On the occasion of International Mathematics Day on March 13, 2026, Associate Professor of the Department of Higher Mathematics and Statistics Halyna Dmytrivna Urum conducted a field practical lesson with mathematics students of the MI11 group in the Library of Ushynsky University. The topic of the lesson was the study of mathematical patterns in the structure of architectural structures. The objects of analysis were engineering structures of staircases, vaults of basements.
During the lesson, the geometric and physical parameters of arched structures were analyzed as a structural element that implements the properties of a quadratic function. The arched shape ideally converts the vertical load of the building into compressive forces, which allows fragile materials (brick or stone) to hold a huge weight without destruction. Due to the properties of the parabola, arches work as giant reflectors. Students practically analyzed the effect of the “whispering gallery”, where sound is focused at certain points, allowing even the quietest words to be heard at a great distance.
Using the example of staircases, the application of geometric methods for calculating the parameters of the kosour and determining the optimal angle of inclination for safe operation was demonstrated.
Special attention was paid to bridge structures. Students learned that the main cables of bridges under load take the shape of a parabola. This fact allows us to accurately calculate the length of each suspension.
The lesson program integrated mathematical modeling with the analysis of historical and architectural heritage. Library specialists Lada Dmytrivna Marynchenko and Iryna Volodymyrivna Panchenko presented a historical sketch of the architectural complex, which today houses the Ushynsky University Library. In particular, attention was focused on the fact that these buildings are part of the historical area of the city, built in the late 19th and early 20th centuries, which allowed students to trace the evolution of engineering approaches.
The results of the practical session confirmed the fact that mathematics is a fundamental tool for ensuring the reliability and functionality of architectural and engineering objects. The mathematical apparatus allows architects and engineers to carry out accurate design of high-strength buildings and complex structures, which directly affects the safety and comfort of the urban environment.
