Collection of publications compositing the Nutrigonometry series.
Aren't triangles remarkable? Pythagoras and other geometers certainly think so! In homage to triangle's beauty, we present a simple trigonometric model to measure nutritional trade-offs in multidimensional landscapes (Nutrigonometry), which relies on the trigonometric relationships of right-angle triangles and thus, is both conceptually and computationally easier to understand and use than previous quantitative approaches.
Ecology and Evolution
We test alternative experimental designs to explore the full range of the performance landscape in studies using the Geometric Framework (GF) for Nutrition. Standard GF design did not reconstruct the properties of baseline performance landscape appropriately particularly for traits that respond strongly to the interaction between nutrients. Thus, we conclude that alternative experimental designs can maximise information from performance landscapes in GF studies, enabling reliable biological insights into nutritional trade-offs and physiological limits within and across species.
Royal Society Open Science
We propose a new model to investigate the curvature of landscapes from Geometric Framework for Nutrition experiments. In particular, we integrate concepts from differential geometry such as Mean and Gauss curvatures. We also estimate the surface-area of multidimensional performance landscapes as means to measure landscape deviations from flat. Lastly, we introduce Hausdorff distance as metric to compare the similarity of multidimensional landscapes.
Shapes within shapes: we propose the use of the Thales' theorem of inscribed triangles to measure the rules of dietary compromise in animals. Thales' theorem states that an inscribed triangle will have an angle of 90 degrees if the hypothenuse of the triangle is the diameter of the inscribing circle and the three vertices lie on the circle. We leveraged this theorem to propose a model to test whether animals minimise the distance between an imbalanced diet and the optimal diet balance (if they were given a choice).
Journal of Mathematical Biology
In 1957, Hutchinson proposed a complex concept known as the n-dimensional niche hypervolume. Hypervolumes have now been used to, amongst other things, understand species responses to climate change. Interestingly, niche hypervolumes can have holes (Blonder, 2010; Am Nat), but funny things happen in high dimensions, and finding holes in these hypervolunmes are tricky. In this paper, we proposed the use of a concept known as persistence homology to address this issue. Check it out!
We build on previous methods and introduce a generalized vector-based approach—the vector of position approach—to study nutritional trade-offs in complex multidimensional spaces. The vector of position approach allows the estimate of performance variations across entire landscapes (peaks and valleys) and comparison of these variations between animals. The vector of position approach provides a generalized framework for investigating nutritional differences in life-history trait expression within and between species, an essential step for the development of comparative research on the evolution of animal nutritional strategies.
What do males need to eat to in order to produce offspring? We investigated this question using the model organism Drosophila melanogaster. Using the Geometric Framework for Nutrition, we showed how the balance of carbohydrate and protein affect the ability of males to attract and mate with females as well as sire their offspring.
GEOMETRIA POÉTICA (POETIC GEOMETRY)
Dificil entender Geometria, não é? Mas seus problemas ficam um pouco menos complicados. Nosso livro, Geometria Poética, veio para te ajudar a entender conceitos de Geometria de uma maneira simples e descomplicada.