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The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate spiral growth simulations. Using Mathematica, students can experiment, explore and discover how varying a small number of parameters leads to a wide variety of simulated plant forms. The Mathematica code presented here can be easily modified for experimentation and easily rewritten for use with other maths software packages such as Maple and Matlab.

Abstract A covariance analysis of constructs related to the process of mathematical discovery is presented. The constructs are derived from Polya's ideas on problem solving and include sophistication, traits that [...]

Objective: This article presents a logistic model that describes the mean number of unique methicillin-resistant Staphylococcus aureus (MRSA) isolates collected daily at a 150-bed community hospital in central Massachusetts. The model is used to derive a long-term forecast of the mean MRSA isolate frequency., Methods: The mean number of MRSA isolates collected daily was found for each quarter from the first quarter of 1996 to the first quarter of 2008. A logistic model was fit to the data and then extrapolated to obtain a long-term forecast., Setting: Data was collected at a one-hundred-fifty bed community hospital in central Massachusetts., Results: The coefficient of determination indicates that 87% of the variation in transformed data is explained by the model. The extrapolated logistic model prediction is that the mean number of MRSA isolates collected daily approaches 1.42 MRSA isolates per day., Conclusion: Logistic modeling of empirical data using modest mathematical assumptions is an effective way to understand, visualize, and forecast MRSA daily frequencies over time. The advantage for laboratorians and epidemiologists is that logistic models provide reliable trending and long-term prediction ability of multi-drug resistant organism frequencies. Moreover, as additional data is obtained, the logistic model assumptions can be checked, the model updated, and forecasts improved.

Objective: This study was designed to demonstrate that the number of methicillin-resistant Staphylococcus aureus (MRSA) isolates collected daily in a community hospital is Poisson distributed and that using a one-sided Poisson control table is a fast and easy way to recognize unusually high numbers of MRSA isolates collected daily that may signal possible outbreaks., Methods: A retrospective analysis of MRSA isolates collected daily over a three year period (2005-2007, N = 934) was performed. Observed MRSA isolate frequencies are compared to Poisson frequencies using chi-square goodness-of-fit tests. A regression equation on the mean number of MRSA isolates collected daily for the years 2005, 2006, and 2007 is used to predict the mean number of MRSA isolates for 2008. A warning system for MRSA isolates collected daily is presented and a one-tailed, mean + 2 sigma control table is provided., Setting: One-hundred-fifty bed community hospital in central Massachusetts., Results: Goodness-of-fit tests showed close agreement between actual MRSA isolates collected daily and Poisson frequencies for 2005 (chi4(2) = 4.045, p = 0.39), 2006 (chi4(2) = 2.807, p = 0.59), and 2007 (chi4(2) = 1.494, p = 0.83)., Conclusion: Theoretical and empirical support is provided for the Poisson probability model. The model can be used to identify unusually high occurrences ofMRSA isolates collected daily. This study was limited to a single community healthcare system but the results may be generalized to other types of healthcare settings.