• Journal for History of Mathematics
• /
• v.25 no.3
• /
• pp.53-75
• /
• 2012

When imaginary numbers were first encountered in the 16th century, mathematicians were able to calculate the imaginary numbers the same as they are today. However, it required 200 years to mathematically acknowledge the existence of imaginary numbers. The new mathematical situation that arose with a development in mathematics required a harmony of real numbers and imaginary numbers. As a result, the concept of complex number became clear. A history behind the development of complex numbers involved a process of determining a comprehensive perspective that ties real numbers and imaginary numbers in a single category, complex numbers. This came after a resolution of conflict between real numbers and imaginary numbers. This study identified the new perspective and way of mathematical thinking emerging from resolving the conflicts. Also educational implications of the analysis were discussed.

• Journal for History of Mathematics
• /
• v.25 no.4
• /
• pp.69-82
• /
• 2012

The objective of this paper is to study De Morgan's perspective on teaching and learning complex numbers. De Morgan's didactical approaches reflect the process of development of his thoughts about algebra from universal arithmetic, symbolic algebra to meaning algebra. De Morgan develop his perspective on algebra by justifying and explaining complex numbers. This implies that teaching and learning complex numbers is a catalyst for mathematical development of De Morgan.

• 건강소식
• /
• v.23 no.10 s.251
• /
• pp.22-24
• /
• 1999

• Journal of the Korean hospital association
• /
• v.14 no.4 s.123
• /
• pp.24-28
• /
• 1985

• The monthly packaging world
• /
• s.25
• /
• pp.44-48
• /
• 1995

• River and Culture
• /
• v.2 no.3
• /
• pp.80-85
• /
• 2006

• Journal of the Korean hospital association
• /
• v.15 no.3 s.132
• /
• pp.37-45
• /
• 1986

• Proceedings of the Korean Geotechical Society Conference
• /
• 2005.03a
• /
• pp.499-506
• /
• 2005

지반오염조사에 대한 유전상수 측정기법의 적용성을 평가하기 위하여 중금속 오염도에 따른 흙의 유전특성 변화를 분석하였다. 유전상수의 실수부와 허수부 모두 체적함수비에 따른 증가경향을 나타내었으며, 특히 MHz 범위에서 유전상수 실수부는 쌍극자모멘트에 비례하기 때문에 흙의 유전상수는 체적함수비에 따른 선형적인 증가경향을 나타내었다. 중금속 용액은 50kHz 이하의 저주파영역에서 전극 분극효과에 의해 농도 증가에 따라 유전상수 실수부가 증가하는 경향을 나타내었으나, 고주파 영역에서는 이온의 수화작용에 의한 물분자의 배향분극 발현 감소로 인하여 유전상수 실수부가 감소하였다. 유전상수 허수부의 경우에는 모든 주파수 영역에서 중금속 농도 증가에 따른 전도손실에 의하여 증가하는 경향을 나타내었다. 흙과 중금속 혼합시료의 경우 함수비가 큰 시료에서는 중금속 용액 자체의 유전특성이 그대로 발현되었으나, 함수비가 작은 시료에서는 공간전하분극의 영향이 우세하여 유전상수 실수부가 10-20%정도 증가하는 경향을 나타내었다. 유전상수 허수부의 경우에는 중금속 농도 증가에 따른 뚜렷한 증가경향을 확인할 수 있었다. 본 연구의 결과에 의하면 중금속의 오염감지에 대해서는 유전상수 실수부보다는 허수부의 적용성이 높은 것으로 나타났으며, 현장에서의 정확한 오염도 평가를 위해서는 함수비에 대한 평가가 선행되어야 할 것으로 판단된다.

• Journal of Soil and Groundwater Environment
• /
• v.9 no.3
• /
• pp.1-11
• /
• 2004

To evaluate the applicability of dielectric constant measurement method on the geoenvironmental investigation of subsurface contaminated by landfill leachate, the analysis on dielectric characteristics of sand containing contaminated pore water by landfill leachate was performed. The separate real and imaginary parts of dielectric constant were investigated in the frequency range of 75kHz to 12MHz. The real part of dielectric constant increased at the lower frequency wherea the real part of dielectric constant decreased at the higher frequency as the concentration of leachate increased. These results can be explained by the frequency dependence of space charge polarization and orientation polarization. The imaginary part of dielectric constant on the contaminated sand with leachate increased with their concentration for whole frequency range. These results are caused by the increase of energy loss due to the enhancement of conduction in soil with leachate concentration. The results in this study indicate that the dielectric constant measurement method has potential in evaluating the contaminated soil and pore water by landfill leachate.

• Geotechnical Engineering
• /
• v.6 no.4
• /
• pp.43-52
• /
• 1990

To investigate the effects of soil properties of the soft zone around a pile subjected 1,o the horizontal harmonic vibration, the parametric study is perfomed. The determination of the soil reaction or stiffness of the Winkler springs representing the soil around a pile is performed by dividing the soil profile into a number of homogeneous obtained from this study are as follows : 1) The real and imaginary parts of the stiffness show clear variations for the different shear modulus ratios, poisson's ratios, and distance retios to outer boundary as the dimensionless frequency increases. The differences are more pronounced for the imaginary part of the stiffness. 2) The stiffness of soil shows clear decrease. The real parts of the stiffness show larger as the frequency increases. On the other hand, the imaginary parts of the stiffness show smaller.