• Journal for History of Mathematics
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• v.20 no.3
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• pp.59-72
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• 2007

In this paper we find the germ of geometric interpretation of complex number in the Euclid Element and try to show the evolution of geometric interpretation of complex number by through Descarte, Wallis, Vessel. As a result, relations and differences between them are found. They related line with complex number and interpreted complex number geometrically by generalizing the multiplication operation.

• Journal of the Mineralogical Society of Korea
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• v.15 no.2
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• pp.95-103
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• 2002

The object of this study was to interpret the ralationship between expandability (% $S_{XRD}$), MacEwan crystallite thickness ( $N_{CSD}$), and mean fundamental particle thickness ( $N_{F}$ ) in illite-semctite mixed layer (I-S), quantitatively. This interpretation was extracted from comparison of two structural models (MacEwan crystallite model and fundamental particle model) of I-S mixed layers. In I-S structure, % $S_{XRD}$, $N_{CSD}$, and $N_{F}$ are not independent parameters but are related to each others by particular geometric relations. % $S_{XRD}$ is dependent on $N_{CSD}$ by short-stack effect, whereas, % $S_{XRD}$ and $N_{F}$ have relation to smectite interlayer number (Ns)=( $N_{F-}$1)/(100%/% $S_{XRD-}$ $N_{F}$ . Therefore, % $S_{XRD}$ and $N_{F}$ should satisfy a specific physical condition, 1< $N_{F}$ <100%/% $S_{XRD}$, because $N_{s}$ is positive. Based on this condition, this study suggested % $S_{XRD}$ vs $N_{F}$ diagram which can be used to interpret % $S_{XRD}$, $N_{F}$ , $N_{S}$ , and ordering, quantitatively. The diagram was examined by XRD data for I-S samples from Ceumseongsan volcanic complex, Korea. I-S samples showed that $N_{F}$ departs from the physical upper-limit ( $N_{F}$ =100%/% $S_{XRD}$) with decrease in % $S_{XRD}$. This phenomenon may happen due to decrease of stacking-capability of fundamental particles with their thickening.g.s with their thickening.g.