Line segments meet with the same endpoints, greet each other, and measure the angle created to determine the degree of intimacy between them.
As we greeted each other like that, a shape was created where three line segments went around each other and had the same endpoint.
Looking at that shape, it was strangely divided into an inside part and an outside part with three line segments as the boundary.
A shape that can be distinguished inside and outside like this is called a closed shape, and this is how the first closed shape was created.
It's a triangle!
--- p.32

Wow! Amazing, isn't it? If you follow this process, you'll see that the sum of the exterior angles of any polygon is always 360°.
Let's think about it another way this time. Looking at the following figure, you can see that the larger the exterior angle, the sharper the interior angle.
This means, conversely, that the smaller the exterior angle, the more blunt the sharpness of the triangle.
So, let's cut off one side of the triangle. What shape do you think it will be? It's a square.

--- p.67

If you continue this process indefinitely, what you will eventually reach is a circle.
A circle has a larger area than any polygon with the same perimeter.
So, the attempts of shapes to increase their area end up in circles.
In the end, when you think about it by adding extension to extension, it turns out that the shape with the largest area among the shapes with the same perimeter is a circle.
How about relating this to the human world? The polygons have come to possess a kind of wish they could never achieve on their own.
The goal was to grow to an increasingly larger area.

--- p.91

Let's find point B. Finally, the shape of triangle ABC came to mind.
All of this was possible because we found the location of point B with the help of line segment AC.
This is how important it is to maintain your own position.
A triangle is made up of three sides and three angles, and the six pieces of information derived from these are the information that determines everything about the triangle, that is, the DNA of the triangle.

--- p.109

Then one day, a straight line passed through the circle.
I felt a sense of encounter with something, warmth, comfort, and comfort.
To soothe my regret, I tried to remember the point where the circle met the straight line.
At first, they met at one point, and as the line moved, they met at two other points, and eventually they met at a point in the middle of the circle.
The first encounter with circles and straight lines began at A0 and ended at A4.
Although the circle and the line have parted ways, we decided to name them to remember their meeting.

--- p.117

The circle is a mature shape that can create beautiful relationships while maintaining perfect harmony with other shapes.
In that sense, the circle is the shape of perfect shapes and the dream and hope of all shapes.
Right triangles with the same hypotenuse or quadrilaterals with opposite angles summing to 180° can also be combined to form a circle.
In that sense, I think it could be said that the circle is the romance of all shapes.
However, the circle does not ignore or reject the triangle or square, thinking that it is better than itself.
Just embrace them.

--- p.130

Each of the three points has the potential to become a triangle or a circle, but that power is invisible to the eye.
But just because you can't see it doesn't mean it's not possible.
Sometimes they exist alone and live as a single point, and sometimes they join forces to form a triangle.
And you can make a circle by maximizing the possibilities.
At this point, what we need to create a circle is the help of a perpendicular bisector.

--- p.137

In fact, there can be numerous strings within a circle.
Some strings are very short, and some strings are very long.
Perhaps the short strings complained and grumbled about their own shortness? The circle must have been aware of that discontent. The circle's solution, which encompassed everything, was to have that string meet another string.
It is the product of the lengths of the line segments divided by the intersection point where it meets another chord and the product of the lengths of the line segments divided by the other chord that intersects that intersection point.

--- p.187