Tackling trigonometry - up the slippery slope?

This paper challenges mathematics teachers to go back and re-examine ideas as far as possible from the genuine beginner's point of view rather than in terms of being experts on the subject. It suggests tasks that teachers can do to achieve this. Topics covered are the shock of the new, the best single short lesson on trigonometry, the difficulty of remembering not knowing, first student trigonometric steps (scouts and flagpoles), first human steps in trigonometry (examining the stars), rotation becomes number, showing relations and learning ideas, plus a lengthy discussion on trigonometry.

Friction changes during compression tests using tool rotation technique

A compression test with rotating dies was employed to estimate the friction factor between aluminum samples and steel tooling during large plastic deformations. A cylindrical workpiece was compressed under dry and cold conditions. The magnitudes of torque and normal force were measured and
the average friction factor was calculated using the Coulomb friction law. It was found that under certain conditions the friction increased with increasing angular velocity of the die. This finding led to the conclusion that the choice of die rotation speed is important in interpreting the results from the twist compression test.

Evolution of egg size and fertilisation efficiency in sea stars: large eggs are not fertilised more readily than small eggs in Patiriella (Echinodermata: Asteroidea)

Fertilisation kinetics theory suggests that, when sperm are limiting, the larger eggs of broadcast-spawning marine organisms ought to be fertilised more frequently than smaller eggs, because they provide a bigger target for searching sperm. Whilst this effect has been demonstrated within species, it is not known if this pattern holds among species. We tested whether a large difference in egg size between congeneric seastars with contrasting planktotrophic and lecithotrophic modes of development results in differences in the likelihood of eggs being fertilised in sperm-limiting situations. Measurement of egg sizes and sperm swimming speeds led to the prediction that the sperm–egg collision rate constant for Patiriella calcar (420-µm-diameter egg) should be nine times greater than for P. regularis (140-µm-diameter egg). Although the eggs of P. calcar should be fertilised at greater rates in low sperm concentrations, they were not. When gametes were allowed to mix for 10 s, the hypothesis that P. calcar eggs required less sperm than P. regularis to ensure 50% of eggs were fertilised was rejected. When gametes were mixed for 5 min, P. regularis eggs were more frequently fertilised, but the difference was not statistically significant. We conclude there must be a difference between these species in the likelihood that when a sperm finds a conspecific egg it can successfully fertilise. This apparent uncoupling of egg size and likelihood of fertilisation suggests that fertilisation is not a major constraint on the evolution of egg size in these seastars.

Internal representation of movement in children with developmental coordination disorder : a mental rotation task

Recent studies show that children with developmental coordination disorder (DCD) have difficulties in generating an accurate visuospatial representation of an intended action, which are shown by deficits in motor imagery. This study sought to test this hypothesis further using a mental rotation paradigm. It was predicted that children with DCD would not conform to the typical pattern of responding when required to imagine movement of their limbs. Participants included 16 children with DCD and 18 control children; mean age for the DCD group was 10 years 4 months, and for controls 10 years. The task required children to judge the handedness of single-hand images that were presented at angles between 0° and 180° at 45° intervals in either direction. Results were broadly consistent with the hypothesis above. Responses of the control children conformed to the typical pattern of mental rotation: a moderate trade-off between response time and angle of rotation. The response pattern for the DCD group was less typical, with a small trade-off function. Response accuracy did not differ between groups. It was suggested that children with DCD, unlike controls, do not automatically enlist motor imagery when performing mental rotation, but rely on an alternative object-based strategy that preserves speed and accuracy. This occurs because these children manifest a reduced ability to make imagined transformations from an egocentric or first-person perspective.

Influences of steady and cyclic die rotation on the compression of aluminium

A series of experiments are reported for compression of an aluminum cylinder with monotonic and cyclic die rotation. When the die is monotonically rotated, a higher angular velocity or a lower compression speed of the tool leads to a greater load reduction in comparison of that seen with a stationary die. The test results also show that cyclic die rotation causes a cyclic fluctuation in the load-displacement curve. During the die deceleration phase, the compression load increases until it reaches the level obtained in conventional compression with stationary dies. However, the compression load is observed to reduce to levels lower than those obtained in monotonic rotating compression tests during the die acceleration phase. The frequency of rotating direction change seems to affect the position of load peaks only, not the amplitude of the peaks.

Regulation of STARS and its downstream target suggest a novel pathway involved in human skeletal hypertrophy and atrophy

Skeletal muscle atrophy is a severe consequence of ageing, neurological disorders and chronic disease. Identifying the intracellular signalling pathways controlling changes in skeletal muscle size and function is vital for the future development of potential therapeutic interventions. Striated activator of Rho signalling (STARS), an actin-binding protein, has been implicated in rodent cardiac hypertrophy; however its role in human skeletal muscle has not been determined. This study aimed to establish if STARS, as well as its downstream signalling targets, RhoA, myocardin-related transcription factors A and B (MRTF-A/B) and serum response factor (SRF), were increased and decreased respectively, in human quadriceps muscle biopsies taken after 8 weeks of both hypertrophy-stimulating resistance training and atrophy-stimulating de-training. The mRNA levels of the SRF target genes involved in muscle structure, function and growth, such as α-actin, myosin heavy chain IIa (MHCIIa) and insulin-like growth factor-1 (IGF-1), were also measured. Following resistance training, STARS, MRTF-A, MRTF-B, SRF, α-actin, MHCIIa and IGF-1 mRNA, as well as RhoA and nuclear SRF protein levels were all significantly increased by between 1.25- and 3.6-fold. Following the de-training period all measured targets, except for RhoA, which remained elevated, returned to base-line. Our results show that the STARS signalling pathway is responsive to changes in skeletal muscle loading and appears to play a role in both human skeletal muscle hypertrophy and atrophy.

