
The sum of the 1/n^2, for all n from 1 to infinity is pi^2/6:
https://www.wolframalpha.com/input?i=...
pi ≅ 355/113
p. 197.
Pythagorean triples:
For a right triangle, short sides a and b, hypotenuse c:
Where a, b, c are whole numbers, they're called a "Pythagorean triple."
For any two positive integers (m, n), m > n, the numbers
a = m^2 - n^2
b = 2mn
c = m^2 + n^2
are a Pythagorean triple. Notice that a^2 + b^2 = c^2. p. 205.
Every Pythagorean triple can be created by some choice of (m, n). p. 205.
Law of cosines: for any triangle, sides a, b, c, angle C opposite side c:
c^2 = a^2 + b^2 - 2 a b cos C
proof p. 216.
Area of any triangle, sides of lengths a, b form angle C:
area = (1/2) a b sin C
proof p. 217.
Law of sines: for any triangle, sides a, b, c, opposite angles A, B, C:
(sin A)/a = (sin B)/b = (sin C)/c
proof pp. 217-218.
Hero's formula: for any triangle, sides a, b, c, semiperimeter s = (a + b + c)/2,
area of triangle = Sqrt[ s(s - a)(s - b)(s - c) ]
p. 219.
Trigonometric identities
sin^2 x + cos^2 x = 1
many others p. 225.
For any polyhedron with a number F of flat faces, a number E of straight-line edges, and a number V of vertices,
F + V = 2 + E
p. 232
Multiplying complex numbers:
The magnitude (length) of the product is the product of the magnitudes.
The argument (angle) of the product is the sum of the arguments.
Dividing complex numbers, divide the lengths and subtract the angles. p. 240.
The limit, as n goes to infinity, of (1 + 1/n)^n, is e. p. 241.
https://www.wolframalpha.com/input?i=...
log(x y) = log x + log y
log( x^n ) = n log x
log_b(x) = log x / log b is the base-b log of x.
Bell curve
y = ( 1/sqrt(2 pi) ) e^-(x^2/2)
The infinite sum,
Sum[x^n/n!, {n, 0, Infinity}] = e^x p. 246.
https://www.wolframalpha.com/input?i=...
e^(i theta) = cos theta + i sin theta
e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + …
cos x = 1 - x^2/2! + x^4/4! - x^6/6! + …
sin x = x - x^3/3! + x^5/5! - x^7/7! + …
p. 251
For y = x^n, y' = n x^(n - 1)
p. 263
Proof that e^x is its own derivative, p. 265.
Conditionally convergent series, p. 301.
Magic squares, pp. 302-305.
This, I think, will be terrific for a middle-school kid. Benjamin expresses enthusiasm for, and enjoyment of, math. Conversational tone, a little humor.
How to do arithmetic easily in your head.
Elementary algebra.
Modular arithmetic.
Combinatorics, poker, Pascal's triangle, Sierpinski triangle.
Fibonacci numbers, Lucas numbers, golden ratio.
Proofs: constructive, combinatorial, by induction, by geometry, by algebra. Rational numbers, repeating decimals, irrational numbers, prime numbers, pseudoprimes, perfect numbers, Goldbach's conjecture.
Geometry (Euclidean plane geometry. Contrast hyperbolic geometry of M.C. Escher.) Triangles. Pythagorean theorem.
Pi
Trigonometry, Pythagorean triples, trig functions, finding heights of trees and mountains, law of cosines, law of sines, Hero's formula, trigonometric identities, radians, graphs of trig functions
Imaginary number i, Euler's number e, e^(i theta) notation, polyhedrons, complex arithmetic, compound interest, exponential functions, logarithms
Calculus: optimization, differentiation, derivatives of products of functions, quotients of functions, polynomials, exponentials, trig functions; chain rule; Taylor series
Infinity: infinite series: geometric series, harmonic series. Magic squares.
