Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design

Effect of sitagliptin on cardiovascular outcomes in type 2 diabetes

BACKGROUND: Data are lacking on the long-term effect on cardiovascular events of adding sitagliptin, a dipeptidyl peptidase 4 inhibitor, to usual care in patients with type 2 diabetes and cardiovascular disease. METHODS: In this randomized, double-blind study, we assigned 14,671 patients to add either sitagliptin or placebo to their existing therapy. Open-label use of antihyperglycemic therapy was encouraged as required, aimed at reaching individually appropriate glycemic targets in all patients. To determine whether sitagliptin was noninferior to placebo, we used a relative risk of 1.3 as the marginal upper boundary. The primary cardiovascular outcome was a composite of cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for unstable angina. RESULTS: During a median follow-up of 3.0 years, there was a small difference in glycated hemoglobin levels (least-squares mean difference for sitagliptin vs. placebo, -0.29 percentage points; 95% confidence interval [CI], -0.32 to -0.27). Overall, the primary outcome occurred in 839 patients in the sitagliptin group (11.4%; 4.06 per 100 person-years) and 851 patients in the placebo group (11.6%; 4.17 per 100 person-years). Sitagliptin was noninferior to placebo for the primary composite cardiovascular outcome (hazard ratio, 0.98; 95% CI, 0.88 to 1.09; P<0.001). Rates of hospitalization for heart failure did not differ between the two groups (hazard ratio, 1.00; 95% CI, 0.83 to 1.20; P = 0.98). There were no significant between-group differences in rates of acute pancreatitis (P = 0.07) or pancreatic cancer (P = 0.32). CONCLUSIONS: Among patients with type 2 diabetes and established cardiovascular disease, adding sitagliptin to usual care did not appear to increase the risk of major adverse cardiovascular events, hospitalization for heart failure, or other adverse events

Canagliflozin and Renal Outcomes in Type 2 Diabetes and Nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to 300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m 2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Canagliflozin and Cardiovascular and Renal Outcomes in Type 2 Diabetes Mellitus and Chronic Kidney Disease in Primary and Secondary Cardiovascular Prevention Groups

Background: Canagliflozin reduces the risk of kidney failure in patients with type 2 diabetes mellitus and chronic kidney disease, but effects on specific cardiovascular outcomes are uncertain, as are effects in people without previous cardiovascular disease (primary prevention). Methods: In CREDENCE (Canagliflozin and Renal Events in Diabetes With Established Nephropathy Clinical Evaluation), 4401 participants with type 2 diabetes mellitus and chronic kidney disease were randomly assigned to canagliflozin or placebo on a background of optimized standard of care. Results: Primary prevention participants (n=2181, 49.6%) were younger (61 versus 65 years), were more often female (37% versus 31%), and had shorter duration of diabetes mellitus (15 years versus 16 years) compared with secondary prevention participants (n=2220, 50.4%). Canagliflozin reduced the risk of major cardiovascular events overall (hazard ratio [HR], 0.80 [95% CI, 0.67-0.95]; P=0.01), with consistent reductions in both the primary (HR, 0.68 [95% CI, 0.49-0.94]) and secondary (HR, 0.85 [95% CI, 0.69-1.06]) prevention groups (P for interaction=0.25). Effects were also similar for the components of the composite including cardiovascular death (HR, 0.78 [95% CI, 0.61-1.00]), nonfatal myocardial infarction (HR, 0.81 [95% CI, 0.59-1.10]), and nonfatal stroke (HR, 0.80 [95% CI, 0.56-1.15]). The risk of the primary composite renal outcome and the composite of cardiovascular death or hospitalization for heart failure were also consistently reduced in both the primary and secondary prevention groups (P for interaction &gt;0.5 for each outcome). Conclusions: Canagliflozin significantly reduced major cardiovascular events and kidney failure in patients with type 2 diabetes mellitus and chronic kidney disease, including in participants who did not have previous cardiovascular disease