Lines, conics, and all that

Fitting conics to paracatadioptric projections of lines

The paracatadioptric camera is one of the most popular panoramic systems currently available in the market. It provides a wide field of view by combining a parabolic shaped mirror with a camera inducing an orthographic projection. Previous work proved that the paracatadioptric projection of a line is a conic curve, and that the sensor can be fully calibrated from the image of three or more line...

The Intersection Conics of Six Straight Lines

We investigate and visualize the manifold M of planes that intersect six straight lines of real projective three space in points of a conic section. It is dual to the apex-locus of the cones of second order that have six given tangents. In general M is algebraic of dimension two and class eight. It has 30 single and six double lines. We consider special cases, derive an algebraic equation of th...

Dark Chocolate and Metabolic Syndrome; Do Polyphenols All that Matter?

Academic nepotism – all that glitters is not gold

Dear Editor With increasing emphasis on publications forfaculty recruitment, career advancementand obtaining research grants, the issues relatedto author kinship and academic nepotism havegrown significantly and these probably reflectthe inflationary growth rather than the optimalgrowth warranted due to increasing researchcomplexity. Allesina S (1) measured the fullmagnitude of nepotism in the ...

2178 and All That

For integers g ≥ 3, k ≥ 2, call a number N a (g, k)-reverse multiple if the reversal of N in base g is equal to k times N . The numbers 1089 and 2178 are the two smallest (10, k)reverse multiples, their reversals being 9801 = 9 · 1089 and 8712 = 4 · 2178. In 1992, A. L. Young introduced certain trees in order to study the problem of finding all (g, k)-reverse multiples. By using modified versio...