Read also:
/Proofs that really count: the art of combinatorial proof/, Arthur Benjamin & Jennifer J. Quinn
Biscuits of Number Theory, Arthur Benjamin & Ezra Brown, editors
The Fascinating World of Graph Theory, Arthur Benjamin, Gary Chartrand, and Ping Zhang
books by Martin Gardner
books by Alex Bellos
books by Ivars Peterson
books by Ian Stewart
/The Joy of X: A Guided Tour of Math, from One to Infinity/, Steven Strogatz
/The Art of Problem Solving/ series by Richard Rusczyk
ArtOfProblemSolving.com
www.math.hmc.edu/funfacts
Cut-The-Knot.org
Numberphile.com
The sum of the first n integers:
Sum[i, {i, 1, n}] = n (n + 1)/2 https://www.wolframalpha.com/input?i=... p. 7
The sum of the cubes of the first n integers is the square of the sum of the first n integers:
Sum[i^3, {i, 1, n}] = (Sum[i, {i, 1, n}])^2 = (1/4)(n^2)(n + 1)^2
https://www.wolframalpha.com/input?i=... p. 12
How to find the day of the week for any date. pp. 65-70.
Sum[i i!, {i, 1, n}] = (n + 1)! - 1
https://www.wolframalpha.com/input?i=... p. 73.
Sierpinski triangle: a fractal pattern of the odd (black) and even (white) numbers in Pascal's triangle: https://www.wolframalpha.com/input?i=... pp. 92-94. The larger the triangle, the more nearly white it is.
Wilson's theorem: n is a prime number if and only if (n - 1)! + 1 is a multiple of n. p. 144.
If p is an odd prime number, then 2^( p - 1) - 1 is a multiple of p . (Fermat. p. 145) A number that has this property, but is not prime, is called a pseudoprime.
Goldbach's conjecture: Every even number greater than 2 is the sum of two primes. https://www.wolframalpha.com/input?i=... p. 147.
Connecting the midpoints of any quadrilateral always produces a parallelogram. p. 150.
There are over 300 proofs of the Pythagorean Theorem. p. 174. Benjamin gives us five of them.
Three points on a circle, two of them forming the diameter, are a right triangle. Proof p. 185.
Central angle theorem: For any two points X and Y on a circle centered at O, the angle XPY at /any/ point P on the major (larger) arc of the circle, from X around to Y, will be half of the angle XOY. The angle XQY at any point Q on the minor arc of the circle, from X to Y, will be 180 degrees minus the angle XPY. p. 186.
Area of circle of radius r = pi r^2. Proofs pp. 187-188.
Ellipse, semimajor and semiminor axes a and b:
(x/a)^2 + (y/b)^2 = 1
p. 189.
Drawing an ellipse: p. 190.
Approximate formula for the circumference of an ellipse, semimajor and semiminor axes a and b:
pi( 3a + 3b - sqrt( (3a + b)(3b + a) ) )
Notice that if a = b = r, it's a circle, circumference 2 pi r.
Srinivasa Ramanujan (1887-1920). p. 191.
Volume of sphere = (4/3) pi r^3
Area of sphere = 4 pi r^2
Cone of height h, on a circle of radius r, slant height s (s^2 = r^2 + h^2):
Volume of cone = pi r^2 h/3
Area of cone = pi r s
p. 192.
Volume of a pizza, radius z, thickness a, V = pi z z a
p. 193.
Pi also appears in surprising places:
Stirling's approximation to n! ≅ ( (n/e)^n ) * Sqrt(2 pi n) p. 193.
This is better than Log(n!) ≅ ( n Log[n] - n ) for small n.
Plots: https://www.wolframalpha.com/input?i=...
Theory: https://mathworld.wolfram.com/Stirlin...
The sum of the 1/n^2, for all n from 1 to infinity is pi^2/6:
https://www.wolframalpha.com/input?i=...
pi ≅ 355/113
p. 197.
Pythagorean triples:
For a right triangle, short sides a and b, hypotenuse c:
Where a, b, c are whole numbers, they're called a "Pythagorean triple."
For any two positive integers (m, n), m > n, the numbers
a = m^2 - n^2
b = 2mn
c = m^2 + n^2
are a Pythagorean triple. Notice that a^2 + b^2 = c^2. p. 205.
