Geometrical Mosaics

Mosaics are the covering of the plane with figures, on a way that are no overlapping and that don't leave black spaces between them. The pieces that are used are called "teselas". 

There are a lot of forms of getting a mosaic. The most simple are formed by regular polygons of the same type (for example squares, regular hexagons or equilateral triangles), but also can be combined with other kind of polygons.

TYPES OF MOSAICS

• Regular Mosaic: There is a regular mosaic when it is only used a regular polygon.

  

• Uniform mosaic: In all the vertex concur the same regular polygons, and in the same order. 

  

• Non uniform mosaic: They are composed by regular polygons too but can't be repeated on the plane.

  

Games for geometry 2.0.

The "geoplano" is a  didactic resource very interesting to work with geometry, it is useful to introduce the geometric concepts on a hands-on way.  

With it we can construct geometric forms, discover the properties of the polygons and, also, solve mathematical problems. All in all, it is a essential tool to learn maths.

It was created by Caleb Gattegno an mathematician Egiptian in 1960, who was looking for a method to teach geometry on a more didactic way. Although, nowadays most of them are done in plastic, the original one was a wood squared board with cloves which can be hooked with elastic rubber bands.

Here you can see and example of how you can do a "geoplano" by your own. It is really interesting and you also can see how to create the different forms.

Geometry and its figures.

Throughout the time, simple figures had been used in art: the circle, the line, the triangle, the square and the spiral. Angeles Arrien, a cultural anthropologist, investigated and documentes some common characteristics in the cultural artistic shapes during some decades and she found the same figures in every type of art. She called these figures "Las cinco figuras universales".

Any fundamental form changes in its basic function, each one of them achieve an aim. A circle round freely, the lines travel around and cross with themselves, a triangle is secure while point to the sides, a square is a n immediately stable figure with four sides and a spiral roll up with herself with elegance. Because they are simple, they have the ability to rise constantly and to be used as construction elements of the nature and the human being world.

The circle is well-known as the mother of all figures because is the form from which all geometric shapes are drawn. 

The circle must be cloned to create the next figure. If you create a circle right next to the first one, with the same diameter you will have a duplicated circle. That represent an opportunity of connecting the two central points creating a line. The line can be moved only one direction. There can be also the possibility of doing a second line connecting the two superimposed circles, creating four right angles of 90º.

The triangle is really sure when is located on its base or when it is combined with upside down versions of itself, so that it is usually confused with a structural support of the construction of buildings and as a design of dimensional border.

The square and rectangles are probably the less interesting of the figures but they still being useful.

The spiral is a visual representation of the cyclic time in the space that is repeated constantly, but with a new cicle on each rotation. 

Geometry and Fashion

Patterns and geometry is always present in the world of fashion. It is not necessary create really complex geometric designs, you can create a really simple design and it will appear geometry on it.

Geometric patterns are always the most relevant in fashion design. Black and white squares, colourful circles, hexagonal shapes and we can forget lines. All these elements are able to be seen in the new collections of clothes. 

Rectangles, triangles, trapezoids, all these shapes inspire and make crazy all designers that makes everyone life much fun and interesting. Nowadays, we are so concerned about be fashion and follow trends. By using these clothes, we can be fashion and learn about geometry. In addition, if we know the shape of our body, we can know with kind of clothes suit us better.

But, how are we going to use geometry to create a design or find a dress that suits better our shape? It is not easy. However, we don't notice that geometry is strongly related with out daily life and, specially, on clothes.

There are some examples:

   

There aren't much people that, nowadays, buy clothes or accessories without thinking in the shape of the fabric, the style of the geometric shape, if it is going to make her/him elegant or if it is fashionable.

Due to this fact, people have started to investigate and analyse about the  influence of geometry in fashion and in the vestry. For example, the main types of clothes of Romans were a toga, a tunic and a cloak. The first one was made of white wool with an elliptic shape. They used geometric shapes because it was easier to cut and to produce many of them.

