Magician in a White Coat

In this article, the author describes integrated science and mathematics activities developed for fourthgrade students to explore and investigate three-dimensional geometric shapes, Bernoulli's principle, estimation, and art with and through bubbles. Students were engaged in thinking and reflection on the questions their teachers asked and were also encouraged to use prior knowledge to make conjectures about what they believed would happen at each center with the materials provided and to record their ideas, conjectures, and findings in a journal.     

Powers of Chords for Convex Sets

The powers of chords S_n of planar convex sets are generally known only for n = 0, 1, and 3. They depend on the special shape of the convex set. Here integral formulas for the equilateral triangle, the square, and the ellipse are given. Furthermore, using area moments of the convex sets, S₅ and S₇ are derived in general form. For the 3-dimensional space S₆ and S₈ are given.     

Mechanical response of periodontal ligament: Effects of specimen geometry, preconditioning cycles and time lapse

This study was conducted as part of research line addressing the mechanical response of periodontal ligament (PDL) to tensile–compressive sinusoidal loading. The aim of the present project was to determine the effect of three potential sources of variability: (1) specimen geometry, (2) tissue preconditioning and (3) tissue structural degradation over time. For the three conditions, selected mechanical parameters were evaluated and compared.(1) Standard flat specimens (obtained by sequentially slicing portions of bone, PDL and dentin using a precision band saw) and new cylindrical specimens (extracted with a diamond-coated trephine drill) were obtained from bovine mandibular first molars and subjected to a sinusoidal load profile. (2) Specimens were loaded with up to 2000 cycles. (3) Specimens were immersed in saline and tested after 0, 30 and 60 min.From the data generated, the following was concluded: (1) specimen geometry and preparation technique do not influence the mechanical response of the PDL; (2) the mechanical response stabilizes after approximately 1000 cycles; and (3) no major structural degradation occurs when PDL is immersed in saline for a time lapse up to 60 min.     

Mouse hallucal metatarsal cross‐sectional geometry in a simulated fine branch niche

Mice raised in experimental habitats containing an artificial network of narrow “arboreal” supports frequently use hallucal grasps during locomotion. Therefore, mice in these experiments can be used to model a rudimentary form of arboreal locomotion in an animal without other morphological specializations for using a fine branch niche. This model would prove useful to better understand the origins of arboreal behaviors in mammals like primates. In this study, we examined if locomotion on these substrates influences the mid‐diaphyseal cross‐sectional geometry of mouse metatarsals. Thirty CD‐1/ICR mice were raised in either arboreal (composed of elevated narrow branches of varying orientation) or terrestrial (flat ramps and walkways that are stratified) habitats from weaning (21 days) to adulthood (≥4 months). After experiments, the hallucal metatarsal (Mt1) and third metatarsal (Mt3) for each individual were isolated and micro‐computed tomography (micro‐CT) scans were obtained to calculate mid‐shaft cross‐sectional area and polar section modulus. Arboreal mice had Mt1s that were significantly more robust. Mt3 cross sections were not significantly different between groups. The arboreal group also exhibited a significantly greater Mt1/Mt3 ratio for both robusticity measures. We conclude that the hallucal metatarsal exhibits significant phenotypic plasticity in response to arboreal treatment due to habitual locomotion that uses a rudimentary hallucal grasp. Our results support the hypothesis that early adaptive stages of fine branch arboreality should be accompanied by a slightly more robust hallux associated with the biomechanical demands of this niche. J. Morphol. 276:759–765, 2015. © 2015 Wiley Periodicals, Inc.     

Landscape geometry and travelling waves in the larch budmoth

Travelling waves in cyclic populations refer to temporal shifts in peak densities moving across space in a wave‐like fashion. The epicentre hypothesis states that peak densities begin in specific geographic foci and then spread into adjoining areas. Travelling waves have been confirmed in a number of population systems, begging questions about their causes. Herein we apply a newly developed statistical technique, wavelet phase analysis, to historical data to document that the travelling waves in larch budmoth (LBM) outbreaks arise from two epicentres, both located in areas with high concentrations of favourable habitat. We propose that the spatial arrangement of the landscape mosaic is responsible for initiating the travelling waves. We use a tri‐trophic model of LBM dynamics to demonstrate that landscape heterogeneity (specifically gradients in density of favourable habitat) alone, is capable of inducing waves from epicentres. Our study provides unique evidence of how landscape features can mould travelling waves.     

