On the Surface Area of Scalene Cones and Other Conical Bodies

This paper first appeared in the Novi Commentarii academiae scientiarum Petropolitanae vol. 1, 1750, pp. 3-19 and is reprinted in the Opera Omnia: Series 1, Volume 27, pp. 181–199. Its Eneström number is E133. This translation and the Latin original are available from the Euler Archive

The Surface Area of a Scalene Cone as Solved by Varignon, Leibniz, and Euler

In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon\u27s in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz\u27s solution, which he corrected, after extending Varignon\u27s solution in the case of circular base. Euler then used Leibniz\u27s approach to solve the general problem. This paper examines all three articles, including English translations

Antitrust Comes to the Cities - Analysis of City of Lafayette v. Louisiana Power & (and) Light Co. and Its Effect on Municipal Antitrust Liability

On March 29, 1978, the United States Supreme Court ruled, in City of Lafayette v. Louisiana Power & Light Co., that cities could not claim a state action exemption from the federal antitrust laws, absent evidence that the state authorized or directed a given municipality to act as it did. The Court rejected the argument of the cities of Lafayette and Plaquemine, Louisiana, that the 1943 Supreme Court decision of Parker v. Brown, which established an antitrust immunity for states and state mandated activities, applied with equal force to political subdivisions of a state. Rather, the Court concluded that the Parker doctrine exempts only anticompetitive conduct engaged in as an act of government by the state as sovereign, or, by its subdivisions, pursuant to state policy to displace competition with regulation or monopoly public service.” Under Lafayette, municipalities will be held accountable for conduct which contravenes a national policy as critical to the nations wellbeing as the Sherman Antitrust Act. The decision exposes all municipalities and their officials to felony criminal penalties ranging up to one million dollars and to civil damage awards that are commonly trebled, with an additive for the prevailing plaintiff\u27s attorney\u27s fees. In addition to forcing municipal attorneys to add antitrust law to the ever growing list of subjects on which they must be well informed, the decision has awakened the interest of private lawyers in antitrust litigation as a means of collecting money damages from a previously immune municipality. Because of possible treble damages and attorney fees the private sector might find this field most attractive. This article will discuss the effect of this landmark decision on municipalities. However, a detailed review of the law before Lafayette and an analysis of the Lafayette decision are important in setting the proper framework to determine as far as possible the effect of Lafayette on municipalities

Windfalls, Wipeouts, Givings, and Takings in Dramatic Redevelopment Projects: Bargaining for Better Zoning on Density, Views, and Public Spaces

Large-scale redevelopment projects such as Boston’s “Big Dig” bestow numerous public benefits—often without charge—to nearby property owners. In the case of the Big Dig, these benefits include twenty-seven acres of newly created parkland, where once an elevated freeway stood. Beyond the immediate and obvious beneficiaries are nearby landowners seeking “better zoning” that might include a relaxation of maximum height or floor area ratios to enjoy the new view. This Article explores the often hidden impact of the nearby landowners’ means of accomplishing their desired result: bargaining with municipalities for private, derivative benefits. The Article compares legislative and judicial responses to land use bargaining in California and Massachusetts, states with dramatically different approaches to land use planning. The Article concludes that bargaining in the absence of a guiding land use plan—the Massachusetts “model”—results in a chaotic land use policy and unpredictable development

Do Wealth and Market Access Explain Inconsistent Relationships Between Crop Diversity and Dietary Diversity? Evidence from 10 Sub-Saharan African Countries

Despite a robust literature base that has explored links between household crop diversity and children’s dietary diversity, evidence continues to yield mixed results regarding the significance and efficacy of crop diversity to improve childhood dietary outcomes. Given wide variance in the association between agrobiodiversity and dietary diversity across contexts, identifying factors that influence the direction and significance of the relationship can help inform targeted and appropriate development policies and interventions to maximize beneficial impact on livelihoods. Household characteristics such as wealth and distance to markets may provide important insight into the linkages between crop diversity and dietary diversity, given that low-resource households are often more reliant on localized production (including their own) for nutritional needs as compared to wealthier households with the resources to purchase more diverse foods from markets. This study examines the associations between crop diversity and dietary diversity among farm households at different levels of wealth in 10 sub-Saharan African countries. Drawing on the Integrated Public Use Microdata Series (IPUMS)-Demographic and Health Surveys (DHS) system, we show that the significance and direction of the association between crop diversity (as proxied by the Simpsons Diversity Index (SDI)) and children’s dietary diversity (as measured by the Household Dietary Diversity Score (HDDS)) varies by wealth quintile across all study countries. We find that the significance and direction of the relationship between crop diversity and dietary diversity depends on the socioeconomic status of a household: in richer households, crop diversity has a negative effect on dietary diversity and in poorer households, there is no significant effect. Further, findings demonstrate the importance of considering contextual factors, such as wealth and distance to markets, in assessing how the presence of crop diversity may improve nutritional outcomes. This study indicates the need to better understand the factors that impact the relationship between agricultural diversity and dietary diversity in order to inform agricultural development strategies

Acute alcohol administration dampens central extended amygdala reactivity.

Alcohol use is common, imposes a staggering burden on public health, and often resists treatment. The central extended amygdala (EAc)-including the bed nucleus of the stria terminalis (BST) and the central nucleus of the amygdala (Ce)-plays a key role in prominent neuroscientific models of alcohol drinking, but the relevance of these regions to acute alcohol consumption in humans remains poorly understood. Using a single-blind, randomized-groups design, multiband fMRI data were acquired from 49 social drinkers while they performed a well-established emotional faces paradigm after consuming either alcohol or placebo. Relative to placebo, alcohol significantly dampened reactivity to emotional faces in the BST. To rigorously assess potential regional differences in activation, data were extracted from unbiased, anatomically predefined regions of interest. Analyses revealed similar levels of dampening in the BST and Ce. In short, alcohol transiently reduces reactivity to emotional faces and it does so similarly across the two major divisions of the human EAc. These observations reinforce the translational relevance of addiction models derived from preclinical work in rodents and provide new insights into the neural systems most relevant to the consumption of alcohol and to the initial development of alcohol abuse in humans