Every Pythagorean triple can be created by some choice of (m, n). p. 205.
Law of cosines: for any triangle, sides a, b, c, angle C opposite side c:
c^2 = a^2 + b^2 - 2 a b cos C
proof p. 216.
Area of any triangle, sides of lengths a, b form angle C:
area = (1/2) a b sin C
proof p. 217.
Law of sines: for any triangle, sides a, b, c, opposite angles A, B, C:
(sin A)/a = (sin B)/b = (sin C)/c
proof pp. 217-218.
Hero's formula: for any triangle, sides a, b, c, semiperimeter s = (a + b + c)/2,
area of triangle = Sqrt[ s(s - a)(s - b)(s - c) ]
p. 219.
Trigonometric identities
sin^2 x + cos^2 x = 1
many others p. 225.
For any polyhedron with a number F of flat faces, a number E of straight-line edges, and a number V of vertices,
F + V = 2 + E
p. 232
Multiplying complex numbers:
The magnitude (length) of the product is the product of the magnitudes.
The argument (angle) of the product is the sum of the arguments.
Dividing complex numbers, divide the lengths and subtract the angles. p. 240.
The limit, as n goes to infinity, of (1 + 1/n)^n, is e. p. 241.
https://www.wolframalpha.com/input?i=...
log(x y) = log x + log y
log( x^n ) = n log x
log_b(x) = log x / log b is the base-b log of x.
Bell curve
y = ( 1/sqrt(2 pi) ) e^-(x^2/2)
The infinite sum,
Sum[x^n/n!, {n, 0, Infinity}] = e^x p. 246.
https://www.wolframalpha.com/input?i=...
e^(i theta) = cos theta + i sin theta
e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + …
cos x = 1 - x^2/2! + x^4/4! - x^6/6! + …
sin x = x - x^3/3! + x^5/5! - x^7/7! + …
p. 251
For y = x^n, y' = n x^(n - 1)
p. 263
Proof that e^x is its own derivative, p. 265.
Conditionally convergent series, p. 301.
Magic squares, pp. 302-305.
September 7, 2015
*I received this book through Netgalley in exchange for an honest review.*
I really enjoyed this book. There's a lot of interesting math that's explored. I do think this would probably be most interesting to people who already know quite a bit of math, but there is something here for everyone.
I've always enjoyed puzzles (that's what got me interested in math) so I liked seeing the patterns and puzzles within the math.
Full review will be up on my blog September 8th: http://courtneysreads.blogspot.com/20...
I really enjoyed this book. There's a lot of interesting math that's explored. I do think this would probably be most interesting to people who already know quite a bit of math, but there is something here for everyone.
I've always enjoyed puzzles (that's what got me interested in math) so I liked seeing the patterns and puzzles within the math.
Full review will be up on my blog September 8th: http://courtneysreads.blogspot.com/20...
October 16, 2015
There are broadly three types of popular maths. There are books like A Brief History of Infinity which introduce mathematical concepts and history without actually doing any maths - and these can be fascinating. There are books of recreational maths, like Martin Gardner's classic Mathematical Puzzles and Diversions, or Ian Stewart's Cabinet of Mathematical Curiosities, which explore the weird and wonderful of maths, with a need for a bit of practical working out, but almost always provide plenty of fun along the way. And there are book like the Magic of Maths. (Could I say, by the way, how grateful I am that the UK edition has that 's' on 'maths'.) Almost always written by mathematicians, such books set out to prove to the masses who think that actually getting your hands dirty and doing mathematics is too hard or too boring that it's really easy and enjoyable too.
To give him his due, Arthur Benjamin makes a good stab at this - one of the best I've seen. He tells us we're going to learn clever little tricks that will allow us to do amazing things with mental arithmetic - for instance multiplying surprisingly big numbers in our heads. And he delivers. It really works, and we can amaze ourselves, though probably not our friends, because if other readers are anything like me they will have forgotten most of the techniques by the time they finish the next chapter.
