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An Analysis of the Mathematical Accuracy of Perspective in Paintings

Grewal et al. | Dec 13, 2019

An Analysis of the Mathematical Accuracy of Perspective in Paintings

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.

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Characterization and Phylogenetic Analysis of the Cytochrome B Gene (cytb) in Salvelinus fontinalis, Salmo trutta and Salvelinus fontinalis X Salmo trutta Within the Lake Champlain Basin

Palermo et al. | Jan 24, 2014

Characterization and Phylogenetic Analysis of the Cytochrome B Gene (<em>cytb</em>) in <em>Salvelinus fontinalis</em>,<em> Salmo trutta</em> and <em>Salvelinus fontinalis X Salmo trutta</em> Within the Lake Champlain Basin

Recent declines in the brook trout population of the Lake Champlain Basin have made the genetic screening of this and other trout species of utmost importance. In this study, the authors collected and analyzed 21 DNA samples from Lake Champlain Basin trout populations and performed a phylogenetic analysis on these samples using the cytochrome b gene. The findings presented in this study may influence future habitat decisions in this region.

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An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

Grewal et al. | Oct 05, 2020

An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

In this study, the authors sought to find out how many mathematical solutions there were to the Indian mathematician Ramanujan's formula, which is a3 + b3 + c3 = d3, and also quantify the densities its solutions. They wrote their own computer program to do so and kept values of a, b, and c less than 10,000. While conducting the analysis, they were also looking for perfect power taxicab numbers and their frequency. They were able to find solutions and densities for the equation. Additionally, while they found that most perfect cube taxicab numbers had a frequency of 2 or 3, they also found on number with a frequency of 42!

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