Muitos professores de Matem´atica relatam que a maioria dos livros did´aticos de Matem´atica utilizados no Ensino M´edio n˜ao abordam o conceito de ´area e per´ımetro da elipse. Neste trabalho, ...abordaremos esse tema, que tem como objetivos deduzir as f´ormulas que permitem calcular a ´area e o per´ımetro de uma elipse, utilizando uma linguagem simples e de facil compreens˜ao, mas sem perder o rigor matem´atico. Para isso, utilizamos as no¸c˜oes de derivada e integral, t´opicos que geralmente s˜ao abordados em um primeiro curso de C´alculo. Utilizando as no¸c˜oes de derivada e integral, encontramos a ´area e o per´ımetro, que denotaremos por S e C, respectivamente, de uma elipse de focos F1(−c, 0) e F2(c, 0), centro O(0, 0) e v´ertices A1(−a, 0), A2(a, 0), B1(0, −b) e B2(0, b), onde A1A2 ´e o eixo maior de comprimento 2a e B1B2 ´e o eixo menor de comprimento 2b.
Segmentos cônicos e suas propriedades Rogério César dos Santos; Wescley Well Vicente Bezerra
C.Q.D.,
07/2022, Letnik:
22, Številka:
1
Journal Article
Recenzirano
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Este artigo tem por objetivo definir segmento elíptico e segmento hiperbólico, e apresentar suas interessantes propriedades, em cada uma das respectivas cônicas. Foi utilizada, para a prova, a mesma ...estratégia de demonstração adotada no caso da parábola que se tornou conhecido por meio de um recente trabalho. A conclusão a que chegamos no presente artigo é que a razão entre os comprimentos de dois segmentos cônicos, tanto na elipse quanto na hipérbole, depende unicamente das distâncias de cada segmento ao(s) vértice(s) da cônica respectiva, assim como ocorre na parábola. Precisamente, na hipérbole, o quadrado da razão entre os comprimentos de dois segmentos hiperbólicos é igual ao produto das distâncias do primeiro segmento aos vértices da hipérbole, dividido pelo produto das distâncias do segundo segmento aos vértices dessa cônica. No caso da elipse, o resultado é precisamente o mesmo, porém considerando os vértices inferior e superior da curva.
La rama principal de la familia Mendoza mantuvo una estrecha relación con el convento de San Francisco de Guadalajara y eligieron la capilla mayor del templo conventual como lugar para ser ...enterrados. En el siglo XVII, D. Juan de Dios de Mendoza y Silva, X Duque del Infantado, decidió construir en este templo un Panteón en el que reunir los restos familiares encargando el proyecto a Felipe Sánchez. Se trata de un magnífico conjunto barroco inspirado en diseñado por Juan Bautista Crescenzi para los Reyes en El Escorial. El panteón de los Duques del Infantado no tiene la grandiosidad ni la riqueza decorativa del de los Reyes del Escorial, sin embargo, desde un punto compositivo, sus espacios son más ricos y sus soluciones más avanzadas y sobre todo destaca sobre él por el uso que hace de la luz para sorprender y emocionar al espectador.
El trazado de la elipse en la pintura hasta Caravaggio Fraga, Fernando; Amado Lorenzo, Antonio; Colón Alonso, Marta
EGA : revista de expresión gráfica arquitectónica,
03/2020, Letnik:
25, Številka:
38
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El círculo está presente en infinidad de elementos de nuestro entorno. Debido a que, visto en perspectiva, es percibido por el ojo como una elipse perfecta, no es descabellado afirmar que esta última ...es la curva más frecuente en la arquitectura, el arte o la ingeniería. Además, a diferencia de otras formas geométricas simples, su trazado, aún con la ayuda de herramientas como compases o plantillas, conlleva una complejidad importante. Repasar la innumerable cantidad de elipses dibujadas y pintadas desde la antigüedad, confirma que hacerlo con exactitud, a mano alzada, es prácticamente imposible. El artículo estudia la problemática del trazado de la elipse en el arte occidental hasta el siglo xvii. Se parte de la experiencia de Giotto y de los estudios acerca de las cónicas de Durero, para analizar posteriormente cómo una selección representativa de pintores (Campin, Leonardo o Rafael) se enfrentaron a la cuestión sin conseguir resolverla, a diferencia de Caravaggio quien, de alguna manera, lo soluciona (Figs. 1 y 2).