Benjamin also takes on the likes of algebra, Fibonacci numbers, geometry, trigonometry, imaginary numbers, calculus and more. And going on the pages of testimonials from maths professors in the front, this is the kind of thing maths-heavy people love. And that's fine. But for most of us I'd say 80 per cent of the book is not going to be appreciated. Early on, Benjamin tells us we shouldn't mind skipping pages or even chapters. But when you find yourself skipping most of the content, it begins to feel as if it wasn't a great thing to read in the first place.
In one of those fruitless exercises in saying the whole world is your audience, Benjamin comments that the book is for anyone who will one day take a maths course, is taking a maths course or is finished taking maths courses. I'd say the audience is a lot tighter. It's for people who one day will take a maths degree, or took one years ago and wants to reminisce. It's just too number heavy and narrative light to work for me. And I have taken a maths course. But I certainly don't want take another - and this has reminded me why.
I have to emphasise that the book is by no means all bad. Benjamin does introduce some fun, and weird and wonderful stuff, like the apparent demonstration that infinity is equal to -1/12 (though I've seen better explanations of why this demonstration falls apart). But far too often what Benjamin thinks is fun is just 'So what?' to us lesser mortals.
To give him his due, Arthur Benjamin makes a good stab at this - one of the best I've seen. He tells us we're going to learn clever little tricks that will allow us to do amazing things with mental arithmetic - for instance multiplying surprisingly big numbers in our heads. And he delivers. It really works, and we can amaze ourselves, though probably not our friends, because if other readers are anything like me they will have forgotten most of the techniques by the time they finish the next chapter.
Benjamin also takes on the likes of algebra, Fibonacci numbers, geometry, trigonometry, imaginary numbers, calculus and more. And going on the pages of testimonials from maths professors in the front, this is the kind of thing maths-heavy people love. And that's fine. But for most of us I'd say 80 per cent of the book is not going to be appreciated. Early on, Benjamin tells us we shouldn't mind skipping pages or even chapters. But when you find yourself skipping most of the content, it begins to feel as if it wasn't a great thing to read in the first place.
In one of those fruitless exercises in saying the whole world is your audience, Benjamin comments that the book is for anyone who will one day take a maths course, is taking a maths course or is finished taking maths courses. I'd say the audience is a lot tighter. It's for people who one day will take a maths degree, or took one years ago and wants to reminisce. It's just too number heavy and narrative light to work for me. And I have taken a maths course. But I certainly don't want take another - and this has reminded me why.
I have to emphasise that the book is by no means all bad. Benjamin does introduce some fun, and weird and wonderful stuff, like the apparent demonstration that infinity is equal to -1/12 (though I've seen better explanations of why this demonstration falls apart). But far too often what Benjamin thinks is fun is just 'So what?' to us lesser mortals.
August 22, 2015
(I received a free copy of this book from Net Galley in exchange for an honest review.)
The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples, from ice cream scoops and poker hands that teach you factorials to mnemonics that help you memorize pi, this book empowers you to see the beauty, simplicity, and fun behind those formulas and equations that once left your head spinning. You’ll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus; but you’ll also have fun playing with pi, fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks. A tour of the greatest hits of mathematics, The Magic of Math is a book for both fans of mathematics and those who want to be proven wrong about their previous prejudices of math.
Arthur Benjamin is a mathematician - known throughout the world as the “mathemagician” - who mixes mathematics and magic to make the subject fun and beautiful. Math lovers are going to find new ways to look at old friends, the way a view from a mountaintop puts a beautiful valley in a new perspective. For everyone who never particularly liked or understood math - The Magic of Math is going to put you under its spell.
Mathematics was always a favourite subject at school. I have always loved the ways that numbers work, I love the truth of numbers and the magic that they contain (I know, nerd!!) When I saw that this book was available for review, I jumped at the chance and I am so glad I did.
This was a treasure trove of cool maths facts, with an explanation from the author of the "whys and hows" of each "trick."
There really isn't a whole lot more to say other than if you love maths, love the way numbers work and want to discover some really neat truths - this is the book for you.
