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Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are...
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Related Experiment Video

Updated: Jul 31, 2025

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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Nutrigonometry I: Using Right-Angle Triangles to Quantify Nutritional Trade-Offs in Performance Landscapes.

Juliano Morimoto, Pedro Conceição, Christen Mirth

    The American Naturalist
    |May 2, 2023
    PubMed
    Summary

    We developed nutrigonometry, a simple trigonometric model, to easily quantify nutritional trade-offs in animals. This new method simplifies analysis of complex diet-performance data, aiding evolutionary nutrition research.

    Keywords:
    fitness mapslife span–reproduction trade-offnutritional geometrytrigonometry

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    Area of Science:

    • Animal physiology
    • Nutritional science
    • Evolutionary biology

    Background:

    • Animals balance nutrient intake for fitness traits, but nutrient requirements create trade-offs.
    • The geometric framework for nutrition (GF) identifies these trade-offs.
    • Current GF analysis methods are complex, subjective, or computationally intensive.

    Purpose of the Study:

    • To introduce a simpler, more accurate method for quantifying nutritional trade-offs.
    • To validate the new method using established data and models.
    • To facilitate broader research in the evolution of animal nutrition.

    Main Methods:

    • Developed 'nutrigonometry,' a trigonometric model for analyzing multidimensional performance landscapes.
    • Applied nutrigonometry to a geometric framework for nutrition dataset.
    • Compared nutrigonometry with standard statistical models, including polynomial (Bayesian) regressions.

    Main Results:

    • Nutrigonometry provides a conceptually simple and computationally efficient way to measure nutritional trade-offs.
    • Polynomial (Bayesian) regressions accurately predict performance landscape peaks and valleys.
    • The model successfully quantified the trade-off between lifespan and reproduction.

    Conclusions:

    • Nutrigonometry offers a fast, reliable, and reproducible method for analyzing nutritional trade-offs.
    • This approach simplifies complex analyses in animal nutrition research.
    • The method has broad potential for comparative studies on the evolution of animal diets and fitness.