A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpiński Geometry †
Abstract
1. Introduction
2. Philosophy, Mathematics, and Art
2.1. Plato
2.2. Ancient Art and Cosmatesque Decorations
2.3. Other Cultural Environments Using Triangles
3. Mathematics and Geometry of Sierpiński Fractals
4. High-Frequency Applications
4.1. Resonance Frequencies
4.2. Antennas
4.3. Resonators
4.4. Further Considerations, Limitations, and Future Work for Microwave Applications
5. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Resonator | Resonance Frequencies [GHz] | ||
---|---|---|---|
Fres1 | Fres2 | Difference | |
C0 asym | 9.46 | --- | --- |
C1 asym | 4.42 | 7.98 | 3.56 |
C2 asym | 5.66 | 9.22 | 3.56 |
C3 asym | 7.18 | 8.94 | 1.76 |
C0 sym | 9.62 | --- | --- |
C1 sym | 4.34 | 7.82 | 3.48 |
C2 sym | 5.54 | 9.30 | 3.76 |
C3 sym | 7.38 | 8.98 | 1.60 |
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Marcelli, R. A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpiński Geometry. Fractal Fract. 2025, 9, 444. https://doi.org/10.3390/fractalfract9070444
Marcelli R. A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpiński Geometry. Fractal and Fractional. 2025; 9(7):444. https://doi.org/10.3390/fractalfract9070444
Chicago/Turabian StyleMarcelli, Romolo. 2025. "A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpiński Geometry" Fractal and Fractional 9, no. 7: 444. https://doi.org/10.3390/fractalfract9070444
APA StyleMarcelli, R. (2025). A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpiński Geometry. Fractal and Fractional, 9(7), 444. https://doi.org/10.3390/fractalfract9070444