Bivariate coordinate systems in triangle geometry

Autor: Peter J. C. Moses, Clark Kimberling

Publikováno v: Journal of Geometry. 114

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ecbdb231b74ff7efdcf5f32d6504c208
https://doi.org/10.1007/s00022-023-00666-6

The Geometry of Elliptical Probability Contours for a Fix using Multiple Lines of Position

Autor: Peter J. C. Moses, Clark Kimberling, William R. B. Lionheart

Publikováno v: Lionheart, W, Moses, P J C & Kimberling, C 2019, ' The Geometry of Elliptical Probability Contours for a Fix using Multiple Lines of Position ', Journal of Navigation . https://doi.org/10.1017/S0373463319000675

Navigation methods, traditional and modern, use lines of position in the plane. Standard Gaussian assumptions about errors leads to a constant sum of squared distances from the lines defining a probability contour. It is well known these contours are

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32138f9dc2bc88d72a95c32a49a06d23
https://doi.org/10.1017/s0373463319000675

Inequalities Involving Six Numbers, with Applications to Triangle Geometry

Autor: Peter J. C. Moses, Clark Kimberling

Publikováno v: Mathematics Magazine. 85:221-227

SummaryThe Cauchy-Schwarz inequality is generalized in a new way. The method is motivated by extremal properties of the incenter and symmedian point in the plane of a triangle with sidelengths a, b, c. Remarkably, in some of the inequalities involvin

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b3af57edd69caa13d4d915cef5ba2f21
https://doi.org/10.4169/math.mag.85.3.221

Intersections of Lines and Circles

Autor: Clark Kimberling, Peter J. C. Moses

Publikováno v: Missouri J. Math. Sci. 19, iss. 3 (2007), 176-187

A method is presented for determining barycentric coordinates of points of intersection of a line and a circle. The method is applied specifically to the Euler line, the line of the circumcenter and incenter, the Brocard axis, and several circles, in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e44b4ef597f7864d74ccffd9d737a80e
https://doi.org/10.35834/mjms/1316032975