Geometry and Sports

Everyday, we can see so many spaces that has different measures. We only have to go to a basketball court to see that there are different shapes there, circles, squares, rectangles, etc.

Geometry and basketball.
As we can observe everyday on a school playground, the basketball court is a straight surface which has a rectangular shape with 28 meters on length and 15 meters on width. We can also see that it's divided in two identical parts, and in the centre there is a circle with 3,6 meters of diameter.

Geometry and tennis.
Even tough we can't see very often a tennis court, we know that it is a big rectangle divided in two rectangles that are littler. We can observe so many lines which are parallels and perpendiculars. These lines are used to delimit the service zone, each player court, etc.

Geometry and football.
It is the most played game in the world and its court also has relation with the geometry. It is also played on a rectangular place which is divided in two sections. It has a circle in the centre and two semi-circles in the goalkeeper zone. It has rectangles and parallel lines.

Games for geometry.

Many children think maths are not useful for their daily life, but mathematical games for primary education can help them to discover that numbers are also a source for fun.

Maths are very important to specify the distances between different objects, to know the areas of surfaces and volumes, to understand weights and capacities of containers and to calculate the time.

To learn a subjects as important as maths, there's any other way funnier than playing?

There are many students that for many reasons when they face maths get blocked. For this reason, I think by using games we can help them to understand them better and to even love them.

The following videos show games or materials that can help them to learn more things and to understand the geometric shapes. 

In this first video we can see and understand better 2D shapes. These sticks are really interesting for children as they can combine them as they want.

In this second video, using playdough and toothpick, children can learn the 3D shapes. The materials are used by them everyday.

The Origin of "Geometry"

Geometry (from Greek geo, "land"; metrein, "mesure"), a branch of mathematics which takes into account the proprieties of the space. On its more elemental form, geometry bear in mind metric problems, like the calculation of the area and the diameter of plane figures, the surface and volume of solid figures. Other fields of geometry are the analytics geometry, the descriptive geometry, topology, geometry of spaces with four or more dimensions, the fractal geometry and the non euclidean geometry.

The origin of the term "geometry" is a description of the work of the first geometers who were interested in problems with the size of the fields or with the construction of buildings. This kind of empiric geometry which emerged in the Ancient Egypt, was refined and systematised by the Greeks.

In the VI century B.C.,  Thales of Miletus started the Greek geometry as a mathematical discipline, the first one.

THALES OF MILETUS

In the book "The elements" of Euclid, from 350 B.C. is the written agreement of geometry. For Euclid and for lots of other generations of mathematicians, the geometry was the study of the regular forms which can be observed in the world around them. Nowadays, this study is called Euclidean Geometry or Metric Geometry.

EUCLID

Archimedes and Apollonius were important too in geometry in the ancient world. The first one analysed on a exhaustive way the conic sections, apart from his famous calculation of figures volume.

APOLLONIUS

Apollonius worked in the resolution of tangencias between circles, so as in the curves of conic figures and other types.

ARCHIMEDES 

Geometric Shapes in daily life

Nowadays, if we look around we can see many geometric shapes in simple objects. For example, if we see a pizza we can count 3 different shapes: square that is the box of the pizza, a circle which is the pizza and triangles which are the different pieces or divisions of the pizza.

              

A square is a plane figure which has four sides which are straight and the same length. The angles are right angles.

A circle is a round plane figure whose circumference consists on points equidistant from a fixed point.

A triangle is a polygon with three sides, three angles and three vertices. 

Introduction

Hello everyone! It’s me, Lucía Molina. I'm studying a Degree of Primary Education at the University of Málaga. In addition, I’m in the bilingual group, so that all the entrances will be in English.

In this blog I will sum up, collect and put interesting information related to the lessons of Geometry. I think that it will be fun if I write down some peculiar contents or facts in relation with this subject.

I will also use so many objects or things related to our real life, like for example, food, sports, fashion, buildings...

I hope you find interesting my blog and that you can learn something with it.

See you!