Here the authors investigate whether there are mathematical inaccuracies of perspective in artists' paintings that are undetectable with our naked eyes. Using the cross-ratio method, they find that there are three significant errors in various famous paintings which increase as the structures in the paintings recede from the viewer.

Here recognizing the importance of urban green space for the health of humans and other organisms, the authors investigated if mathematical modeling can be used to develop an urban greenery management plan with high eco-sustainability by calculating the composition of a plant community. They optimized and tested their model against green fields in a Beijing city park. Although the compositions predicted by their models differed somewhat from the composition of testing fields, they conclude that by using a mathematical model such as this urban green space can be finely designed to be ecologically and economically sustainable.

In this experiment, the authors modify the heat equation to account for imperfect insulation during heat transfer and compare it to experimental data to determine which is more accurate.

This study aimed to predict and explain chaotic behavior in the Mandelbrot Set, one of the world’s most popular models of fractals and exhibitors of Chaos Theory. The authors hypothesized that repeatedly iterating the Mandelbrot Set’s characteristic function would give rise to a more intricate layout of the fractal and elliptical models that predict and highlight “hotspots” of chaos through their overlaps. The positive and negative results from this study may provide a new perspective on fractals and their chaotic nature, helping to solve problems involving chaotic phenomena.

The sequence of nitrogenous bases that make up the DNA of organisms can contain hidden mathematical sequences. Here the authors used BioPython, a programming tool, to find an organism that displays Gijswijt’s Sequence in its genome. In this manner they found that the common carp best displays Gijswijt’s Sequence in its genome.

In this study, the authors use existing mathematical models to how high school athletes pace 800 m, 1600 m, and 3200 m distance track events compared to elite athletes.

This study examines the higher harmonics in an oscillating string by analyzing the sound produced by a guitar with a spectrum analyzer. The authors mathematically hypothesized that the higher harmonics in the series of the directly excited 2^nd harmonic contain the alternate frequencies of the fundamental series, the higher harmonics of the directly excited 3^rd harmonic series contain every third frequency of fundamental series, and so on. To test the hypotheses, they enforced artificial nodes to excite the 2^nd, 3^rd, and 4^th harmonics directly, and analyzed the resulting spectrum to verify the mathematical hypothesis. The data analysis corroborates both hypotheses.

In this study, the authors test whether a gravity vehicle, which is a vehicle powered by its own gravity on a ramp, could be designed to move faster when mathematical calculations for optimal mass and center of gravity were applied in the design.

These authors mathematically deduce a model that explains the interesting (and unintuitive) physical phenomenon that occurs when water falls.

Bubbles! In this study, the authors investigate the effects that different materials, temperature, and distance have on the formation of water bubbles on the surface of copper and steel. They calculated mathematical relations based on the outcomes to better understand whether interstitial hydrogen present in the d-block metals form hydrogen bonds with the water bubbles to account for the structural and mechanical stability.