Math Question Box
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Description
Book Introduction
Math gets easier the moment you ask questions!
Math Question Box
Kentaro Yano's "Math Question Box" is a book that helps students solve mathematics like an interesting puzzle that stimulates their curiosity, rather than a difficult and rigid subject.
This book collects questions that students might have wondered about while studying mathematics and provides friendly and easy-to-understand explanations.
It goes beyond simple conceptual explanations and utilizes a variety of thought experiments and real-life examples to develop mathematical thinking skills, making it easy for even readers unfamiliar with mathematics to read.
The book covers a wide range of topics, from the mysterious nature of numbers to operations, geometric intuition, and concepts of probability and logic, and poses a variety of questions that stimulate mathematical curiosity.
This allows readers to think deeply about why this principle holds true.
This is a useful book for anyone who wants to enjoy mathematics and develop logical thinking skills.
Math Question Box
Kentaro Yano's "Math Question Box" is a book that helps students solve mathematics like an interesting puzzle that stimulates their curiosity, rather than a difficult and rigid subject.
This book collects questions that students might have wondered about while studying mathematics and provides friendly and easy-to-understand explanations.
It goes beyond simple conceptual explanations and utilizes a variety of thought experiments and real-life examples to develop mathematical thinking skills, making it easy for even readers unfamiliar with mathematics to read.
The book covers a wide range of topics, from the mysterious nature of numbers to operations, geometric intuition, and concepts of probability and logic, and poses a variety of questions that stimulate mathematical curiosity.
This allows readers to think deeply about why this principle holds true.
This is a useful book for anyone who wants to enjoy mathematics and develop logical thinking skills.
- You can preview some of the book's contents.
Preview
index
preface
Translator's Note
Chapter 1: The Mystery of Numbers
When, where, and how did 0 develop?
Is 0 even or odd?
How were negative numbers discovered?
Which number is larger, rational or irrational?
Why is the decimal system so widely used?
The way we count in our country is by adding a new unit every four digits.
I'm naming it, but please tell me the name of a unit larger than a trillion.
Are there infinitely many prime numbers?
Is there a general way to find prime numbers?
Why isn't 1 included in the prime numbers?
Why did you think of the imaginary number i?
How do complex numbers help?
, are there any other numbers like this?
What are trigonal and tetragonal numbers?
Chapter 2: Why is 'Calculation' Like That?
In mathematics, we use various symbols. Please explain the reasons for this.
Why are letters like x, y, z used to represent unknowns?
What is the etymology of sin, cos, and tan?
When dividing fractions, why do we calculate like this?
Why does multiplying negative numbers result in a positive number?
Why does the sign of an inequality change when you multiply both sides by a negative number?
Why does 0.9999… … = 1?
6×0=0 is fine, but why can't we divide by 0, like 6÷0?
Why is it =1?
When you convert a fraction to a decimal, why does it always become a finite decimal or a repeating decimal?
How to convert a recurring decimal to a fraction?
Why is it that 1+1=2, 2+1=3, and why can't we create math like 1+1=2, 2+1=0?
How do we find the value of pi?
Why is tan90° infinite?
How can I get it?
Why is the logarithm with a base called the natural log?
Why is binary used in computers?
Chapter 3: I Want to Know About Geometry
Please tell me why one rotation is 360°, 1° is divided into 60′, and 1′ is divided into 60″
Why is the sum of the interior angles of a triangle 180°?
Is it possible to create a square that has the same area as a given circle?
Why is it impossible to divide any angle into three equal parts using a ruler and a compass?
There are several ways to prove the Pythagorean theorem. Could you please teach me how?
Please explain why the area of a circle with radius r is
Please explain why the surface area of a sphere with radius r is
Please tell me why the volume of a pyramid and a cone is , where s is the area of the base and h is the height.
Please explain why the volume of a sphere with radius r is
Regular polyhedra include the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
They say there are only five types, but why is that?
How was the golden ratio discovered?
How did non-Euclidean geometry come into being?
Why were the Möbius strip and the Klein jar invented?
The difficult problem of finding area
The difficult problem of finding an angle
Chapter 4: Paradoxes and Games
Please teach me how to distinguish between a single stroke and a non-single stroke.
Can you combine squares of different sizes to make one square?
How can I make a dustproof room?
In the Achilles and the Tortoise problem, why can't Achilles overtake the tortoise?
What kind of thought is infinity?
What's wrong with the proof that 1=2?
Are all numbers equal to zero?
Are all triangles isosceles?
Sharing Father's Legacy
Chapter 5 Previous Questions
It has been revealed that there is no root formula for equations of degree 5 or higher.
Why is that?
Why do differential equations have general and singular solutions?
How did the beautiful and magical Euler's formula come about?
What is a Markov process?
What do the terms one-dimensional, two-dimensional, and three-dimensional mean in mathematics?
Also, what kind of world is the four-dimensional world that physics talks about?
