• 한국수학교육학회지시리즈E:수학교육논문집
• /
• 제37권3호
• /
• pp.483-495
• /
• 2023

17세기 수학자 van Schooten(1657)은 저서 'Exercitationum mathematicarum'에서 포물선, 타원, 쌍곡선을 그리기 위한 연동장치를 제시하였다. van Schooten이 제시한 연동장치는 활동 중심 수학교육과 학교수학에서 수학사를 활용하기 위한 소재로 사용될 수 있다. 특히 학생들이 고등학교 교육과정에서 이차곡선을 조작하며 학습할 기회를 제공받지 못하고 있다는 점에서, van Schooten의 연동장치는 활동과 탐구 중심의 수학교육을 실현하는 데 도움을 줄 수 있다. 이를 위해 van Schooten의 연동장치를 동적 기하 환경에서 구현하는 방법을 제시하고, van Schooten의 연동장치를 이용하여 그린 도형의 자취가 포물선, 타원, 쌍곡선임을 증명하였다.

• BMB Reports
• /
• 제36권1호
• /
• pp.1-11
• /
• 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.