Paul
ARH
The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples, from ice cream scoops and poker hands that teach you factorials to mnemonics that help you memorize pi, this book empowers you to see the beauty, simplicity, and fun behind those formulas and equations that once left your head spinning. You’ll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus; but you’ll also have fun playing with pi, fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks. A tour of the greatest hits of mathematics, The Magic of Math is a book for both fans of mathematics and those who want to be proven wrong about their previous prejudices of math.
Arthur Benjamin is a mathematician - known throughout the world as the “mathemagician” - who mixes mathematics and magic to make the subject fun and beautiful. Math lovers are going to find new ways to look at old friends, the way a view from a mountaintop puts a beautiful valley in a new perspective. For everyone who never particularly liked or understood math - The Magic of Math is going to put you under its spell.
Mathematics was always a favourite subject at school. I have always loved the ways that numbers work, I love the truth of numbers and the magic that they contain (I know, nerd!!) When I saw that this book was available for review, I jumped at the chance and I am so glad I did.
This was a treasure trove of cool maths facts, with an explanation from the author of the "whys and hows" of each "trick."
There really isn't a whole lot more to say other than if you love maths, love the way numbers work and want to discover some really neat truths - this is the book for you.
Paul
ARH
December 7, 2019
Книжка цікава, але підійде тим у кого рівень математики трохи вищий за середній. Однозначно рекомендую школярам і студентам, що цікавляться математикою, або читачам, які мають в свому багажі математичні класи, або математичні факультети.
July 22, 2016
This book is definitely written for the reader who has an interest in math, but may not remember a lot of what they learned in school. For me, the first few chapters dragged, then the interest picked up once the author moved past arithmetic, then it lagged again once he got to calculus, and then finally picked up once again in the final chapter. There were some new and interesting ideas presented, and there were some proofs of some ideas that I've read about ut haven't followed up on that I appreciated. In all, the author strikes me as a professor that you will either really really enjoy or decide is a complete waste of time. For me, he falls into the former category.
August 29, 2023
At the beginning of this book, the author explains that readers should feel free to skim over and even skip those portions or subsections which they feel are not interesting or are over their heads. I took this advice, and as a result, I really enjoyed it.
For people like me, who appreciate math and understand it reasonably well, this book offers a lot of interesting notions. One example that I will always remember is that the volume of a pizza that has a radius of z and a depth of a can be found by the formula ... : pizza (pi * z^2 *a).
For people like me, who appreciate math and understand it reasonably well, this book offers a lot of interesting notions. One example that I will always remember is that the volume of a pizza that has a radius of z and a depth of a can be found by the formula ... : pizza (pi * z^2 *a).
began-but-dnf
November 2, 2015Yyyyyyeah, not for the lay person. :)
July 4, 2024
This a book that deserves a close read. There is no point in looking at math, you need to do math if you really want to learn it. That said, I found about 85% of the examples were doable (although admittedly I took calculus in college, so it was more of a review). Most enjoyable for me were multiplication shortcuts, trigonometry examples, working with pi, and the magic of calculus.
December 23, 2017
Chi ha detto che la matematica è noiosa? Al contrario, è piena di sorprese inaspettate. In questo libro vengono mostrati moltissimi esempi della "magia della matematica", dall'algebra ai numeri di Fibonacci, dalla trigonometria all'infinito, dai numeri irrazionali a quelli immaginari. Non servono particolari conoscenze pregresse per riuscire a leggere agevolmente il libro, è sufficiente essere affascinati dai numeri.
È un peccato che l'edizione non sia sufficientemente curata, come dimostrano i troppi e fastidiosi errori di stampa. :/ Ma ovviamente questo non è un difetto del libro in sé.
È un peccato che l'edizione non sia sufficientemente curata, come dimostrano i troppi e fastidiosi errori di stampa. :/ Ma ovviamente questo non è un difetto del libro in sé.