O estudo das cônicas tem início basicamente no ensino médio como geometria analítica e segue no ensino superior com o estudo das cônicas. Em geral esse assunto é encontrado dentro de capítulos de ...livros; poucos são os livros que abordam as cônicas com devida profundidade. As equações polares parecem ser as mais negligenciadas, pois alguns textos não abordam tais equações, outros apenas trazem a equação por excentricidade sem apresentar suas deduções. Observada esta lacuna, questionamos a necessidade de produzir um único material que contenha as equações polares das cônicas não degeneradas. Para isto, foi feita uma ampla pesquisa bibliográfica nas bases acadêmicas de dados e reunidas todas as equações das cônicas encontradas, em particular das cônicas não degeneradas. Aqui temos como objetivo apresentar a definição geral de cônica que nos conduz à equação geral das cônicas e às equações polares das cônicas não degeneradas (Parábola, Elipse e Hipérbole) de duas formas: via excentricidade e por substituição direta das coordenadas cartesianas por polares (não encontrada na literatura pesquisada). Ao longo deste trabalho mostramos que é possível desenvolver detalhadamente todas as equações polares das cônicas não degeneradas em relação à excentricidade, mas também por substituição direta.
Purpose
The Elipse balloon is a novel, non-endoscopic option for weight loss. It is swallowed and filled with fluid. After 4 months, the balloon self-empties and is excreted naturally. Aim of the ...study was to evaluate safety and efficacy of Elipse balloon in a large, multicenter, population.
Materials and Methods
Data from 1770 consecutive Elipse balloon patients was analyzed. Data included weight loss, metabolic parameters, ease of placement, device performance, and complications.
Results
Baseline patient characteristics were mean age 38.8 ± 12, mean weight 94.6 ± 18.9 kg, and mean BMI 34.4 ± 5.3 kg/m
2
. Triglycerides were 145.1 ± 62.8 mg/dL, LDL cholesterol was 133.1 ± 48.1 mg/dL, and HbA1c was 5.1 ± 1.1%. Four-month results were WL 13.5 ± 5.8 kg, %EWL 67.0 ± 64.1, BMI reduction 4.9 ± 2.0, and %TBWL 14.2 ± 5.0. All metabolic parameters improved. 99.9% of patients were able to swallow the device with 35.9% requiring stylet assistance. Eleven (0.6%) empty balloons were vomited after residence. Fifty-two (2.9%) patients had intolerance requiring balloon removal. Eleven (0.6%) balloons deflated early. There were three small bowel obstructions requiring laparoscopic surgery. All three occurred in 2016 from an earlier design of the balloon. Four (0.02%) spontaneous hyperinflations occurred. There was one (0.06%) case each of esophagitis, pancreatitis, gastric dilation, gastric outlet obstruction, delayed intestinal balloon transit, and gastric perforation (repaired laparoscopically).
Conclusion
The Elipse™ Balloon demonstrated an excellent safety profile. The balloon also exhibited remarkable efficacy with 14.2% TBWL and improvement across all metabolic parameters.
Background
Intragastric balloons have been used to bridge the obesity treatment gap with the benefits of being minimally invasive but still required endoscopy. The Elipse intragastric balloon (EIGB) ...is a swallowable balloon that is spontaneously excreted through a natural orifice at approximately 16 weeks. Several concerns exist, including the treatment efficacy and risk of bowel obstruction. Our meta-analysis aimed to evaluate the efficacy and safety of EIGB.
Methods
A literature search was performed from several databases from database inception to November 2019. Eligible studies must report percent total weight loss (%TWL) after completion of treatment and adverse events. The pooled means and proportions of our data were analyzed using random effects model, generic inverse variance method.
