Area Of Triangle Research Articles

On Heron’s Formula for the Area of a Plane Triangle

Summary This paper provides a review of proofs of Heron’s formula for the area of a plane triangle. We groups proofs together into analogy/experimental evidence, geometry (incircle radius multiplied by semi-perimeter), algebra (equivalence with the Pythagorean Theorem), trigonometric proofs (often via the cosine rule), and specialization from a more general theorem. Lastly, we discuss a neglected paper by Baker of 1885 that lists 110 distinct formulae for the area of a plane triangle and relate some of these formulae to those used in proving Heron’s formula.

The Use of Injectable Platelet-Rich Fibrin As an Alternative Treatment for Interdental Papilla Reconstruction in Black Triangle Case

Introduction: Interdental papilla is triangular soft tissues that fill the gaps between teeth andfunction as protective periodontal tissues and are important in terms of aesthetics, ifinadequate, they will form black triangles, which are blackish areas between teeth. Non-surgical treatment of black triangle is preferred by patients as it is painless. Injectable Platelet-Rich Fibrin (i-PRF) is a platelet concentrate derived from the patient's blood that does notcause immunological reactions and contains growth factors for remodeling the interdentalpapilla. Case Report: A 20-year-old female patient, systemically healthy, came to Prof.Soedomo UGM Dental Hospital with complaints that the gums of the middle part of her upperteeth had a blackish area and disturbed her confidence. An objective examination was carriedout including, gingival biotype, black triangle area, and radiographs, so it was concluded thatthe black triangle was classified as class I Nordland and Tarnow and interdental papillareconstruction to correct the black triangle could be planned. The patient refused surgery so i-PRF can be used as an alternative non-surgical treatment. The black triangle closed completelyafter the i-PRF injection was given. Discussion: I-PRF has the ability to accelerate cellproliferation and migration as well as angiogenesis so that it can modulate fibroblastregeneration in the interdental papilla area. Conclusion: The use of i-PRF can be an alternativenon-surgical option for the treatment of interdental papilla reconstruction.

Building indicators for trans-boundary natural resource management in the Cambodia–Laos–Vietnam Development Triangle Area based on experts’ opinion using Delphi method

Building indicators for trans-boundary natural resource management in the Cambodia–Laos–Vietnam Development Triangle Area based on experts’ opinion using Delphi method

Improvement of postural control in the frail older adults through foot care: A pre- and post-intervention study

Frailty in older adults often leads to foot issues, increasing fall-related fracture risk. Mechanoreceptors, the pressure receptors in the foot sole, are pivotal for postural control. Foot problems can impair mechanoreceptor function, compromising balance. This study aimed to examine the effect of foot care on postural control in frail older adults. Forty-eight participants underwent a five-month monthly foot care intervention. Measurements were taken before and after this intervention. Participants stood for 45 s in a static, open-eyed position on a stabilometer. Center-of-pressure (CoP) analysis included total trajectory length, integrated triangle area, rectangular area, and range of motion in anterior–posterior and medio-lateral directions. Results indicated that foot care significantly increased toe ground contact area by 1.3 times and improved anterior–posterior motion control during static standing. Enhanced postural control resulted from improved skin condition due to foot care that intensified mechanoreceptor signal input and improved postural control output. These findings underscore the potential for reducing fracture risks in older adults through proactive foot care. The study highlights the vital role of foot care in enhancing postural control, with broader implications for aging population well-being and safety.

Radiofrequency ablation for solitary T1N0M0 papillary thyroid carcinoma in the danger triangle area: a preliminary analysis

Objectives To evaluate the feasibility, efficacy, and safety of radiofrequency ablation (RFA) for solitary T1N0M0 papillary thyroid carcinoma (PTC) in the danger triangle area. Methods 94 participants (mean age 44.45 ± 13.08; 73 females) with solitary T1N0M0 PTC in the danger triangle area who underwent percutaneous RFA at the hospital from January 2018 to April 2020 were retrospectively analyzed. Key ablation procedures included sufficient paratracheal fluid isolation, low-power, and short active tip (5 mm working electrode). Tumor size changes at different time points after RFA, technical success rates, tumor disappearance, disease progression, and complications were recorded and compared. Results Contrast-enhanced ultrasonography revealed that complete tumor ablation was performed with a 100% success rate in these patients. Post-ablation, the maximum diameter and volume of the ablation zone increased at the first and third month (p < 0.001), followed by a gradual decrease in size, without significant difference by the 6th month. The tumor disappearance rate was 76.59% (72/94), with higher rates in the T1a group compared to the T1b group (80% [64/80] VS57.1% [8/14], p < 0.001). There were no local recurrences. The incidence of new lesions and LNM was 3.2% (3/94), limited to the T1a subgroup. Further ablation was successfully applied to all new lesions and LMN. Mild voice changes were the only complication, with a rate of 3.2% (3/94), resolved within 4 months after RFA. Conclusions Sufficient paratracheal fluid isolation combined with a low-power, short active tip radiofrequency ablation strategy is a safe and effective method for treating solitary T1N0M0 PTC in the danger triangle area.

