Most stable form in two dimensions
You don't need to be a mathematician to understand why combs are the most stable shapes. A small experiment is enough and it becomes understandable.
What you need:
- wooden stick
- adhesive strips
Build unstable and stable shapes
Make yourself clear which form is more stable by building the following figures from the sticks
- Cut the sticks into 10, 5 and 3 cm long pieces.
- Connect two sticks 10 cm long and two sticks 5 cm long to form a square with the sticks of the same length facing each other. You should connect the sticks in such a way that you do not stick sleeves over the sticks at the corners made of adhesive tape.
- Connect 3 sticks of 10, 5 and 3 cm in the same way.
- Now do the same with 3 sticks that are 10 cm long.
- Make 10 of each triangle.
Difference between rectangle and square
In geometry you may sometimes come across shapes that you see very differently in everyday life...
Find the most stable figure
- Now look at the shapes you made. You will immediately notice that the square is not stable. You can the angle postpone. If you give a side press, the square just folds away.
- It looks a lot better with the triangles, if you press against the edge of a triangle, then nothing moves. Because in a triangle there is a concrete relationship between side lengths and angles.
- A triangle is z. B. Conceivably unsuitable as living space, because the very small angles mean that only part of the inner surface can be used. Try to lay shapes that result in a large stable shape without the instability observed with the square.
- You will surely get a honeycomb shape after a few tries with the triangles if you put 6 of the equilateral triangles together. This is also the most stable form.
Advantages of the honeycomb shape
A figure with six equal sides is an equilateral hexagon. In this figure there are very concrete angle relationships.
- The interior angle between two adjacent sides is always 120° because it is made up of the two 60° angles of the equilateral triangle.
- Put two hexagons together on one side, then two of the 120° interior angles will be adjacent. The remaining angle to the full circle of 360° is therefore 360° - 120° - 120° = 120°. So you can add another hexagon at this point.
Due to this angular relationship, structures consisting of such honeycombs cannot shift. So it is the most stable form in the two-dimensional realm.
How helpful do you find this article?
