introduction
Geometry originated from land surveying / Thales, who first 'proved' the theorem of geometry / Pythagoras, who discovered the 'Pythagorean theorem' / Euclid, who created a geometry textbook

Chapter 1 Polygons and Polyhedra
Points, lines, and angles / Basic construction / Triangles / Rectangles / Area / Polygons / Polyhedrons /

Chapter 2: Geometry of Circles and Spheres
Circles and spheres around us / Properties of circles and spheres / Find the center of a circle! / What is pi? / How to calculate pi / How to calculate the area of ​​a circle / Volume of a sphere / Surface area of ​​a sphere / Geometry on the surface of a sphere

I Want to Know More! Column
π is a special 'irrational number' / If the radius increases by 1m, how much does the circumference increase?

Chapter 3: The Science of Circles, Spheres, and π
Why are water drops round? / Why are celestial bodies round? / The disk of the universe / Conic sections / Kepler's predictions / Creating a sphere / How to calculate π / Euler's equation / Record of calculations of π / The mystery of π

Chapter 4: The Mystery of the Golden Number φ
Golden number φ / Golden ratio and golden number / Fibonacci sequence / Golden number in nature

I Want to Know More! Column
Rectangles with golden ratio sides / Penrose tiles and the golden ratio

Chapter 5 Let's challenge the shape problem!
Let's fold an equilateral triangle with colored paper / Pythagorean theorem and puzzles / Let's try a cut-and-paste puzzle! / Reulo triangle and a four-dimensional manhole / Let's make a shape with the 'maximum area'! / The International Congress of Mathematicians and the Möbius strip / Challenge Escher's impossible picture!

The properties of shapes and the principles of mathematics all at once!

"Why learn 'painful' math? Isn't adding, subtracting, multiplying, and dividing enough for everyday life?" Many people have probably thought this at least once.
Is mathematics really unrelated to everyday life?

Let's think about this problem.
The 'manhole cover', which is commonly seen on the street, is an essential item related to the treatment of sewage produced as a result of our daily lives.
However, most manhole covers are circular.
Why are square or equilateral triangle manholes so hard to find? This has nothing to do with design.
As discussed in this book, there are clear mathematical (geometric) reasons why there are so few square or equilateral triangle manholes.
Also, when you drill a hole, you usually end up with a round hole.
But can't you drill a square hole with a drill? There are drills that do that.
The principles of geometry and mathematics are also hidden in the background (see pages 134-137).


This book was designed with the goal of helping students 'acquire' the mathematical principles hidden in shapes.
As we often experience, there is a huge difference in mathematics between those who fully understand the principles and those who do not.
We all have experienced that without a clear understanding of the principles, we cannot properly address various application problems.

Chapter 1 of this book explains the characteristics, properties, and basic principles of shapes such as points, lines, angles, construction, triangles, squares, polygons, areas, and polyhedra.
Chapter 2 covers circles, spheres (?, π, etc.).
It explains in detail the properties of circles, spheres, and π, finding the center, calculating pi and area, and the principles for calculating the volume and surface area of ​​a sphere.
Chapter 3 consists of applications to circles, spheres, and π.
It introduces various topics such as why water drops and celestial bodies are round, making conic sections and spheres, Kepler's predictions, and Euler's equation.

Chapter 4 explains the golden ratio, the Fibonacci sequence, and golden numbers hidden in nature.
Chapter 5 explains various application problems related to shapes, such as making regular triangles and regular hexagons with origami, the Pythagorean theorem and puzzles, the Reulo triangle, making the shape with the largest area, the Möbius strip, and Escher's impossible picture.


All content is presented through a variety of colorful illustrations that allow you to understand the principles at a glance, along with easy-to-understand and detailed explanations by experts.
This will be a good opportunity to properly understand the ‘mathematical principles hidden in shapes.’


characteristic

- Explanation of the properties and principles of shapes such as points, lines, angles, polygons, and polyhedra
There are few fields where the 'basics' are as important as mathematics.
So, if you don't have a strong foundation in mathematics, you won't be able to solve various application problems.
The same is true in the field of geometry.
This book carefully organizes the characteristics, properties, and principles of shapes such as points, lines, angles, constructions, triangles, squares, polygons, areas, and polyhedra.
A solid foundation of 'basic knowledge' about shapes will remain as a skill that can be applied anytime, anywhere.


-The mathematical and scientific principles hidden in circles, spheres, π, and the golden ratio
Many of the problems related to geometry are complex problems involving circles.
If you understand the various properties of a circle and its circumference ratio π, you will be able to deal with these situations in no time.
A sphere can also be considered a representative spatial figure.
The basic principles of calculating the volume and surface area of ​​a sphere, an application explanation of the Earth as a rod, and the golden ratio that has been known for over 2000 years****

- Application problems such as the Pythagorean theorem and shape puzzles, and 'shape with maximum area'
This is a content that solves various application problems related to shapes.
It is designed to solve fun application problems together, such as folding regular triangles, regular hexagons, and regular octagons with colored paper, solving the Pythagorean theorem as a shape puzzle, making polygons of different shapes with the same area, Reulo's triangle, proving that 'the shape with the largest area is a circle', Möbius strips, and Escher's impossible pictures.

-Various primary color reference pictures that help you understand the properties and principles of shapes at a glance
The principles of mathematics and science can be more clearly seen through pictures.
Over 350 accurate, primary-color illustrations that hit the nail on the head, combined with expert commentary, make the content easier to understand.