What is the Riemannian geometry used in the theory of relativity?
Translator's Note
Chapter 1: The Mystery of Numbers
When, where, and how did 0 develop?
Is 0 even or odd?
How were negative numbers discovered?
Which number is larger, rational or irrational?
Why is the decimal system so widely used?
The way we count in our country is by adding a new unit every four digits.
I'm naming it, but please tell me the name of a unit larger than a trillion.
Are there infinitely many prime numbers?
Is there a general way to find prime numbers?
Why isn't 1 included in the prime numbers?
Why did you think of the imaginary number i?
How do complex numbers help?
, are there any other numbers like this?
What are trigonal and tetragonal numbers?
Chapter 2: Why is 'Calculation' Like That?
In mathematics, we use various symbols. Please explain the reasons for this.
Why are letters like x, y, z used to represent unknowns?
What is the etymology of sin, cos, and tan?
When dividing fractions, why do we calculate like this?
Why does multiplying negative numbers result in a positive number?
Why does the sign of an inequality change when you multiply both sides by a negative number?
Why does 0.9999… … = 1?
6×0=0 is fine, but why can't we divide by 0, like 6÷0?
Why is it =1?
When you convert a fraction to a decimal, why does it always become a finite decimal or a repeating decimal?
How to convert a recurring decimal to a fraction?
Why is it that 1+1=2, 2+1=3, and why can't we create math like 1+1=2, 2+1=0?
How do we find the value of pi?
Why is tan90° infinite?
How can I get it?
Why is the logarithm with a base called the natural log?
Why is binary used in computers?
Chapter 3: I Want to Know About Geometry
Please tell me why one rotation is 360°, 1° is divided into 60′, and 1′ is divided into 60″
Why is the sum of the interior angles of a triangle 180°?
Is it possible to create a square that has the same area as a given circle?
Why is it impossible to divide any angle into three equal parts using a ruler and a compass?
There are several ways to prove the Pythagorean theorem. Could you please teach me how?
Please explain why the area of a circle with radius r is
Please explain why the surface area of a sphere with radius r is
Please tell me why the volume of a pyramid and a cone is , where s is the area of the base and h is the height.
Please explain why the volume of a sphere with radius r is
Regular polyhedra include the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
They say there are only five types, but why is that?
How was the golden ratio discovered?
How did non-Euclidean geometry come into being?
Why were the Möbius strip and the Klein jar invented?
The difficult problem of finding area
The difficult problem of finding an angle
Chapter 4: Paradoxes and Games
Please teach me how to distinguish between a single stroke and a non-single stroke.
Can you combine squares of different sizes to make one square?
How can I make a dustproof room?
In the Achilles and the Tortoise problem, why can't Achilles overtake the tortoise?
What kind of thought is infinity?
What's wrong with the proof that 1=2?
Are all numbers equal to zero?
Are all triangles isosceles?
Sharing Father's Legacy
Chapter 5 Previous Questions
It has been revealed that there is no root formula for equations of degree 5 or higher.
Why is that?
Why do differential equations have general and singular solutions?
How did the beautiful and magical Euler's formula come about?
What is a Markov process?
What do the terms one-dimensional, two-dimensional, and three-dimensional mean in mathematics?
Also, what kind of world is the four-dimensional world that physics talks about?
What is the Riemannian geometry used in the theory of relativity?
Detailed image
Into the book
"Is 0 even or odd? 0 is even.
Usually … … , -4, -2, 0, 2, 4, 6, 8, 10, 12, … … are called even numbers, and … … , -3, -1, 1, 3, 5, 7, 9, … … are called odd numbers." --- p.20
"Why is the decimal system so widely used? It is thought that in the process of thinking about counting, humans made the most of the fingers and toes attached to their hands and feet.
If you count using your fingers, it is natural to think that you are finished when you have finished counting to 5 on one hand.
If you count using your fingers, you can think of three types of numbers: quinary, decimal, and xii, but I think the decimal system was used because 5 is too small to be combined into one, and 20 is too large to be combined into one. --- p.28
"Why does multiplying negative numbers result in a positive number? For example, right now, 'The temperature drops by 2 degrees every day, and today it is zero degrees.
Let's think about the question, 'What was the temperature three days ago?'
As you can easily see from the picture above, if the temperature drops by 2 degrees every day, if it is 0 degrees today, it would have been 6 degrees 3 days ago.
Meanwhile, since a temperature drop of 2 degrees every day is -2, and 3 days ago is -3, this shows that it is reasonable to set it as (-2) × (-3) = 6.” --- p.58
"Why is binary used in computers? When trying to represent numbers electrically, the only way to do so is to combine states where current is flowing and states where current is not flowing.
There, we decided to represent numbers in binary, because it is sufficient to represent 1 as a state of current flowing and 0 as a state of no current flowing." --- p.84
"There are several ways to prove the Pythagorean theorem. Please teach me how.
This is a proof by the Indian mathematician Bhaskara, who draws the two pictures next to each other and simply says, “Look.”
