These are the photos taken by students from IES Trassierra

polar rose

Author: María Sánchez Donoso
Description: in this image we can see a flower that nobody would think about it could have mathematics but there is the polar rose.
In mathematics, polar rose is the name that all the members of a family of equation curves receives r( θ)=cos(kθ) for resemblings a flower of petals.
From what we can see that in nature we also find mathematics and in all segments of life.

Alcazar of Seville

Autora: Rafi Tardáguila Alcaide
On its walls it represents figures such as rectangles, squares, triangles and some arch.

Fundamental pillars

Author: Marta Valenzuela del Río
Rank: cultural heritage
Description: In this photo we can see the part of mosque of Cordoba. It's formed by axial symmetry which is a circle within a square.
In the corners of the square there are some portraits of some evangelical characters

Blueprints

Author: Luna Expósito Hidalgo
Category: General mathematics
Descrption: The picture is written on how the society since the most easy, that could be the order of the streets, use some mathematical blueprints to build the floor and the wall using the geometry and that's figures.

Orange to Fibonacci

the fibonacci law/fibonacci succession is the succession of numbers which, starting with unity, each term is the sum of the previous two, and this can be seen in the points of the trees, which go up little by little, to the top

Autor: Manuel Reyes Serrano

incubated houses

Houses with the shape of cubes

Autor: Manuel Reyes Serrano

The ``Sitting-down-mosaics´´

benches decorated with mosaics

Sundial Complexity

Photograph taken by Mario Calvo, 1st year BACH SCIENCES
Topic: The photo shows a southern vertical sundial. Vertical sundials are tables that are positioned perpendicular to the ground and that have a gnomon (the needle that casts the shadow) that points to the different cardinal points, so that the shadow forms angles with respect to the vertical line. In southern sundials (like this one), the gnomon forms an angle equal to the colatitude of the place (90 degrees - latitude) with the table. In this case it is approximately of 53 degrees, since the latitude of the place was approximately 37 degrees and a half. gnomons in vertical sundials are always placed parallel to the earth's axis.

Natural Fractals

Photo taken by Irene Calvo 2nd grade ESO B.
A fractal is a geometric object whose fragmented or apparently irregular basic structure is repeated at different scales It is a word derived from the Latin "fractus" that means broken or fractured. The key mathematical property of a genuinely fractal object is that its fractal metric dimension is a non-rational number The following characteristics are attributed to a fractal geometric object. It is too irregular to be described in traditional geometric terms. Its shape is made of smaller copies of the same figure.

Everything a door hides

Photo taken by Irene Calvo 2nd grade ESO B.
I have chosen this photograph especially because of the symmetry but also due to the straight lines that are positioned parallel to each other, because of the circumference in the door and due to the different decorations. Even the stairs of the house have the shape of a quadrilateral.

Rocky Maths

Photograph taken by Mario Calvo Hernández, 1st year BACH SCIENCES
Topic: In this photograph, taken near Zuheros, you can see two mountains that meet at their skirts, forming a hole through which you can see the town (Zuheros) and the countryside. This gap forms an angle of 37 ° that is impressive to the eye and shows us that we can find mathematical elements anywhere, and that even nature itself hides mathematical elements.

Starry Fountain

Photograph taken by Mario Calvo, 1st year BACH SCIENCES
Topic: In the photo you can see a fountain that is located in a viewpoint in Iznájar, Córdoba. The fountain is shaped like an eight-pointed star (tartessic star). A tartessic star is formed by superimposing 2 equal squares and turning one 45 °. This star is also known as magic star for the reasons I will explain:
-If we took numbers from 1 to 2n (where n is the number of corners of the star), these could be placed at the corners of the superimposed squares and at the intersections between the squares so that, by adding up 4 numbers placed on the same line, the result would always be the same. This result is known as magic constant. The magic constant (M) can also be found using the formula M = 4n + 2.

Finding me

Author: Verónica Marín Santos
Category: General mathematics
Description: We can see the train lanes, which form parallel lines, and in the grid we can see squares or rhombuses and the buildings look like rectangles.

Getaway

Author: Verónica Marín Santos
Category: Mathematics in cultural heritage
Description: We can see the arches, which look like semicircles, these are made of bricks which are rectangles. Also in the fence we can interpret parallel lines or a succession of these.

