The problem of determining the slope at a point on a map using level curves has practical applicability in designing the roads. This problem is reduced to the problem of finding the shortest length segment through a point that connects two coplanar lines. Two methods to solve this problem are presented: a fast approximate method and a slower but exact algorithmic method. The results are compared at the end.

The paper aims to study a concrete structure, currently used in civil engineering, which has certain symmetries. This type of problem is common in engineering practice, especially in civil engineering. There are many reasons why structures with identical elements or certain symmetries are used in industry, related to economic considerations, shortening the design time, for constructive, simplicity, cost or logistical reasons. There are many reasons why the presence of symmetries has benefits for designers, builders, and beneficiaries. In the end, the result of these benefits materializes through short execution times and reduced costs. The paper studies the eigenvalue and eigenmode properties of vibration for components of the constructions’ structure, often encountered in current practice. The identification of such properties allows the simplification and easing of the effort necessary for the dynamic analysis of such a structure.

Human interference with the Earth’s climate cannot be ignored any longer. Renewable energy sources need utmost attention in all energy sectors. For buildings, geothermal energy for heating, cooling, and domestic hot water is a sustainable solution. Horizontal ground heat exchangers (HGHE) demonstrate promising results with low installation costs. Research is focused on increasing their thermal performances by structural improvements and ground thermal proprieties improvements, with little research on using auxiliary heat to increase their performances. A numerical model for an HGHE was established to investigate the effects of auxiliary heat sources on the performances of the HGHE. The results demonstrate that heat transfer into the HGHE increases the overall ground temperature at the end of the heating season by 138.50% compared with no heat transfer from auxiliary heat sources. The ground freezing period decreased by approximately 24.74% by having a heated basement, approximately 40.20% by transferring heat with solar thermal panels, and approximately 62.88% by using both auxiliary heat sources. The difference between the undisturbed ground temperature and the ground temperature with no auxiliary heat sources at the end of the season was 3.45 °C. The difference between the undisturbed ground temperature and the ground temperature with all auxiliary heat sources resulted in 0.92 °C.

The rural areas of Transylvania offer important resources for developing research in diversity of the cultural heritage. Many of these communities have seen great changes in demographics over the last 30-50 years, and important cultural heritage from previous generations is being lost in lack of understanding, human resources and willingness to preserve the value of our joint cultural heritage. The research seeks a digitisation approach to preserving and promoting the local cultural heritage, as well as a social science approach, which seeks to find answers to how one can be able to preserve, maintain and promote this cultural heritage, something which, according to the study hypothesis, can only be done if the communities see the benefits of doing so. The digital shift has the ability to create another level of understanding, opening a vast horizon for accessibility and progress linked with BIM technology. As an answer to dealing with the climate changes, degradation of the buildings due to natural disasters or more from the indifference of the young generations in regard of history inheritance, the study could be a valuable instrument in enhancing BIM-Heritage methodologies.

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