Attila,
One question.
What is the purpose of a triangle in bonsai design and also in a display?
Will
The triangle is the module of spatial organization in Japanese aesthetics for several reasons:
1)It is the simplest two-dimensional shape, generated by the fewest points. This is very important in a culture where simplicity is key.
2)It is the most stable form of stransmitting forces from one point to another (structural engineers use it a lot in their designs, such as bridges, buildings, etc.)
The three sides of a triangle represent the three forces: horizontal, vertical, and diagonal. You can imagine the sides as vectors.
3)The triangle has a powerful capacity to create a sense of movement. We start with the perfectly stable, equilateral triangle that has no movement (see the pyramids, sitting Buddha - these are symbols of stability) and, as you change the length of the sides, you start creating movement. It is a very versatile tool to create visual movement.
These are just a few. There are others, such as the power of number 3 in the history of mankind, linking heaven to earth, etc, but these are more or less culturally influenced reasons.
Naturally, the triangle is not a Japanese invention, but they have made the most effort in incorporating it in their aesthetics and also articulated its use from a practical standpoint.