A bucket full of math

Author: Álvaro Alcántara
Category: General Mathematics
Description: In this photo you can see a rubic cube, which is full of mathematics, as combinatorics, in this case there is a combination of colors which is understood as correct, in the cube you can made 43,252,003,274,489,856,000 different combinations Written in a more mathematical way, that number is (3 ^ 8 8!) (2 ^ 12 12!) / 12.
It is impressive to see how such a simple thing is both complex, full of combinations, trigonometric figures, etc.

The Four of the Birds

Photograph taken by Mario Calvo Hernández, 1st BACH Sciences
Topic: In the photo you can see a piece of polychrome talavera pottery with animals. The photo was taken in the Cordoba municipality of Iznájar. This image stands out mathematically for its easy to perceive symmetry,that is even and axial. Another aspect is the proportionality between the two concentric circles that surround the peacocks. Both have the same center. It is curious that the number 4 is constantly repeated on the tile: the number of colours used, the little birds, the sum of semicircumferences, there are 4 flowers inside the big peacocks´ circle and the 4 blooming plants inside the space between the concentric circles show 4 flowers each, not to mention that the square (which has four sides,) has four axes of symmetry.

Circular Symmetry

Author: Ignacio Alcántara Alcántara
Category: General Maths
Description: A few weeks ago I went on a trip with my family to a curious little town called Iznájar. The village seemed to be trapped in time, because of its ancient and deteriorated streets you could see magnificent geometric figures belonging to another era, perhaps much quieter and simpler than ours. Upon entering a small courtyard, there were other tourists admiring certain plants and flowers, but I noticed a beautiful piece of pottery that was stuck on a lonely wall. The piece had a circular shape, endowed with a symmetry full of cold and beautiful colors, and I was surprised by its perfect shape and beauty. How was it possible that such a simple piece was in turn so complicit and beautiful? Then I saw it clearly, that's the way mathematics is.

Lévy flight

Photograph taken by Mario Calvo Hernández 1st year BACH SCIENCES
Topic: In the picture you can see a group of passers-by walking along a zebra crossing in the city-centre in Córdoba. Some mathematicians from the University of Tokyo discovered last year that passers-by who cross pedestrian crossings in agglomeration tend to act collectively according to the Lévy Flight principle. When large groups of people stand on both sides of a street waiting and then find themselves walking towards each other, they tend to walk predictably. They do not take the most direct or fastest route, they take into account the people around. People tend to deviate from their straight route and face compensation between their speed and direction in order to arrive earlier. The Lévy Flight process is a mathematical description of a type of walk in which the pedestrian takes small steps, but then takes long steps following regular intervals.

triamgulation of structures

Author: Miriam Hernández Gómez
Category: General mathematics
Description:
In the photo We can see how the architecture uses the triangulation to create firmer and rigid structures because the balance is done directly from the base. A triangulation is a structure formed by triangles. It used because it is the only polygon that can´t be deformed.

Primary Hexagonal Cells

Author: Miriam Hernández Gómez
Category: General mathematics
Description:
This photography shows a honeycomb in the nature. And it shows how nature uses mathematical structures, for example in this case like a hexagonal shape, which is composed of six sides. This structure that We find in the honeycombs makes it lighter and stronger. In addition, another charasteristic of these forms is that they help take advantage of the maximun possible space with the least material used.

The swimming pool

Author: Julio V. Muñoz Staarthof
Description:
A Dutch woman decided that when her son turned three years old he had to learn to swim at a swimming club called Sport Club Vista Alegre. In Spain there are many drowning accidents and she wanted to avoid this.
After some years the boy grew up wonderfully because of the swimming and he continued his adventure. Athough he had to spend hours and hours waiting until it was his turn to start his trainning he didn't mind and began to observe attentively many details which nobody else unfortunately appreciated.
The swimmer who was a teenager now watched every detail within a universe of details.
In this photo, there aren't just mathematic components but they are also connected to his memories.
Which mathematic elements can you find in the photo?
Why tell them?
The best thing is to discover these details for yourself and without someone telling you the story.

Cordoban Proportion

Author of the photograph: Daniel Cebrián Castillo.
Field: Mathematics in Cultural Historical Heritage
Photo title: Cordoban Proportion
Brief explanation of the mathematical content:
The image, taken from the dome above the mihrab of the Mosque-Cathedral, shows the transport of the radius and the octagon side, to form a rectangle of Cordoban Proportion. This proportion was discovered and studied by the architect Rafael de La Hoz, in the study of the reasons in the dimensions of the Mosque and other Arab designs of Córdoba. The Cordoban Ratio corresponds to the relationship between the radius of the circumference that circumscribes a regular octagon, and it's side, being approximately 1.306562964.

