• Journal for History of Mathematics
• /
• v.28 no.5
• /
• pp.249-262
• /
• 2015

Simon Stevin, a mathematician active in the Netherlands in early seventeenth century, parlayed his mathematical talents into improving navigation skills. In 1605, he introduced a technique of calculating the distance of loxodrome employed in long-distance voyages in his book, Navigation. He explained how to calculate distance by 8 different angles, and even depicted how to make a copper loxodrome model for navigators. Particularly, Stevin clarified in the 7th copper loxodrome model on the unique features of equiangular spiral curve that keeps spinning and gradually accesses from the vicinity to the center. These findings predate those of Descartes on equiangular spiral curve by more than 30 years. Navigation, a branch of actual mathematics devised for the survival of sailors on the bosom of the ocean, was also the first step to the discovery of new mathematical object.

• Journal of the Korean Society of Radiology
• /
• v.16 no.1
• /
• pp.67-75
• /
• 2022

The aim of this study is to establish a new QC method that can simultaneously evaluate the resolution of the x/y plane and the z-axis by producing a phantom that can reflect exposure and reconstruction parameter of MDCT system. It was used with Aquilion ONE(Cannon Medical System, Otawara, Japan), and the examination was scanned using of 120 kV, 260 mA, and the D-FOV of 300 mm². It produced new SSP phantom modules in which two aluminum plates inclined at 45° to a vertical axis and a transverse axis to evaluate high contrast resolution of x/y plane and z axis. And it changed factors such as the algorithm, distance from gantry iso-center. All images were reconstructed in five steps from 0.6 mm to 10.0 mm slice thickness to measure resolution of x/y plane and z-axis. The image data measured FWHM and FWTM using Profile tool of Aquarius iNtusion Edition ver. 4.4.13 P6 software(Terarecon, California, USA), and analysed SPQI and signal intensity by ImageJ program(v1.53n, National Institutes of Health, USA). It decreased by 4.09~11.99%, 4.12~35.52%, and 4.70~37.64% in slice thickness of 2.5 mm, 5.0 mm, and 10.0 mm for evaluating the high contrast resolution of x/y plane according to distance from gantry iso-center. Therefore, the high contrast resolution of the x/y plane decreased when the distance from the iso-center increased or the slice thickness increased. Additionally, the slice thicknesses of 2.5 mm, 5.0 mm, and 10.0 mm with a high algorithm increased 74.83, 15.18 and 81.25%. The FWHM was almost constant on the measured SSP graph for evaluating the accuracy of slice thickness which represents the resolution of x/y plane and z-axis, but it was measured to be higher than the nominal slice thickness set by user. The FWHM and FWTM of z-axis with axial scan mode tended to increase significantly as the distance increased from gantry iso-center than the helical mode. Particularly, the thinner slice thickness that increased error range compare with the nominal slice thickness. The SPQI increased with thick slice thickness, and that was closer to 90% in the helical scan than the axial scan. In conclusion, by producing a phantom suitable for MDCT detectors and capable of quantitative resolution evaluation, it can be used as a specific method in the management of research quality and management of outdated equipment. Thus, it is expected to contribute greatly to the discrimination of lesions in the field of CT imaging.