January 30, 2016
I found several parts of the book to be very entertaining and worthy of all the introductory comments by the author in regards to the book being accessible to all. However, there were too many chapters that were too much like the normal high school curriculum. Being one of those math teachers, I find this material to be interesting, but know that there are many people that would not be as enthralled.
August 14, 2016
The important concepts (algebra, geometry, proofs, calculus, infinity) were not well enough explained for someone who doesn't already know it, and mostly too basic for someone who does.
November 15, 2017
Usually for math, for most, is either a hit or a miss for people. Some people love math and some people hate it. If you love math this book is definitely for you. Arthur Benjamin does a great job on this book making it interesting all the way through. He mixed in personal experiences and packed it full of cool tips tricks. The tricks involve the “magic” of math this book is based on and you can use them to trick your friends and teachers. Aside from the tips and tricks there are small lessons in each chapter and those chapters range from calculus to the magic of the number 9. All of these section have great information, magic tricks and interesting techniques to solve problems and to simply enjoy the beauty of math.
I would recommend this book to people who want to get better at math, or to people who love math. If you absolutely love math, like me, this book is a great read to enjoy and have fun with the “magic” tricks. If you want to improve upon your math skills, also me, this book is also for you. The book isn’t written at all like a textbook, but it still improved my math skills. For example, I now know a formula to figure out the day of the week in any given year and date, which is mostly just for fun, but can come in handy. These are the types of cool, nearly useless, magical math tricks that are taught in the book that will help you to think and give someone one more trick in their trickbook.
I would recommend this book to people who want to get better at math, or to people who love math. If you absolutely love math, like me, this book is a great read to enjoy and have fun with the “magic” tricks. If you want to improve upon your math skills, also me, this book is also for you. The book isn’t written at all like a textbook, but it still improved my math skills. For example, I now know a formula to figure out the day of the week in any given year and date, which is mostly just for fun, but can come in handy. These are the types of cool, nearly useless, magical math tricks that are taught in the book that will help you to think and give someone one more trick in their trickbook.
November 14, 2017
I read most of the reviews on here, but I think a good majority of them have missed the overall purpose of the book. If you expect a few hundred pages full of quick tricks and tips for math this probably isn't for you (check out his previous book for that). The content in here is in greater depth than that as it goes into proofs and shows how all the ideas in mathematics untimely connect together. Most have never seen this connected view of math because in school, we're never really taught it. That's where this book shines. It shows how you can start off with one idea and logically progress to figure out more and more information. It's not as in depth as a textbook, but it fills a gap in most people's knowledge.
So how is this book entertaining then? Because figuring out the puzzle of how everything fits together is enormously rewarding in and of itself. The author throws in humor and anecdotes every once in a while, as well, but no interlude could beat the joy of learning the content. Overall, I recommend this to anyone who enjoys learning or is at all interested in math. I think that if you go in enthusiastically, there is much to learn and much fun to be had.
So how is this book entertaining then? Because figuring out the puzzle of how everything fits together is enormously rewarding in and of itself. The author throws in humor and anecdotes every once in a while, as well, but no interlude could beat the joy of learning the content. Overall, I recommend this to anyone who enjoys learning or is at all interested in math. I think that if you go in enthusiastically, there is much to learn and much fun to be had.
May 26, 2018
This was an ok math book for a non-maths person. I could follow most of the logic, and about half of the higher level math jargon and notation, but there were a few things that author assumed I knew that really obscured some of his points because I didn’t know them. Made me wish I had kept going with math in high school and college instead of just taking the required courses, but life choices are life choices (you have to live with them).
Now that I’ve read the book, I want to explore some of the topics he covered in more detail just on their own. In particular, I loved his chapter on the magic of numbers and the magic of infinity.
Benjamin has a very clear writing style (only obfuscated by my unfamiliarity with the appropriate vocabulary!), and peppers the book with lots of light humor and a clear sense of joy in working with all aspects of maths.
I recommend this book if you have a basic grasp of high school level trig and calculus, or at least the vocabulary that accompanies them. Even if you don’t, though, you can still glean a lot of insight into how and why numbers sometimes act the way they do.
