From natural numbers to imaginary numbers

Prologue | Promising Numbers

Part 1 Integers, the basic numbers
1.
positive integer (natural number)
2.
0
3.
negative integer
4.
Comparing the sizes of integers
Take a break | How ancient people counted

Part 2 Rational Numbers, Logical Numbers
1.
fountain
2.
decimal
Take a break | The decimal point is a great invention

Part 3 Real Numbers, Numbers on the Number Line
1.
surd
2.
mistake
3.
Absolute value
Take a break | It's a secret that there are irrational numbers

Part 4 Complex Numbers, All the Numbers in the World
1.
Scarecrow
2.
complex number
Take a break | The Beginning of the Universe and the Imaginary


From addition to logarithms

Prologue | What Mathematics Says

Part 1: Addition, the basis of all operations
1.
addition
2.
Sigma, simple addition
3.
Subtraction and addition in reverse
Take a break | Addition in Egypt is complicated

Part 2 Multiplication, a versatile operation
1.
multiplication
2.
Number of cases
3.
Factorial, multiplication made simple
4.
Division and multiplication in reverse
Take a Break | Division in Ancient Egypt

3rd part exponent, simple operation
1.
jisoo
2.
Square root, reverse exponent
Take a break | Move 64 discs!

Part 4 Logarithms, operations dealing with astronomical numbers
1.
log
2.
Law of logarithms
Take a Break | Astronomers Who Reaped the Benefits of Logs


From the origin to the equation of a circle

Prologue | When I look at the night sky, I see a circle.

Part 1: Circles, dots come together to form a circle
1.
A circle is a promise
2.
Circles and lines
Take a break | The Earth rotates in an elliptical shape

Part 2: Pi, the unchanging ratio of a circle
1.
Pi
2.
Measurement of a circle
3.
Measurement of a sphere
Take a break | Inventions made from circles

Part 3: Angles and Radius, How to Represent Angles
1.
angle
2.
Hodo method
Take a break | Why are manhole covers round?

Part 4: Equations of circles, relationships between shapes
1.
Equation of a circle
2.
The relationship between circles and lines
Take a break | Earthquakes and the circle equation


From right triangle angles to trigonometric functions

Prologue | The World in a Triangle

Part 1 Triangles, figures with three angles
1.
each
2.
Properties of triangles
Take a break | There is an acute triangle in a heavy place

Part 2: Pythagorean theorem, formulas for right triangles
1.
three sides of a right triangle
2.
Pythagorean theorem
Take a break | Who was Pythagoras?

Part 3 Trigonometry, the ratio of sides determined by angles
1.
Trigonometric ratios
2.
Trigonometric symbols
Taking a break | How Napoleon measured the width of a river

Part 4 Trigonometric functions, trigonometric ratios
1.
Trigonometric functions
2.
Trigonometric function graphs
Take a break | Music and sign graphs

From natural numbers to imaginary numbers

The number section contains all number concepts learned in elementary, middle, and high school.
Starting with numbers that have been used in daily life since the primitive era, such as natural numbers and fractions, we will examine negative integers, decimals, irrational numbers and rational numbers, imaginary numbers, and complex numbers according to the stages of number development.
Rather than simply explaining various numerical concepts and providing guidance on the system, it details the process by which new numbers are created.
The stories and histories of each number concept unfold, including the prime numbers invented to make loan interest calculations easier, and the irrational numbers that unexpectedly appeared during the study of right triangles and baffled mathematicians.
Because we understand the concept of numbers through stories, we can encounter numbers more deeply and familiarly, and we also learn the meaning behind the names of numbers.
As you follow the concept of expanding from integers to real numbers to complex numbers, you will naturally grasp all the number systems you learn in school math classes, and furthermore, you will understand why the distinction and system of rational numbers, irrational numbers, real numbers, and imaginary numbers are necessary.



From addition to logarithms

The operations section contains all the operations learned in school.
First, the story of how symbols for addition, subtraction, multiplication, and division were agreed upon, and why some symbols became agreed upon and others were ignored by mathematicians unfolds in an interesting way.
This book begins with addition, the basis of all operations, and expands the concept to multiplication, exponentiation, and logarithms.

As the equation 3+3+3+3+3+3+3+3+3+3+3=3×10 shows, each operation is connected to each other because the operations have been expanded in the process of simplifying existing calculations.
This book mathematically demonstrates the relationships between operations, while also introducing the historical mathematical background that led to the creation of new operations.
For example, logarithms were invented by the 16th century English mathematician John Napier.
At that time, calculating the positions of stars was important because they were used as maps for navigation, but multiplying astronomical units was difficult to calculate and mistakes were common.
So Napier invented logarithms to simplify the multiplication of exponents.
In this way, by introducing mathematical concepts through stories, we were able to understand the relationships between mathematical concepts and feel the usefulness of those concepts.