Influence of posture on the range of axial rotation and coupled lateral flexion of the thoracic spine

Objective
This study examines the influence of posture on the range of axial rotation of the thorax and the range and direction of the coupled lateral flexion.

Methods
The ranges of mid thoracic axial rotation and coupled lateral flexion were measured in 52 asymptomatic subjects (aged 18-43 years) using an optical motion analysis system. To examine the influence of posture on primary and coupled motion, we initiated axial rotation from a neutral sitting posture and from end-range thoracic flexion and extension.

Results
There was a significant decrease in the range of thoracic rotation in flexion compared with the neutral and extended postures (P < .001). The mean range of coupled lateral flexion was 8.9% of the axial rotation range in the neutral posture and increased to 14.3% and 23.2% in the extended and flexed postures, respectively. Patterns of coupled motion varied between subjects, but an ipsilateral pattern was more common in the flexed posture, whereas a contralateral pattern was more common in the neutral and extended postures.

Conclusions
The ranges and patterns of coupled motion of the thorax appear to be strongly influenced by the posture from which the movement is initiated. This has important implications in relation to the interpretation of clinical tests of thoracic motion and in consideration of mechanisms of development of thoracic pain disorders.

Evaluating New Zealand sports stars as celebrity endorsers : intriguing results

Celebrity athlete endorsement of products and services has become prominent in the promotional mixes of New Zealand companies and organisations. For years advertisers and researchers have pondered how successful celebrity athlete endorsement really works. Most suggest some form of transfer of positive images takes place between celebrity and the product or service they are endorsing and source-credibility models have become the preferred research design. The overall objective of this research was to assist sport marketing managers and their advertising agencies in matching celebrities with products and services. An ancillary objective was to compare results obtained from multiple-item and single-item scales. An exploratory study with tertiary students was conducted, using both Ohanian’s (1990) 15 item source-credibility scale and two single-item measures to examine potential “endorsement fit” for four New Zealand sporting heroes. They were Bernice Mene (recently retired national netball team captain), Dean Barker (America’s Cup yachting defender’s helmsman), Mandy Smith (recently retired national women’s hockey team star) and Justin Marshall (All Black rugby’s most capped halfback), all of whom were adjudged by students as physically attractive sports stars. The product reported here against which these athletes were scored was an isotonic sports drink. Results were mixed; the Ohanian source-credibility scale yielded selection of different celebrity athletes to the single-item measures. The research results show that matching celebrities to products for potential endorsement opportunities is a complex issue, leaving scope for judgement and intuition alongside quantification. Still unresolved is the question of multiple-item measures versus single-item measures in advertising and service research.

Striated muscle activator of Rho signalling (STARS) is a PGC-1α/oestrogen-related receptor-α target gene and is upregulated in human skeletal muscle after endurance exercise

Exercise improves the ability of skeletal muscle to metabolise fats and sugars. For these improvements to occur the muscle detects a signal caused by exercise, resulting in changes in genes and proteins that control metabolism. We show that endurance exercise increases the amount of a protein called striated muscle activator of Rho signalling (STARS) as well as several other proteins influenced by STARS.We also show that the amount of STARS can be increased by signals directed from proteins called peroxisome proliferator-activated receptor gamma co-activator 1-α (PGC-1α) and oestrogen-related receptor-α (ERRα). We also observed that when we reduce the amount of STARS in muscle cells, we block the ability of PGC-1α/ERRα to increase a gene called carnitine palmitoyltransferase-1β (CPT-1β), which is important for fat metabolism. Our study has shown that the STARS pathway is regulated by endurance exercise. STARS may also play a role in fat metabolism in muscle.

Parallel manipulators with a rotation-symmetric arm system

Parallel manipulators with a rotation-symmetric arm system possess all the typical advantages of parallel robots, such as high acceleration and high-accuracy positioning. Contrary to the majority of proposed parallel manipulators, the rotation-symmetric arm system leads to a large workspace in relation to the footprint of the manipulator. This paper focuses on a subclass of these manipulators with additional favorable qualities, including low inertia and high eigenfrequencies. These qualities are achieved using only 5-DOF lower arm links and by mounting all actuators on the nonmoving base column of the manipulator. The common feature of all previously proposed manipulators in this subclass is identified and several novel 3-DOF and 4-DOF members are introduced.

The regulation and function of the striated muscle activator of rho signaling (STARS) protein

Healthy living throughout the lifespan requires continual growth and repair of cardiac, smooth, and skeletal muscle. To effectively maintain these processes muscle cells detect extracellular stress signals and efficiently transmit them to activate appropriate intracellular transcriptional programs. The striated muscle activator of Rho signaling (STARS) protein, also known as Myocyte Stress-1 (MS1) protein and Actin-binding Rho-activating protein (ABRA) is highly enriched in cardiac, skeletal, and smooth muscle. STARS binds actin, co-localizes to the sarcomere and is able to stabilize the actin cytoskeleton. By regulating actin polymerization, STARS also controls an intracellular signaling cascade that stimulates the serum response factor (SRF) transcriptional pathway; a pathway controlling genes involved in muscle cell proliferation, differentiation, and growth. Understanding the activation, transcriptional control and biological roles of STARS in cardiac, smooth, and skeletal muscle, will improve our understanding of physiological and pathophysiological muscle development and function.