Now that I’ve read the book, I want to explore some of the topics he covered in more detail just on their own. In particular, I loved his chapter on the magic of numbers and the magic of infinity.
Benjamin has a very clear writing style (only obfuscated by my unfamiliarity with the appropriate vocabulary!), and peppers the book with lots of light humor and a clear sense of joy in working with all aspects of maths.
I recommend this book if you have a basic grasp of high school level trig and calculus, or at least the vocabulary that accompanies them. Even if you don’t, though, you can still glean a lot of insight into how and why numbers sometimes act the way they do.
September 13, 2018
I'm going to review this book in two parts. Before chapter 8, it had some fun tips and tricks and some interesting math ideas. That being said, I hated--HATED--that he would say "here's a really easy way to explain this concept. Got it so far? Great. Here, let me vomit some incredibly complex explanations now. Still with me? No? But come on, I told you, this math is so easy." Thank you for making me feel dumber than I usually do about math.
But then, then we got to chapter 8. And after that, I really tried to understand it. Bear in mind, I'm no math genius, but I'm also not a slouch at it either. Some of the stuff he was discussing was just completely beyond me or incredibly useless to know. And the entire last half of the last chapter was, forgive the pun, purely mathsturbatory. Literally no one would care about any of that chapter except math majors. I skimmed it.
I think this book offered enough cool info that I don't regret reading it, but I more suggest it as how not to teach math (a thing I do every day.) Never ever tell someone you are teaching "but it's so easy!" For you, yes--maybe not for them. If you want them to like math, meet them where they are.
But then, then we got to chapter 8. And after that, I really tried to understand it. Bear in mind, I'm no math genius, but I'm also not a slouch at it either. Some of the stuff he was discussing was just completely beyond me or incredibly useless to know. And the entire last half of the last chapter was, forgive the pun, purely mathsturbatory. Literally no one would care about any of that chapter except math majors. I skimmed it.
I think this book offered enough cool info that I don't regret reading it, but I more suggest it as how not to teach math (a thing I do every day.) Never ever tell someone you are teaching "but it's so easy!" For you, yes--maybe not for them. If you want them to like math, meet them where they are.
March 14, 2019
Коли Гокінґ писав свою "Коротку історію часу", він керувався правилом, яке йому надиктував видавець: кожна формула у книзі знижує обсяг її продажу вдвічі. Якби це було правдою, то наклад "Магії математики" заступорився б десь на півтора примірниках.
Книга містить сотні формул, більшість із яких ми бачили ще у школі. Але під час читання я без особливого подиву виявив, що зі школи у моїй пам'яті лишилися тільки сума квадратів катетів та дуже приблизне уявлення про логарифми.
Аби магію, винесену у заголовок, відчути у повні, слід читати книгу із олівцем та великим запасом вільного часу. До свого сорому, я цього робити не став, не заглиблюючись в інтегрально-тригонометричні обґрунтування, а намагався осягнути всі ці скупища цифр і букв інтуїтивно. Десь виходило - на старих шкільних дріжджах, - десь ні. Але це було досить цікаве чтиво.
А ще тут є класичний жарт про нескінченних математиків у барі!
День π - гарний день, аби закінчити читати книгу про магію математики. Хай не надто просту, але в цілому зрозумілу. І трохи надихайну, чи що. Бо бажання відкрити старий підручник з алгебри та початків аналізу вона таки пробуджує.
Математика - це красиво, трясця!
Книга містить сотні формул, більшість із яких ми бачили ще у школі. Але під час читання я без особливого подиву виявив, що зі школи у моїй пам'яті лишилися тільки сума квадратів катетів та дуже приблизне уявлення про логарифми.
Аби магію, винесену у заголовок, відчути у повні, слід читати книгу із олівцем та великим запасом вільного часу. До свого сорому, я цього робити не став, не заглиблюючись в інтегрально-тригонометричні обґрунтування, а намагався осягнути всі ці скупища цифр і букв інтуїтивно. Десь виходило - на старих шкільних дріжджах, - десь ні. Але це було досить цікаве чтиво.
