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.

Geometry in Holy Week

As I said in my presentation, I am passionate about Easter, so I want to dedicate my first entry to talk about the geometry we find in their costumes or belongings.

A very typical thing in Holy Week is the so-called "Paschal Candle", carried out by the Nazarenes, illuminating the procession. The candle has a cylindrical shape.

We also find, in the most typical outfit in the Holy Week, the "hoods", these are carried by the Nazarenes on their heads, and has a conical shape.

Something also very typical in Easter is the "banner", in which the shield of the Brotherhood appears and is usually embroidered in gold. We could say that it is formed by a triangle and under a semicircle.

In the next image we see a throne of a virgin with a Palio. We could say that as a whole it has the shape of a prism. Also, it is made with rods that as we see are also cylindrical. It also has the so-called "backstage", we see them in the Palio and are embroidered fabric, for example, in the front we see three joints in the shape of a pentagon.

Finally, I want to show a cross, which is the image of Christ of Nazareth. There are cylindrical or prismatic shape.

About me

Hello! My name is Andrea, I'm 21 years and I'm from Vélez Málaga, a small city of Malaga.
I love carnival and easter in Andalucia and my hobbies are dancing and listening to music.

I will use this blog to share information and things that I find interesting about geometry for the "Geometry didactics" subject.

I study this subject in the Primary Education degree. I`m studying to become a teacher because I have always wanted to teach, even when I was a child I imagined that I was a teacher with my small cousins.

About geometry, it is a subject that has been difficult to me, I think that I'm better in other parts of the mathematics. On the other hand, I think that is a very interesting subject because the geometry is sorrounding us in our lifes. We see geometry in construction, fashion, nature,etc.