Results
Six studies involving 2013 unique patients met our eligibility criteria and were included. The mean baseline BMI ranged from 30.6 to 36.2. The pooled early removal rate was 2.3% (95% CI, 1.1–3.5%; I
2
31%). The pooled %TWL after completion of treatment (4–6 months) was 12.8% (95% CI, 11.6–13.9%; I
2
83%) and at 12 months was 10.9% (95% CI, 5.0–16.9%, I
2
98%). For serious adverse events, three patients had small bowel obstruction, and one patient had gastric perforation requiring surgery. Early expulsion by emesis and early deflation were seen in 3 and 9 patients, respectively.
Conclusions
This meta-analysis demonstrates that EIGB is a safe device offering an effective weight loss that warrants further studies for its long-term weight loss outcomes. Severe adverse events are rare, and the rate of early removal is low.
Background
The traditional gastric balloons have been used for several years to reduce weight in overweight and obese patients, but the need for sedation and upper endoscopy leading to several ...limitations. The current series is the first study that evaluates the safety and effectiveness of the swallowable gastric (Elipse™) balloon in our population on the national level.
Methods
Ninety-six patients (mean BMI was 33.6 ± 4.3 kg/m
2
) participated in this study. All patients swallowed one Elipse
™
balloon intended to remain in the stomach for 4 months, self-empty, and then pass. Each balloon was filled with 550 mL of filling fluid. Anti-emetics and anti-spasmodic drugs were prescribed for 2–3 days after insertion; proton pump inhibitor was prescribed twice daily 1 week before the procedure and continued until the end of residence time (16–20 weeks).
Results
In the current series, at end of the procedure (after 4 months), the overall mean weight loss (WL) was 11.2 ± 5.1 kg, mean waist circumference reduction was 10.9 ± 2.1 cm, and a mean BMI reduction was 4.9 ± 2.0 kg/m
2
. The percentage of total body weight loss (TBWL%) was 12.1 ± 5.2%. The Elipse
™
therapy reported improvements in the metabolic parameters investigated.
Conclusion
This swallowable gastric balloon (Elipse
™
) can be safely and successfully swallowed, filled, imaged, and passed with accepted weight loss and clinical improvement in factors related to the metabolic syndrome.
Elipse™ is the least invasive IGB for weight loss that needs no sedation or endoscopy. It is a swallowable capsule filled with 550 mL of fluid, which stays in the stomach for 16 weeks and is excreted ...from the gastrointestinal tract. Kuwait is one of the first countries to start using Elipse™ as a weight loss device. This study aims to evaluate the efficacy and safety of Elipse™ intragastric balloon (IGB).
This is a single-center prospective pilot study of 51 Elipse™ insertions at our clinic. The patients were followed for 4 months to monitor their weight and body mass index (BMI) at 1, 2, and 4 months. Total weight loss, % excess weight loss (%EWL), % total body weight loss (%TBWL), and change in BMI and waist circumference (WC) were recorded at the end of the study. A short survey was administered to evaluate symptoms, complications, and overall satisfaction.
Fifty-one patients participated, of which five had Elipse™ removed because of intolerance. One case vomited the balloon; one had early deflation. The total weight loss was 8.84 kg, %TBWL 10.44%, %EWL 40.84%, change in BMI 3.42 kg/m2, and the total WC reduction 8.62 cm. Symptoms after insertion were severe, whereas those during excretion were mild and self-limiting. No serious complications were recorded, and the overall satisfaction was above average.
Our data proves that Elipse™ is a safe and effective device for weight loss. Nevertheless, some limitations were observed that need to be overcome for better outcomes. Larger studies are needed to support our findings.
•Elipse™ is the least invasive intragastric balloon that needs no endoscopy, sedation, or anesthesia.•Our study proves that Elipse™ is a safe weight loss device, with comparable results to other conventional intragastric balloons.•Limitations of Elipse™ IGB have been highlighted and need to be overcome for better outcomes.
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