This is a proof of the Pythagorean theorem, which can be easily seen by writing the length here and drawing a dotted line as shown in the figure above.
That is, the picture on the left is a picture of a square drawn on the hypotenuse AB = c of a right triangle ABC divided into four right triangles and a small square." --- p.99
"Why were the Möbius strip and the Klein jar invented? The Möbius strip and the Klein jar were invented to show examples of surfaces that have no direction." --- p.159
"What kind of thought is infinity? In mathematics, the word infinity is sometimes used, but in mathematics, there cannot be a number called infinity.
In mathematics, infinity is a term that refers to a state of infinite growth. --- p.188
"What is the Riemannian geometry used in relativity? ... Starting from these principles, Einstein viewed spacetime as a Riemannian space in establishing the theory of physics, and discovered that the so-called absolute differential calculus was most suitable for studying it."
Usually … … , -4, -2, 0, 2, 4, 6, 8, 10, 12, … … are called even numbers, and … … , -3, -1, 1, 3, 5, 7, 9, … … are called odd numbers." --- p.20
"Why is the decimal system so widely used? It is thought that in the process of thinking about counting, humans made the most of the fingers and toes attached to their hands and feet.
If you count using your fingers, it is natural to think that you are finished when you have finished counting to 5 on one hand.
If you count using your fingers, you can think of three types of numbers: quinary, decimal, and xii, but I think the decimal system was used because 5 is too small to be combined into one, and 20 is too large to be combined into one. --- p.28
"Why does multiplying negative numbers result in a positive number? For example, right now, 'The temperature drops by 2 degrees every day, and today it is zero degrees.
Let's think about the question, 'What was the temperature three days ago?'
As you can easily see from the picture above, if the temperature drops by 2 degrees every day, if it is 0 degrees today, it would have been 6 degrees 3 days ago.
Meanwhile, since a temperature drop of 2 degrees every day is -2, and 3 days ago is -3, this shows that it is reasonable to set it as (-2) × (-3) = 6.” --- p.58
"Why is binary used in computers? When trying to represent numbers electrically, the only way to do so is to combine states where current is flowing and states where current is not flowing.
There, we decided to represent numbers in binary, because it is sufficient to represent 1 as a state of current flowing and 0 as a state of no current flowing." --- p.84
"There are several ways to prove the Pythagorean theorem. Please teach me how.
This is a proof by the Indian mathematician Bhaskara, who draws the two pictures next to each other and simply says, “Look.”
This is a proof of the Pythagorean theorem, which can be easily seen by writing the length here and drawing a dotted line as shown in the figure above.
That is, the picture on the left is a picture of a square drawn on the hypotenuse AB = c of a right triangle ABC divided into four right triangles and a small square." --- p.99
"Why were the Möbius strip and the Klein jar invented? The Möbius strip and the Klein jar were invented to show examples of surfaces that have no direction." --- p.159
"What kind of thought is infinity? In mathematics, the word infinity is sometimes used, but in mathematics, there cannot be a number called infinity.
In mathematics, infinity is a term that refers to a state of infinite growth. --- p.188
"What is the Riemannian geometry used in relativity? ... Starting from these principles, Einstein viewed spacetime as a Riemannian space in establishing the theory of physics, and discovered that the so-called absolute differential calculus was most suitable for studying it."
--- p.223
Publisher's Review
Solved with intuitive questions and answers
The easiest math question!
Math Question Box
From students who struggle with math to adults who enjoy logical thinking, "Math Question Box" is a friendly guide for everyone.
Unlike conventional, rigid math textbooks, this book unfolds its story around questions related to real life, naturally guiding readers to develop an interest in mathematics.
It helps you understand mathematical concepts naturally because it develops logic centered around the question, “Why is that?” rather than simply memorizing formulas.
In today's world, where the notion of "children failing at math from elementary school" is commonplace, "Math Question Box" serves as a friendly mathematical guide for students and provides adult readers with the intellectual pleasure of developing logical thinking skills.
This book will provide an opportunity to look at mathematics again.
The easiest math question!
Math Question Box
From students who struggle with math to adults who enjoy logical thinking, "Math Question Box" is a friendly guide for everyone.
Unlike conventional, rigid math textbooks, this book unfolds its story around questions related to real life, naturally guiding readers to develop an interest in mathematics.
It helps you understand mathematical concepts naturally because it develops logic centered around the question, “Why is that?” rather than simply memorizing formulas.
In today's world, where the notion of "children failing at math from elementary school" is commonplace, "Math Question Box" serves as a friendly mathematical guide for students and provides adult readers with the intellectual pleasure of developing logical thinking skills.
This book will provide an opportunity to look at mathematics again.
GOODS SPECIFICS
- Date of issue: May 16, 2025
- Page count, weight, size: 228 pages | 148*210*20mm
- ISBN13: 9791194832003
- ISBN10: 1194832008
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