Age and growth of Nassarius reticulatus in the Ria de Aveiro, north-west Portugal

Shell growth of the whelk Nassarius (¼Hinia) reticulatus was studied in the Ria de Aveiro (north-west Portugal) between 1995 and 1998. Temporal analysis of shell height frequency distributions demonstrated that growth occurs during the ¢rst ¢ve years of life, whelks attaining a size of 6.7^7.8 mm in the 1st year, 12.1^14.5 mm in the 2nd year, 18^19.5 mm in the 3rd year, 22.7^23.6 mm in the 4th year and by the 5th year males have achieved an average size of 25 mm whilst females have reached 27 mm. Age estimates from internal microscopic annual growth lines present in the shell lip suggest that large whelks may achieve a longevity of at least 11 years. External annual rings become less discernible as the whelks increase in size and estimates of their age based solely on ring counts can underestimate their age. In males sexual maturation is reached between the 3rd and 4th years whilst in females it is attained between the 4th and 5th years. Imposex was visible in 2 year old females and attained maximum development by the 5th year.

Using GeoGebra to study complex functions

The aim of this workshop to present some of the strategies studied to use GeoGebra in the analysis of complex functions. The proposed tasks focus on complex analysis topics target for students of the 1st year of higher education, which can be easily adapted to pre-university students. In the first part of this workshop we will illustrate how to use the two graphical windows of GeoGebra to represent complex functions of complex variable. The second part will present the use of the dynamic color Geogebra in order to obtain Coloring domains that correspond to the graphic representation of complex functions. Finally, we will use the threedimensional graphics window in GeoGebra to study the component functions of a complex function. During the workshop will be provided scripts orientation of the different tasks proposed to be held on computers with Geogebra version 5.0 or high.