The Degree to which Secondary School Principals in the Northern Triangle Region Practice Electronic Management and its Relationship to Achieve Total Quality Standards

The study aimed to reveal the degree of practice of secondary school principals in the Northern Triangle region within the Green Line of electronic management and its relationship to achieve total quality standards from the point of view of principals and teachers.The researchers used the correlational descriptive survey method. The study population consisted of all principals and teachers in secondary schools in the Northern Triangle area within the Green Line during the 2020/2021 academic year, which totaled (840) principals and teachers. A simple random sample was chosen consisting of (12) principals and (258) teachers, working in (20) secondary schools. The results of the study showed that the degree of electronic management practice among secondary school principals was high, and the results showed that the degree of achieving total quality standards among secondary school principals was high, and the results showed a positive statistically significant correlation between the degree of electronic management practice and the degree of achieving the standards of the total quality of secondary school principals in the Northern Triangle area within the Green Line.

Practicalities and dichotomies of education policy and practice of higher education in the Golden Triangle Area (Southeast Asia): Implications for international development

Following the paradigm of globalization and development as a means of achieving a better life from the domestic sphere to the international landscape, different stakeholders including scholars, researchers, practitioners, policy makers, and institutions have been focusing on better informed policy and practice with an embedded mission of international development. Educational policymaking and implementation processes of a nation-state are constrained by global economic and political environments. The ongoing status of educational efforts in each country and disputing factors to the implementation of the education policies were examined. In this study, systematic literature review was conducted on the research of higher education policy in line with globalization and internationalization to depict the practicalities and dichotomies in implementing the sectors at the Golden Triangle Area (Laos, Myanmar, and Thailand). The internationalization of higher education in Golden Triangle Area needs promoting its strategic advantage in offering business opportunities through government policies to further promoting as an affordable study destination and attracting international students from ASEAN countries. The factors affecting the higher education quality and capacity of Laos, Myanmar, and Thailand include the need for better quality, barriers to research capacity development, the policy process of quality assurance, and the initiatives for internationalization in all three countries.

Quality of life for people with psychiatric disabilities employed in extended employment programs in two Arab towns in Israel: an exploratory study.

This study aims to examine the quality of life (QOL) for people with psychiatric disabilities who are engaged in extended employment programs (homogeneous versus heterogeneous) in the Arab-populated Triangle Area of Israel. The homogeneous program participants are exclusively Arab while the heterogeneous program includes both Arabs and Jews. Quantitative research study of 104 adults with psychiatric disabilities engaged in two communal extended employment programs. Participants completed demographic (age (years), gender, marital status (married, widowed/separated, married, single), religion (Muslim, Jewish, Christian), dichotomous nationality variable (Jewish/Arab), and years of education) and employment questionnaires (length of time in the employment program, number of working days/h and salary satisfaction); SF 12 Scale; and The Personal Wellbeing Index questionnaire. Two-sample T-Test, exploratory factor analysis and multiple linear regressions were conducted for tracking the differences between participants in homogeneous and heterogeneous programs. A significant difference was found between the programs in two QOL components, insofar as satisfaction with the standard of living, together with health satisfaction were rated higher for participants in the heterogeneous program than for their homogeneous program counterparts. Furthermore, the results indicate that physical health and gender were the most important variables in explaining QOL in both programs, while the employment variables were not significant. Since the research findings show that the employment-related-items aren't significant in predicting the employees' QOL, the definition and suitability of extended employment environments as a mental health service must be reexamined. Cultural elements may also have an impact on QOL when the programs are located in a traditional town, with gender playing a key role. The family's role is pivotal in traditional societies, influencing an individual's ability to participate in employment programs and the support they receive. In patriarchal societies, there can be added pressure on men with psychiatric disabilities to conform to societal expectations. Given the general lack of health awareness in Arab communities, there is a need to develop additional projects or incorporate physical health improvement as a rehabilitation goal when working with individuals with psychiatric disabilities, regardless of the type of community rehabilitation program.

