Abstract: With the development of communication means, mobile devices, the use of the Internet is increasingly moving from stationary computers and laptops to mobile devices, tablets, etc. As a result, site developers face an additional task - the development of responsive design. So that the attractiveness of the developed resource can be maintained regardless of the screen size of the user's gadget. As a rule, the problem of adaptability is solved with the help of style tools, program modules, media queries. However, the use of such methods gives a result that does not fully meet the requirements of users. Especially when it comes to the font size of text and headings. The task of adapting the font size of the text was divided by the authors into two subtasks: the adaptation of the font size of the main text of the content and the adaptation of the font size of the headings. The division was due to additional conditions that are imposed on the headings, such as limiting the number of lines, matching the sizes of several headings of the same level. The authors conducted a study of consumer expectations regarding the range of acceptable font sizes and the dynamics of their modification when changing the size of the container containing the text. Based on the survey results, the parameters of the mathematical model of dynamic adaptation of font sizes to block sizes were determined. The software implementation of the obtained mathematical model showed the parameters of the processing speed and quality of the displayed text in the range of user requirements. The use of the obtained mathematical model, algorithms and program texts that implement them will allow developers of Web resources to create better products that meet the needs of users in less time, which means that their use has economic efficiency
Index terms: mathematical modeling, web application development, responsive design.


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