A geometric song

Looking in YouTube I have found this video about a teacher who creates a song to teach the straights and angles. I think it's a very good idea because it is very difficult for children to forget what each kind of angle is. It's much easier to memorize.

Benefits of learning by singing:

- Learning by singing reinforces memory. Do you remember what learning the multiplication table with a song turned out to be more enjoyable? We must take advantage of the fact that some linguistic structures are fixed more easily in our memory if they are accompanied by the rhythm of music. In the same way, it is a good idea to learn the names of the rivers through the songs and look for rhythms between some words and others.

- Benefits for the artistic expression of the little ones. Many times, children make drawings based on a children's song. For example, the popular song "I have a doll" can make children's imagination fly and create drawings that decorate their class or their room.

- Help to organize and better coordinate the movement of children. When they clap their hands or a song is danced, the child works the rhythm together. If a musical instrument is used, the touch is being enhanced since each of them is different and requires different ways to handle it. Do not leave the same feeling in the hands a triangle, a flute or a tambourine.

Music excites us. Thanks to the lyrics of a song, we can get excited or improve our mood. Music therapy works a lot on this aspect. It's amazing how music can help us channel our emotions.


- Singing while learning facilitates social relationships between children. The laughter that occurs when children sing a song together helps them feel more united and have good times together. On many occasions, the children have to work together a song, prepare the stanzas, explain to each other how they can sing it ... it helps them, in short, to create bonds of union between them, and in a very funny way.

Why geometry in primary education?

First of all, we must reflect on the reasons for teaching geometry. Some teachers are based on the areas and volumes of bodies, for example. The teacher must be clear about why, and that will make more accurate decisions. 

One reason that all teachers have to take into account is that it is in our immediate environment, just look at it. In addition, it is used in everyday language: the street parallel to that, the spiral staircase. It also serves to study other topics in the mathematics, for example, a geometric model of the multiplication of numbers or algebraic expressions is the calculation of the area of the rectangle. Finally, it allows the student to develop his/her perception in space, his/her capacity for visualization and abstraction, his/her ability to elaborate conjectures about the geometric relationships in one figure or between several and his/her ability to argue when trying to validate the conjectures he makes.

In the next video we can see other reasons:

Geometry and football

Every day we can observe that the spaces that surround us are different that is to say they have a measure, in our chosen subject that is "The geometry in sports", it is enough to leave the classrooms to the school field to see that they are not The same basketball court as the football lounge, even the balls have different measures as well as throws.

Geometry being a part of mathematics, a subject that sometimes can not be understood, now we know that it is very important even in the practice of sports.

Geometry is one of those topics that do not seem to matter much at all, like mathematics. But the truth is that in sports they use geometry a lot.

Geometry and football



Football is the most played sport in the world also its physical space is related to geometry, it is played in a rectangular field of natural or synthetic grass, has the field divided into two parts as in basketball has a divided circle in the center, on both sides has the goalkeeper or goalkeeper with a net that serves to make goals. The field has a measurement of 90 to 120m in length and 45 to 90m in width.


Formerly, the ball had the shape of a truncated icosahedron, now it has a sphere.

Geometry in nature

Circular and spherical shapes abound in nature, we can see flowers, fruits, celestial bodies,
among many other things that adopt these forms, another side is difficult, if not impossible, to
find objects in nature living organisms that adapt perfectly square shapes or triangular.

A perfect circle is relatively easy to build, but make triangles and square not so easy.
In nature we can find various geometric shapes, in the figure we observe star-shaped flowers,
although the sides of the flower (edges of the petals) are not totally straight they can be
associated with an abstract idea so that it can be said that the flower has ten sides and the same
number of angles (five external and five internal).

All forms present in nature can be associated with abstract ideas (existing only in the mind of the
thinker) some objects have difficult forms to describe as a stone or mountain for example, that by
its shapes irregular ones can not be associated with any of the geometric figures regular (triangles,
squares, circles, polygons, etc).

The pine tree, belongs to the family of conifers, usually grows from regular form,
said tree has a conical contour that reminds us of the one referred to figure with which we
associate the mentioned tree.

Origin of the geometry

The word GEOMETRY comes from the ancient Greek: means "measure of the earth".

The ancestors of the current geometers were the surveyors of ancient Egypt, who had been entrusted with the task of restoring property boundaries, which had been erased by the water due to periodic flooding of the Nile.



It was Egyptian and Babylonian architects who built temples, tombs and pyramids clearly geometric, and the first navigators of the Mediterranean used basic geometric techniques to orient themselves. These civilizations made practical use of numbers without being clear about the concept of number or mathematical theories, and used the practical properties of lines, angles, triangles, circles and other figures without using a detailed mathematical study.



Thales of Miletus, in the sixth century BC, was the one who started Greek geometry as a mathematical discipline, the first mathematical discipline.

The book "The Elements" by Euclid, from 350 a. C. is the first written treatise on Geometry. For Euclid and for many generations of subsequent mathematicians, Geometry was the study of the regular forms that could be observed in the world. Currently, this study is called Euclidean Geometry or Metric Geometry.

Archimedes and Apollonius were also important figures in the Geometry of the ancient world. The first analyzed exhaustively the conic sections, apart from his famous calculation of volumes of revolution figures. Apolonio worked in the resolution of tangencies between circles, as well as in conic and other types of curves.

In the Middle Ages, mathematical science has a boom in the Arab and Hindu world, but is more focused on astronomy. It is not until the Renaissance that the new needs of art and technology push humanists to study geometric properties in order to obtain new instruments to represent reality.

These systems of representation (which make up what we now call descriptive geometry and we will see in other examples of this series) are no more than formal ways of expressing three-dimensional reality in flat documents, and today they are essential methods for transmitting information between the different levels necessary for the execution of any project.

Geometry in fashion.

Geometry will always be present in the world of fashion. They have always been relevant, circles, squares, stripes, etc. Using the geometry to fit the figure is not an easy task. We do not realize that geometry is very much linked to our life and also to fashion. Even the Romans used geometry for their clothes, with an elliptical-shaped toga. The Greeks also wore it on their embroideries. 

In this video we see how geometry is present in fashion.

Islamic Geometry

Geometry is a very important element in Islamic art. We can find all kinds of geometric figures in mosaics made by Muslims, in architecture and in ornaments.

Where more geometric figures are found is in the tiling. The tiles are formed by small pieces of ceramics with different colors and shapes that together forms geometric shapes of great complexity. In the Alhambra there is a great variety of mosaics that advance in complexity over time. In the Nasrid art exist thus simple compositions, based on the repetition of one or two figures; and complex compositions, in which different motives move and rotate to generate  new geometric forms at a higher level.




The geometrical frameworks of the decoration of Hispano-Muslim art are based on three key elements to tessellate the plane, that is to cover a surface using polygons without leaving gaps. Specific:

1. A polygonal motif as the basis of the compositions.

2. The creation of compositions through isometries, that is to say, movements of the plane of said motives conserving their proportions. This is carried out by:

Translation: moving to a new fixed position without changing the orientation.
Rotation: direct rotation of the motif on a fixed point.
Symmetry: reflection or inverse mirror image of the motif.

Slipped symmetry: translation of the reflection on the same axis without a fixed point.

3. The linear growth of such compositions that could be continued to infinity.


These tessellations can be done through polygonal motifs, simpler to make those that abound in the tiling of the Alhambra; or of non-polygonal motifs. These second ones imply a greater mastery because it supposes a more laborious process of creation to obtain non-polygonal forms that fit together. As an example of non-polygonal shapes, the most popular is the trisquel or "bow-tie" shape, created through the transformation of an equilateral triangle.