This element is two-sided, and it has a tangram puzzle on one side, and a panel for learning about movement on the other side. All elements have a magnet and are movable, and they are attached to the panel with a cable.
Tangram is the best-known math puzzle, thousands of years old. Although there are not enough written records, it is believed that this ancient Chinese puzzle was the first mechanical puzzle. At the beginning of 19th century, tangram has become a trend outside of China and even the great general Napoleon used to relax by assembling tangrams. Although many different puzzles have been designed in the times of ancient Greece and the Roman empire, none of them is as famous as tangram. The Chinese name for the puzzle is ch’i ch’iao t’u („a genius set of seven parts“), while the name tangram was given to the puzzle by a toy manufacturer in the 19th century.
Tangram puzzle is an example of a tiling puzzle. Throughout history, tiling has occupied the minds of many great mathematicians, one of whom is the famous Greek mathematician Archimedes, as well as of many artists, one of whom is the famous Dutch graphic artist Maurits Cornelis Escher.
Panel for learning about movement contains six types of elements that can be arranged to compose interesting systems. We can insert the ball into the upper part of the system and observe how it moves through pipes and grooves.
Tangram puzzle is made by dividing a square into 7 geometric shapes: two pairs of mutually congruent isosceles right triangles, isosceles right triangle, square, parallelogram.
Tiling of a plane is a set of mutually disjoint geometrical shapes whose union makes up the entire plane. Tangram is an example of a tiling puzzle because the union of all seven geometrical shapes (without overlapping) forms the initial square whose side is 70 cm long.
The tangram puzzle is interesting precisely because by combining these simple 7 characters we can assemble different interesting shapes. Some of these shapes are drawn on the edge of the element itself and can serve as a template for stacking.
- Assemble one of the shapes that can be found on the edge of the element. Now try to assemble your own shape, one that has not already been drawn.
- How many triangles can be found among the tangram shapes? Which one of them does not have its pair (another triangle that is congruent to it)? What colour is it? Can you determine its surface? How many times is the surface of the smallest triangle smaller than the calculated surface?
- Among the seven tangram shapes, find a square and two triangles whose union is that very square.
- How many triangles are there with a side that is 70 cm long?
- Assemble a square using all seven tangram parts. The length of the side of that square is 70 cm, and the length of its diagonal is approximately 9.9 cm. Calculate the area of the largest triangle. What is the area of the square?
- How many elements do you have at your disposal? Form a system in which you will use all elements.
- Out of given elements, try to assemble a system in which the ball will rest. What elements will you use?
- Try to arrange the system in such a way that makes your ball go uphill for at least a small part of the way.
- Make two identical systems, composed of the same elements in the same positions. Throw a ball through one system, and a die through the other. What do you notice? Now try to throw two balls of different weights, each through its own system. What do you notice?
- Free fall is the movement of a body solely under the influence of gravity. Try to create a system where your ball will fall at a similar speed as the free fall speed.
- Try to arrange the elements so that the ball has a smooth path without skipping and bouncing off the elements.
