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Mathematical modeling of plant community composition for urban greenery plans

Fang et al. | Jul 05, 2023

Mathematical modeling of plant community composition for urban greenery plans
Image credit: CHUTTERSNAP

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.

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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.

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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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Comparison of three large language models as middle school math tutoring assistants

Ramanathan et al. | May 02, 2024

Comparison of three large language models as middle school math tutoring assistants
Image credit: Thirdman

Middle school math forms the basis for advanced mathematical courses leading up to the university level. Large language models (LLMs) have the potential to power next-generation educational technologies, acting as digital tutors to students. The main objective of this study was to determine whether LLMs like ChatGPT, Bard, and Llama 2 can serve as reliable middle school math tutoring assistants on three tutoring tasks: hint generation, comprehensive solution, and exercise creation.

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Part of speech distributions for Grimm versus artificially generated fairy tales

Arvind et al. | Nov 16, 2024

Part of speech distributions for Grimm versus artificially generated fairy tales
Image credit: Nayalia Y.

Here, the authors wanted to explore mathematical paradoxes in which there are multiple contradictory interpretations or analyses for a problem. They used ChatGPT to generate a novel dataset of fairy tales. They found statistical differences between the artificially generated text and human produced text based on the distribution of parts of speech elements.

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