Symmetry

An object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:

• An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.

   

       

Example to practice in Primary Education:

• An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.

Example to practice in Primary Education:

• An object has translational symmetry if it can be translated without changing its overall shape.

Example to practice in Primary Education:

• An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.

The world's highest existing statues

Statue of Unity

The Statue of Unity is a monument dedicated to the Indian politician Sardar Vallabhbhai Patel (one of the founders of modern India). The total height of the statue, from its base, is 240 meters. The base has a height of 58 meters and the statue is 182 meters. It would be built with a steel structure, reinforced concrete cement and bronze cladding.

The Buddha of the Spring Temple

It is a statue in the municipality of Zhaocun in Lushan, province of Henan (China). It was built between 1997 to 2008.

It is 128 meters high, which includes a throne of 20 meters shaped like a lotus flower. If we also take into account the building on which it sits, the total height rises to 153 meters.

The Gautama Buddha of Laykyun Setkyar

It is a monumental statue that with a height of 116 meters, is the third tallest statue in the world. It stands on a 13.5-meter pedestal located in the village of Khatakan Taung, near the neighboring village of Monywa, in the province of Sagaing, in Burma. Its construction began in 1996 and ended in February 2008.

Ushiku Daibutsu

It is a statue found in Ushiku, Ibaraki Prefecture, Japan. It represents Amitābha.

This sculpture was completed in 1995; Its structure is made of steel and is covered in bronze. It is three times higher and thirty times larger than the Statue of Liberty.

Its dimensions have a symbolic reason: the 120 m of height (of which 100 are of the own statue and the 20 remaining correspond to the pedestal) are related to 12 rays of light that arise from the Buddha towards the world. And the dimensions in detail are also surprising: each eye measures 2.5 m; the ear, 10 m; the hands, 18 m each and their position means the acceptance of all the men of the world; and, finally, each finger measures 7 meters.

The Sendai Daikannon

It is a statue of the goddess Kannon located in the city of Sendai, Miyagi prefecture, it is the tallest statue of a goddess in Japan. Its construction was completed in 1991.

Its height is 100 meters. An elevator transports visitors to the top, from where you can contemplate the city of Sendai. The statue carries in its right hand the gem of the nyoihōju desires, while in the left it holds a flask of water.

The geoboard

The geoplano was created by the Egyptian mathematician Caleb Gattegno about 1960, who was looking for a method to teach geometry in a more didactic way. Although today most of them are made of plastic, the original consisted of a square wooden board with nails forming a weave, in such a way that these protruded and could be hooked elastic bands that will serve to represent the different geometric figures.

This consists of a square board of variable size (usually wooden) that has been squared and is determined by a number of these grids. It has a nail in each vertex which protrude about 2cm generally.
On the base, rubber elastic bands are placed that are fastened on the nails forming the desired geometric gums. With the geoplane, geometric shapes can be formed using said elastic rubbers; establish similarities and differences between parallelism and perpendicularity; use a graphic-algebraic language.

Due to its manipulative nature, it allows students a greater understanding of abstract terms, which often they do not understand, or generate misconceptions. With it we can not only measure polygon sizes (counting grids), we can solve mathematical problems, learn about areas, perimeters, etc. it is definitely an essential resource to learn mathematics.

The geoplane is a very interesting didactic resource for working the measurement because you must know how much the board measures to know which grid you have to make. It helps teachers to introduce the measurement in a manipulative way. It can be used with students of all ages, individually, in groups or the teacher can use it to show it to the whole class or to explain the class. On the other hand, this can be introduced at the beginning of primary school for the child to manipulate, play and learn by himself. At this stage it can be fun to make your own geoplane yourself.

The teaching process occurs in a creative way through group activities, in which the teacher asks questions directed by the teacher. In this way, it helps students to construct their answers and at the same time to ask their own questions, creating their own conjectures about a mathematical concept.


TYPES OF GEOPLANO

1. The orthometric geoplano (or square geoplano):
It is squared, the most frequent are those which have 25 points.

2. The isometric geoplano (or triangular geoplano):
It is triangular. The points are located at the vertices of equilateral triangles.

3. The circular geoplano:
It is a collection of points on a circumference that are spaced at the same distance. Normally it has 24 points. It allows to build regular polygons of 3,4,5,6,8,12 and 24 sides.
It also is useful to study the properties of the elements of the circumference and of the figures subscribed in it.