• Communications of Mathematical Education
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• v.37 no.3
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• pp.483-495
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• 2023

In his book "Exercitationum Mathematicalarum," a 17th-century mathematician van Schooten proposed linkages for drawing parabola, ellipse, and hyperbola. The linkages proposed by van Schooten can be used in action-based mathematics education and as a material for using mathematical history in school mathematics. In particular, students are not provided with the opportunity to learn by manipulating the quadratic curves in the high school curriculum, so van Schooten's linkages can be used for school mathematics. To this end, a method of implementing van Schooten's linkage in a dynamic geometry environment was presented, and proved that the traces of the figure drawn using van Schooten's linkage were parabola, ellipse, and hyperbola.

• BMB Reports
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• v.36 no.1
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• pp.1-11
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• 2003

The causative role of polycyclic aromatic hydrocarbons (PAH) in human carcinogenesis is undisputed. Measurements of PAH-DNA adduct levels in easily accessible white blood cells therefore represent useful early endpoints in exposure intervention of chemoprevention studies. The successful applicability of DNA adducts as early endpoints depends on several criteria:i.adduct levels in easily accessible surrogate tissues should reflect adduct levels in target-tissues, ii. toxicokinetics and the temporal relevance should be properly defined.iii. sources of inter- and intra-individual variability must be known and controllable, and finally iv. adduct analyses must have advantages as compared to other markers of PAH-exposure. In general, higher DNA adduct levels or a higher proportion of subjects with detectable DNA adduct levels were found in exposed individuals as compared with non-exposed subjects, but saturation may occur at high exposures. Furthermore, DNA adduct levels varied according to changes in exposure, for example smoking cessation resulted in lower DNA adduct levels and adduct levels paralleled seasonal variations of air-pollution. Intra-individual variation during continuous exposure was low over a short period of time (weeks), but varied significantly when longer time periods (months) were investigated. Inter-individual variation is currently only partly explained by genetic polymorphisms in genes involved in PAH-metabolism and deserves further investigation. DNA adduct measurement may have three advantages over traditional exposure assessment: i. they can smooth the extreme variability in exposure which is typical for environmental toxicants and may integrate exposure over a longer period of time. Therefore, DNA adduct assessment may reduce the monitoring effort. ii. Biological monitoring of DNA adducts accounts for all exposure routes. iii. DNA adducts may account for inter-individual differences in uptake, elimination, distribution, metabolism and repair amongst exposed individuals. In conclusion, there is now a sufficiently large scientific basis to justify the application of DNA adduct measurement as biomarkers in exposure assessment and intervention studies. Their use in risk-assessment, however, requires further investigation.