This article provides a comprehensive survey of the foundational structures and theorems in real projective geometry. Beginning with the construction of projective space via homogeneous coordinates and affine charts, we develop the language of incidence, duality, and subspace intersections. We then explore the cross–ratio and its invariance under -actions, followed by a precise statement and proof sketch of the Fundamental Theorem of Projective Geometry. Finally, we present the classical incidence theorems of Desargues and Pascal-complete with coordinate proofs and geometric interpretations-and discuss extensions to finite fields, complex varieties, and modern applications in computer vision.

This article discusses the main approaches and tools for data visualization in Python, a popular programming language in the field of data analysis and science. Data visualization is an important step in analytical processes, allowing you to clearly present information, identify trends and relationships. Python offers a wide range of libraries for creating graphs, charts, and interactive visualizations, including Matplotlib, Seaborn, Plotly, and Bokeh. The article also provides examples of practical application of data visualization, from time series analysis to interactive and animated graphs. The advantages and limitations of Python for data visualization are considered, as well as prospects for its further development in this direction.

In the field of education, it is widely recognized that individuals have diverse learning styles, and one prominent style is visual learning. Visual learners thrive when information is presented in a visual format, such as images, diagrams, and charts. When it comes to teaching English as a second language, incorporating visual elements into the instructional process can greatly enhance the learning experience for visual learners. This essay explores the benefits and strategies of working with visual learning styles in teaching English.

This article explores the effectiveness, merits, and cons of digitalizing education. Furthermore, digital technologies have the potential to influence student performance and motivation. Some of their advantages include the potential educational value of digital technologies in foreign language teaching, recommendations on techniques for incorporating digital technologies into the educational process for work, and independent work organization of students and learners. Digital education creates new learning opportunities by engaging students in an interactive environment and utilizing hybrid tailored courses and creative learning methodologies.

In the article are using of visualization in English lessons analyzed. Information about types of visualization is given.