Quantifying the maculation of avian eggs using eggshell geometry

Birds’ eggs often exhibit considerable variation in the presence and pattern of superficial pigmentation, or maculation. However, despite long appreciation of the nature of this variation both between and within species, there is still poor understanding of why such a diversity of patterns has evolved. Accurately quantifying eggshell maculation is therefore key to elucidating its functional significance. Maculation is typically quantified from photographs, and so measurements may be biased by the perceived distortion introduced by the curvature of the eggshell. Here, I consider egg geometry in order to derive measures of curved distance and surface area that can be used to characterize eggshell maculation patterns more accurately, and demonstrate the utility of this approach for quantifying and visualizing eggshell maculation from standard photographs.     

Saprotrophic cord systems: dispersal mechanisms in space and time

In natural terrestrial environments, nutrients are often patchily and sparsely distributed, and the microclimate is constantly changing both temporally and spatially. To survive, fungi must be able to transfer to a new resource before the nutrient supplies in their current food base are exhausted. While the majority of fungi propagate as spores, some basidiomycetes can grow out of a resource as mycelium in search of new resources. The mycelium of these fungi typically aggregates to form linear organs, termed cords or rhizomorphs, that ramify at the soil-litter interface in forests, interconnecting disparate litter components to form extensive (many square meters or even hectares), long-lived (many years) systems. These mycelial systems form effective dispersal mechanisms in space and time. This article reviews the two main, but not mutually exclusive, mycelial dispersal (resource capture) strategies: (1) a “sit and wait” strategy, whereby a large mycelial network waits for resources to land on it and then actively colonises those resources; and (2) growing and searching actively for new resources. The way in which mycelia balance exploration and nutrient transport, and robustness to damage, against “cost” of production and speed with which an area can be colonised, is explored using techniques borrowed from graph theory and statistical mechanics.     

Functional significance of genetic variation underlying limb bone diaphyseal structure

Limb bone diaphyseal structure is frequently used to infer hominin activity levels from skeletal remains, an approach based on the well‐documented ability of bone to adjust to its loading environment during life. However, diaphyseal structure is also determined in part by genetic factors. This study investigates the possibility that genetic variation underlying diaphyseal structure is influenced by the activity levels of ancestral populations and might also have functional significance in an evolutionary context. We adopted an experimental evolution approach and tested for differences in femoral diaphyseal structure in 1‐week‐old mice from a line that had been artificially selected (45 generations) for high voluntary wheel running and non‐selected controls. As adults, selected mice are significantly more active on wheels and in home cages, and have thicker diaphyses. Structural differences at 1 week can be assumed to primarily reflect the effects of selective breeding rather than direct mechanical stimuli, given that the onset of locomotion in mice is shortly after Day 7. We hypothesized that if genetically determined diaphyseal structure reflects the activity patterns of members of a lineage, then selected animals will have relatively larger diaphyseal dimensions at 1 week compared to controls. The results provide strong support for this hypothesis and suggest that limb bone cross sections may not always only reflect the activity levels of particular fossil individuals, but also convey an evolutionary signal providing information about hominin activity in the past. Am J Phys Anthropol 143:21–30, 2010. © 2010 Wiley‐Liss, Inc.     

Crown dimensions of deciduous teeth of prehistoric and living populations of western India

Deciduous tooth crown dimensions are poorly known for the people of South Asia. This contribution describes dental crown dimensions of two prehistoric and one living population from the northwestern region of the subcontinent.     

Trajectory of the nodal roots of maize in fields with low mechanical constraints

The trajectories of seventy three nodal roots of maize were studied in two fields with loose soil structure. Their projections on horizontal and vertical planes were traced. These roots tended to remain in a vertical plane. Trajectories were related to each other by an affine transformation. Thus, all the observed trajectories could be obtained by transformation of a common root archetype. The horizontal component of the trajectories was mainly in the first 0.4 m depth of soil, in the layer where soil structure was disturbed by ploughing. This horizontal component decreased with later appearance of roots (upper internodes), but differed between the two sites. The average soil temperature during the week following root appearance accounted for differences between internodes and sites. Lungley's algorithm, which is commonly used in modelling root trajectories, was tested. A general pattern could be simulated, but the model failed to fit the trajectories in the first 100 to 200 mm of soil. As a consequence, the initial angle between the stem and the root, which is a sensitive parameter in Lungley's model, did not account for differences between root trajectories. Laboratoire d'agronomie de Colmar