Fractal's in the street

Author of the photograph: Daniel Cebrián Castillo.
Category: General Mathematics
Photo title: Street Fractal
Short explanation of the mathematical content:
The photograph of a tree located on Paseo de la Rivera street, tries to show the similarity of the division of tree branches and a fractal. Fractals are geometric objects whose basic structure is repeated at different scales. For me, the basic geometric structure of a tree is a segment, and more segments start from it; it is true that for a fractal to be considered, each segment should be divided by the same part and in the same number of segments, but I consider that it exists a aprecable similarity. Some famous fractals are the Mandelbrot Set or the Sierpiński Triangle.

Torricelli + Fibbonacci = Art

Author of the photograph: Daniel Cebrián Castillo.
Filed: Mathematics in the Historical Cultural Heritage.
Photo title: Torricelli + Fibonacci = Art.
Brief explanation of the mathematical content:
This photograph has been taken in a nave of the Mosque-Cathedral of Córdoba, of the decoration of the end of the vault of a nave. The mathematical motifs of a Torricelli Trumpet (held by the central angel of the motif) and of spirals that resemble the Fibonacci Spiral or Golden Spiral have been highlighted. The whole set is in a, more than used in Christian scenes, isosceles triangle shaped composition. The Torricelli Trumpet, which presides over the motif, is a body of revolution of the 1 / x graph around the x-axis, with the curious property of having infinite surface and finite volume. For more information I recommend the video ‘Mathematical apocalypse!’ From the Derivando YouTube channel.

Pentris

Author of the photograph: Daniel Cebrián Castillo.
Category: General Mathematics.
Photo title: Pentris.
Brief explanation of the mathematical content:
The photograph of some street tiles has been selectively colored to represent a tiling of pentominoes; The pentominoes are polymorphs of the polyimino class, and specifically consist of figures composed of five equal squares joined by their sides. I invite the spectator to extract the 12 existing pentominoes and tessellate a rectangle of 60 square units.

Hilbert's Infinite Hotel

Author of the photograph: Daniel Cebrián Castillo.
Category: General Mathematics.
Photo title: Hilbert Infinity Hotel.
Brief explanation of the mathematical content:
The photograph has been taken in the surroundings of Av. Del Gran Capitán Norte Vial, capturing a building. It has been added straight lines that would continue the David Hilbert Infinity Hotel, and a series of transformations with matrices have been applied to the text box that gives title to the photograph, to give the impression of perspective. The Infinite Hotel is an abstract construction devised by the German mathematician David Hilbert, and which brings paradoxical concepts related to the transfinite cardinals of Georg Cantor to intuition. There are many complete stories about this hotel easily accessible through the internet, but I recommend the video of Quantum Fracture ‘The Infinite Hotel’.

Parallelism

Author: Antonio Cosano
This is a photograph that indicates the parallelism of these rows of rocks, the parallelism of the lawn and the square.

The Mosque Cathedral of Cordoba

Eva Caballero Rodríguez 4ESO Sciences
Category: Mathematics in Cultural Historical Heritages
This impressive structure is full of geometric mathematical for all the shapes it has: roof triangles, knit arcs, rectangles, circles, squares and countless figures.

The splendor of the rainbow

Eva Caballero Rodríguez 4ESO Sciences
Category. General
The mathematical content of this photograph is, of course, concentrated in the rainbow, because of its semicircular shape, but also in the composition with which the apartament is built. Where you can see geometric components such as triangles, rectangles, semicircles, parallel lines, squares...

Symmetry

Eva Caballero Rodríguez 4ESO Sciences
Category: Mathematics in Cultural Historical Heritage
We can observe the geometry of the houses of the town of Almodóvar and in turn thet of the castle itself, which is the protagonist of the photo, in unison, if we divided the image in half we could see he idea of symmetry.

Luminosity, flora and composition

Eva Caballero Rodríguez 4ESO Sciences
Category: General Mathematics
In the image you can see a house with lively concept. This is located in Ayamonte, Huelva. The structure contains several rectangles and parallel lines that can be seen both in the window and terrace bars and in the roof beams.

Symmetry of time

Photography author: Ahinoa Sánchez 4ESO
Category: General Mathematics.
We can see how the 12 sectors of 30 degrees form a perfect circle.

Axial simetry

The maths in the photo are in the axial symetry you can see in the puddle.In axial symmetry the same phenomenon occurs as in an image reflected in a mirror.