4 December 2023

Mathematical photography allows us to appreciate the beauty of mathematical shapes and patterns that often go unnoticed in everyday life. Through these, we can discover the aesthetics of symmetry, fractal geometry and other mathematical concepts. Next, we explore more fully about what this discipline is.

## Definition of Mathematical Photographs

Is the still image that through photo techniques, It shows us the patterns that contain the elements of the context that surrounds people, and whose content is directly related to aspects of mathematics. That is to say, that it is the photograph that contains some characteristic of this science, such is the case of arithmetic, geometry, statistics or numerical calculation. It is not just a simple portrait of some structure.

It is also called a branch of geography, since it focuses on the study and visualization of information of this type. Always in it you will find symmetrical or geometric figures, numbers, mosaics, lines, series, angles, points, fractions or curves. This does possible to see it in any structure, for example, in buildings with designs that have some of the elements that were mentioned. It is a subgenre of photography.

Use mathematical concepts in order to devise interesting images and compositions, in which symmetry is a fundamental tool. Through it you can create patterns and geometric structures that come from objects. In this photographic branch there are types of symmetry: the axial, in which the image is divided into two parts by means of a central axis; radial, in which the values ​​of the representation are distributed around a point, and translation, in which the elements are repeated in a regular pattern.

Symmetry gives the possibility of being used in different ways: in the composition of landscapes, in architecture, abstract photography or in portraits. It also provides the ability to create images with great potential and attractive on view that explore the beauty and complexity of geometric shapes and repetitive structures.

## What are the characteristics of mathematical photographs?

The common features of this type of images are:

• Symmetry: A large number of them focus on precise patterns in specific directions, whether they are vertical, horizontal or radial.
• Contrast: he often uses contrasts of shape, texture or color, in order to create illustrations that make an impact.
• Pattern repetition: They are implemented in the elaboration of complete images, in which models are used in a repetitive way.
• Geometry: based on exact forms are built. In them, circles, squares, triangles are taken into account.
• Abstraction: Through a digital process, most of them are subjected to manipulation, which results in abstract images.

## What is the practical value of a mathematical photograph?

They are implemented and are very useful in object location and pattern detection by means of numerical algorithms within specific photographs. In addition, it is implemented in the registration, cataloging and documentation of works of art. In the development of topographic maps in the investigation of sciences such as geometry and physics.

## What are the elements that make up a mathematical photograph?

This is consists of elements that distinguish it:

• Perspective: It is a resource that is used to create three-dimensional effects in an image. It can be altered in order to generate sensations of depth.
• Patterns: Its use is useful for devising interesting, abstract and attractive images. They are found in objects produced by man and in nature.
• Fractals: They are a common element in this type of photography and are repeated at various scales, making use of them in the creation of detailed drawings with a level of complexity.
• golden ratio: It is a mathematical measure found in natural objects and forms that makes them aesthetically attractive.
• Motion: It is used in the design of dynamic and interesting images, and is captured with different techniques.

## What is the history and origins of mathematical photographs?

Its origin dates back to the 19th century, when experts began to use the technique in the study and registration of geometric objects. But it was French mathematician Édouard Lucas the first to use photography in these studies. In the Middle Ages, it was cartographic geographers who developed techniques for measuring distance and direction, and also for making maps with mathematical precision. Then in the era of exploration, between the 15th and 16th centuries, the techniques became more and more precise and one of the most influential geographers of that period was consolidated, Gerardus Mercator.

This expert developed a method to study the Earth in a plane that is used today called a Mercator map. Likewise, in the 17th and 18th centuries, changes in trigonometry and analytic geometry expanded capabilities. The geographers opened up the possibility of using mathematics in topography and morphology. Then in the 19th century, advances in statistics and spatial analysis gave way to the development of new mathematical disciplines and techniques. Since then, geography has continued to evolve and take advantage of the changes that occurred in computing, technology, data analysis and modeling.

These modifications have been carried out satisfactorily and have been used in mathematical photography to improve the experience of what is sought to be achieved. This is how the open XML office format is implemented by many experts to facilitate processes. These are open file and standard and is used in the representation and storage of graphics, spreadsheets, presentations, and documents. Although there is no direct relationship between it and photo math, it does facilitate the creation and presentation of images by using office software in the illustrations.

And in the same way, photo retouching is implemented taking advantage of technological resources, taking into consideration that it is a technique that is used to improve or modify images through editing. requires understanding the mathematical handling of the photo and also admits to improve it and make it more aesthetic. It is an essential tool because it allows the manipulation of the image and creates patterns and structures to improve the clarity and resolution of the photograph.

Another of the programs that is used is the PDF or portable document format, which in the field of this type of image is used in the creation of portfolios, catalogues, books and other kinds of digital files that include illustrations. It is indirectly related to the mathematical photo. Give the option of be used in the publication and distribution of photographic images, which are characterized by the inclusion of illustrations generated by these techniques. Mathematical photography can have various uses, such as scientific research, industrial process portfolios, and the creation of abstract works of art.

It can be used to document the attitude of complex systems such as quantum mechanics. In industry it is used to record manufacturing processes and flows of raw materials and in art to create abstract images. In general terms, mathematical photography focuses its development in exploring precise shapes and patterns. He uses strategic algorithmic techniques, with which he manages to make these images visually striking.