Faces, Edges, Vertices of Some Polyhedra

A proof that: for any given polyhedron so shaped that every closed non-self intersecting broken line composed of edges of the polyhedron divides the surface of the polyhedron into precisely two disjoint regions each of which is bounded by the closed broken line, v - e + f = 2, where v is the number of vertices of the polyhedron, e the number of edges and f the number of faces

Investigating mathematics teacher efficacy beliefs in primary initial teacher education

This paper will discuss the mathematics teacher efficacy beliefs (MTEB) of primary initial teacher education (ITE) students. We are interested in studying how ITE students’ MTEBs are influenced (or not) by mathematics education modules undertaken as part of an undergraduate Bachelor of Education (BEd) programme. We will detail how approximations of practice (Grossman, Compton, Igra, Ronfeldt, Shahan, & Williamson, 2009) have been incorporated into mathematics education modules to create opportunities for the development of MTEBs and will report on focus group interviews which explored MTEBs of ITE student

Using MRI of the Optic Nerve Sheath to Detect Elevated Intracranial Pressure

The current gold standard for the diagnosis of elevated intracranial pressure (ICP) remains invasive monitoring. Given that invasive monitoring is not always available or clinically feasible, there is growing interest in non-invasive methods of assessing ICP using diagnostic modalities such as ultrasound or magnetic resonance imaging (MRI). Increased ICP is transmitted through the cerebrospinal fluid surrounding the optic nerve, causing distention of the optic nerve sheath diameter (ONSD). In this issue of Critical Care, Geeraerts and colleagues describe a non-invasive method of diagnosing elevated ICP using MRI to measure the ONSD. They report a positive correlation between measurements of the ONSD on MRI and invasive ICP measurements. If the findings of this study can be replicated in larger populations, this technique may be a useful non-invasive screening test for elevated ICP in select populations

Ideas that Change and Stay the Same

What will this building become? I interpret this to mean that initial design ideas are subject to various deforming forces at various distances in time from the original conception. Needless to say only a small portion of all built structures have any conscious theoretical content to speak of

Forbidden Zone: Borden on the Borders of War and Gender

Mary Borden\u27s The Forbidden Zone is a starkly modernist approach to writing about The Great War and approaches it from a unique perspective - that of a female nurse on the edges of the front lines. Borden blends memoir, poetry and realism to inform her reader of the blurred realities of a war where borders between nations or people are often uncertain. Borden\u27s unique approach allows her to portray the otherwise incommunicable suffering of war and translate it into a photograph of her experience

The Smallest Particles in Saturn's A and C Rings

Radio occultations of Saturn's main rings by spacecraft suggest a power law particle size-distribution down to sizes of the order of 1 cm (Marouf et al., 1983), (Zebker et al., 1985). The lack of optical depth variations between ultraviolet and near-IR wavelengths indicate a lack of micron-sized particles. Between these two regimes, the particle-size distribution is largely unknown. A cutoff where the particle-size distribution turns over must exist, but the position and shape of it is not clear from existing studies. Using a series of solar occultations performed by the VIMS instrument on-board Cassini in the near-infrared, we are able to measure light forward scattered by particles in the A and C rings. With a model of diffraction by ring particles, and the previous radio work as a constraint on the slope of the particle size distribution, we estimate the minimum particle size using a truncated power-law size distribution. The C Ring shows a minimum particle size of $4.1^{+3.8}_{-1.3}$ mm, with an assumed power law index of q=3.1 and a maximum particle size of 10 m. The A Ring signal shows a similar level of scattered flux, but modeling is complicated by the presence of self-gravity wakes and higher optical depths. If q<3, our A Ring model requires a minimum particle size below one millimeter (< 0.34 mm for an assumed q=2.75, or $0.56^{+0.35}_{-0.16}$ mm for a steeper q=2.9) to be consistent with VIMS observations. These results might seem to contradict previous optical(Dones et al., 1993) and infrared (French and Nicholson, 2000) work, which implied that there were few particles in the A Ring smaller than 1 cm. But, because of the shallow power law, relatively little optical depth (between 0.03 and 0.16 in extinction, or 0.015 - 0.08 in absorption) is provided by these particles.Comment: 47 pages, 16 figures, 3 Table

Episodic Disorders of Vision

Of all our senses, vision is most commonly associated with patient distress, if not overt alarm, when abruptly compromised. Despite patient concern, a rare, or rarely recognizable, clinical entity is perhaps of less significance to the physician than to the patient. When the broad spectrum of episodic disturbance of vision is closely examined, it becomes apparent that these visual symptoms are indeed of common occurrence in the population at large. Surprisingly, despite their ultimate effect on the eye, a majority of the clinical entities that produce episodic disturbance of vision are neurologic. Episodic is defined as being ...made up of separate, loosely connected episodes. In turn, an episode is ...a usually brief unit of action...an occurrence or connected series of occurrences and developments which may be viewed as distinctive and apart, although part of a larger or more comprehensive series

What the Instagram Age Learned from Robert Rauschenberg’s Choreographic Pieces

This article discussing how developments in technology and changes to the economy influence modes of performance, in everyday life and the works of art that reflec it. It establishes how a new wave of choreographic strategies in galleries and museums reflects activities of taking, sharing and performing images online. And it reflects on how exhibition architectures afford visitors a different depth of perspective than the arm’s length between smart screens and users’ eyes