A Generalized Malfatti Problem

Abstract Malfatti's problem, first published in 1803, is commonly understood to ask fitting three circles into a given triangle such that they are tangent to each other, externally, and such that each circle is tangent to a pair of the triangle's sides. There are many solutions based on geometric constructions, as well as generalizations in which the triangle sides are assumed to be circle arcs. A generalization that asks to fit six circles into the triangle, tangent to each other and to the triangle sides, has been considered a good example of a problem that requires sophisticated numerical iteration to solve by computer. We analyze this problem and show how to solve it quickly

Average Labor Taxes and Unemployment: Evidence from Italian Regions

By focusing on the Italian experience, we ask whether the relationship between labor taxes and unemployment varies across regions. In spite of similar national labor market institutions, we show that this relationship is significantly stronger in the highly industrialized North than in the less developed South, where unemployment is much higher. An important source of variation in the regional responsiveness of unemployment originates from the fact that regional gross wages in the North increase more than in the South in response to a hike in labor taxes.regional unemployment, labor taxes.

Schellbach-style Formulae for the Derousseau-Pampuch Generalizations of the Malfatti Circles

It is known that there exist 32 triplets of circles such that each circle is tangent to the other two circles and to two of the sides of the triangle or their extensions. We provide formulae to obtain the radii of the circles for each of the 32 triplets from the side lengths of the reference triangle by means of trigonometric or hyperbolic functions.Comment: 48 pages, 34 figures. A typo in references is fixed. A contact address is adde

Toward a Multicultural Mid-Tudor England

Through close-readings of Mary Tudor's royal entry, the anonymous interlude Wealth and Health, and John Christopherson's Exhortation alongside anecdotes of popular resistance to Mary Tudor's antiimmigrant proclamations, this article shows that rather than a strong identification with the monarch or some sense of Englishness, Londoners more closely identified with their multicultural metropolitan community for religious and economic reasons