А ще тут є класичний жарт про нескінченних математиків у барі!
День π - гарний день, аби закінчити читати книгу про магію математики. Хай не надто просту, але в цілому зрозумілу. І трохи надихайну, чи що. Бо бажання відкрити старий підручник з алгебри та початків аналізу вона таки пробуджує.
Математика - це красиво, трясця!
September 15, 2022
I like mathematics, but this was a little disappointing. It's hard to pin point why, but I guess that the author trying to pitch this at the level of those who haven't really got much more than a high-school level maths education, whilst also trying to make it appeal to those who have more of an interest and understanding of higher concepts, was the (admirable, but flawed) problem.
Don't get me wrong, I have read plenty of maths books which too quickly went off into concepts too advanced for me and failed to adequately explain them, and hence I got a lot more from this understandable book as a consequence - however some of the simple stuff became a bit boring/tedious (I don't like to skip sections when reading, regardless of if they're pitched simple) and no matter how many 'quirky' exclamation points and asides as Benjamin included - not to my taste - quite a bit of this I didn't find that magical. Different books, I know, but the likes of Hannah Fry, Matt Parker, Martin Gardner etc. were more to my palate.
Don't get me wrong, I have read plenty of maths books which too quickly went off into concepts too advanced for me and failed to adequately explain them, and hence I got a lot more from this understandable book as a consequence - however some of the simple stuff became a bit boring/tedious (I don't like to skip sections when reading, regardless of if they're pitched simple) and no matter how many 'quirky' exclamation points and asides as Benjamin included - not to my taste - quite a bit of this I didn't find that magical. Different books, I know, but the likes of Hannah Fry, Matt Parker, Martin Gardner etc. were more to my palate.
November 14, 2020
This starts off with a good deal of "magical" properties and mathematical occurrences. As the book progresses it feels a lot more like an abridged trip through a series of high school math classes. This isn't a complaint. As a high school math teacher, I quite enjoyed the read and in fact came away with some idea to use in class. The entire trig chapter could nearly cover what our current standards expect, to some extent, in Algebra 2.
I don't know that someone not interested in math would get much joy past the 5th chapter, but they'd not lose anything by giving it a chance.
I don't know that someone not interested in math would get much joy past the 5th chapter, but they'd not lose anything by giving it a chance.
May 1, 2021
This book was a fun read, but about half of the way through the math got too challenging for my brain to handle for before-bedtime reading. That said, it was enjoyable, and the author clearly LOVES math, so it's hard not to enjoy it, even if I skimmed or even skipped over some of the proofs when I got to the calculus section... I'll be keeping this book handy as a reference as my kids advance in their own mathematical journeys!
January 26, 2024
I was a pretty good math student in school. I went on to take more advanced math courses in college. I learned a few little tricks and different ways to think about the math I know, but a lot of it was rehashing what I learned in high school, but with more proofs. That being said, the author did say in the beginning that you are encouraged to skip chapters or read out of order.
May 30, 2025
This book is one of my favorite books ever. I loved it so much I gave it to my Calculous professor in university. Its not structured like a textbook, its easy to pick up and put down. The chapters do build on each other but you can skip around. I would recommend this book for anyone who wants to learn math but doesn't know where to start.
January 17, 2018
Great book! The jokes.... OH THE LAME JOKES!! They’re painfully humorous! It reads very well. I thoroughly enjoyed it. I know I’ll look through this book again to write down all the mathematical goodies I found. Thank you, Dr Benjamin and everyone involved in making this book.
February 27, 2019
This was a hard one for me to get through and I think I only fully understood bits and pieces of it. I thought the writing was as fun as writing about math can be and did enjoy learning about some of the different patterns found in mathematics.
July 17, 2019
I probably would have enjoyed this more if I'd read a physical copy not the ebook, as there were formatting issues.
December 27, 2019
Great way to make math more accessible to all people. Loved the examples.
March 8, 2022
A nice overview and more on numbers
August 15, 2022
This book could inspire readers to love the magic of math, though I still couldn't understand some of the math.
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