Browse Articles

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.

Read More...

Discovery of the Heart in Mathematics: Modeling the Chaotic Behaviors of Quantized Periods in the Mandelbrot Set

Golla et al. | Dec 14, 2020

Discovery of the Heart in Mathematics: Modeling the Chaotic Behaviors of Quantized Periods in the Mandelbrot Set

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.

Read More...

Analysis of Patterns in the Harmonics of a String with Artificially Enforced Nodes

Jain et al. | Jan 28, 2021

Analysis of Patterns in the Harmonics of a String with Artificially Enforced Nodes

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 2nd harmonic contain the alternate frequencies of the fundamental series, the higher harmonics of the directly excited 3rd harmonic series contain every third frequency of fundamental series, and so on. To test the hypotheses, they enforced artificial nodes to excite the 2nd, 3rd, and 4th harmonics directly, and analyzed the resulting spectrum to verify the mathematical hypothesis. The data analysis corroborates both hypotheses.

Read More...

Population Forecasting by Population Growth Models based on MATLAB Simulation

Li et al. | Aug 31, 2020

Population Forecasting by Population Growth Models based on MATLAB Simulation

In this work, the authors investigate the accuracy with which two different population growth models can predict population growth over time. They apply the Malthusian law or Logistic law to US population from 1951 until 2019. To assess how closely the growth model fits actual population data, a least-squared curve fit was applied and revealed that the Logistic law of population growth resulted in smaller sum of squared residuals. These findings are important for ensuring optimal population growth models are implemented to data as population forecasting affects a country's economic and social structure.

Read More...

Formation and sticking of air bubbles in water in d-block containers

Gupta et al. | Jun 21, 2021

Formation and sticking of air bubbles in water in d-block containers

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.

Read More...

Optimizing Interplanetary Travel Using a Genetic Algorithm

Murali et al. | Oct 28, 2018

Optimizing Interplanetary Travel Using a Genetic Algorithm

In this work, the authors develop an algorithm that solves the problem of efficient space travel between planets. This is a problem that could soon be of relevance as mankind continues to expand its exploration of outer space, and potentially attempt to inhabit it.

Read More...

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!

Read More...

Search Articles

Search articles by title, author name, or tags

Clear all filters

Popular Tags

Browse by school level