Geological and Geochemical Characteristics and Genesis of the Laoyingqing Zinc Deposit in Northeastern Yunnan

The Laoyingqing zinc deposit is located in the Pb-Zn deposit concentration district in northeastern Yunnan, with a geotectonic location on the southwestern edge of the Yangtze block. This deposit occurs in the interlayer fracture zone of the Huangcaoling Formation slate in the Middle Proterozoic Kunyang Group. In this deposit, zinc is significantly enriched compared to lead, and the sulfur isotopic composition of sphalerite shows δ34SCDT close to negative values. These characteristics are different from the common Pb-Zn deposits that occur in Sinian and Carboniferous carbonate rocks in northeastern Yunnan. The genesis of this deposit and its similarities to and differences from other Pb-Zn deposits hosted in carbonate rocks in the Sichuan–Yunnan–Guizhou Pb-Zn metallogenic triangle area (SYGT) need further research. This article selects typical rock (ore) samples for fluid inclusion, trace element, and H–O isotope analyses. The results show that (1) the homogenization temperature of the fluid inclusions is 130~306.5 °C, the salinity is 7.17 wt%~20.67 wt% NaCleq, and the density of the ore-forming fluids is 0.86–1.07 g/cm3. Overall, these ore-forming fluids belong to medium–low-temperature, medium–low-salinity, and medium–low-density ore-forming fluids, and they have reducibility. The fluid pressure is 36.3~85.6 Mpa, and the mineralization depth is 1.34~3.17 km. (2) The ore-forming fluids mainly came from deep-source metamorphic water and basin brine containing organic matter. (3) The ore-forming materials mainly came from the surrounding rocks (Kunyang Group). (4) The trace element characteristics of this deposit are different from sedimentary-exhalative type, magmatic hydrothermal type, and skarn type of Pb-Zn deposits, and have little difference from MVT Pb-Zn deposits. Based on the comprehensive analysis, this deposit is classified as a medium–low-temperature hydrothermal vein-type zinc deposit unrelated to magmatic activity. This study extends the ore-bearing surrounding rocks of Pb-Zn deposits in the SYGT to the slate of the Kunyang Group, enriching the regional Pb-Zn deposit mineralization theory and providing new ideas for mineralization prediction.

Modulatory effects of dietary saturated fatty acids on platelet mitochondrial function following short-term exposure to ambient Particulate Matter (PM2.5)

ABSTRACT Exposure to ambient fine particulate matter (PM2.5) was found to produce vascular injury, possibly by activating platelets within days after exposure. The aim of this study was to investigate the modulatory effects of dietary saturated fatty acids on platelet mitochondrial respiratory parameters following short-term inhalational exposure to PM2.5. A total of 22 healthy male volunteers were recruited from the Research Triangle area of North Carolina. Platelets were isolated from fresh whole blood samples and mitochondrial respiratory parameters were measured using an extracellular flux analyzer. Intake of saturated fat was averaged from multiple 24-hr dietary recalls. Daily ambient PM2.5 concentrations were obtained from ambient air quality monitoring stations. Correlation and ANOVA were used in data analyses, along with the pick-a-point method and the Johnson-Neyman technique for probing moderation. After controlling for age and omega-3 index, the intake of dietary saturated fatty acids after reaching 9.3% or higher of the total caloric intake significantly moderated the associations between PM2.5 exposure and several platelet mitochondrial respiratory parameters. In conclusion, dietary saturated fatty acids above 9.3% of total caloric intake influenced the relationship between short-term PM2.5 exposure and platelet mitochondrial respiration. Further research is needed to understand these associations and their implications for cardiovascular health.

The accumulation characteristics and exploration potential of oil and gas in the back-arc basin of Japan under the background of high heat flow

The Sea of Japan is located in the southeast margin of Eurasia, in the triangle area of the western Pacific Ocean. Due to the interaction of the Pacific plate, Eurasian plate and Philippine plate, its tectonic environment is complex, forming a typical trench-arc-basin system. At present, 148 oil and gas fields have been discovered in Japan, with an oil and gas resource of 255.78×106 t, showing a good prospect for oil and gas exploration. Based on the previous research and the recently collected geological and geophysical data, the characteristics of tectonic-sedimentary evolution and geothermal field in the basins around the Sea of Japan are analyzed. The results show that the tectonic evolution of the basin is mainly controlled by plate subduction and back-arc oceanic crust expansion, and it mainly undergone four tectonic-sedimentary evolution stages: Subduction period, basin development period, subsidence period and compression deformation period. The overall heat flow value of Japan Sea is high, and it is distributed annularly along Yamato Ridge. The geothermal heat flow value is about 50–130 MW/m2, and the average heat flow is 75.9±19.8 MW/m2, which has a typical “hot basin”. The high heat flow background provides unique thermal evolution conditions for hydrocarbon generation, which leads to the high temperature and rapid evolution. The authors summarized as “early hydrocarbon generation, rapid maturity and shallow and narrow hydrocarbon generation window”. The type of oil and gas is mainly natural gas, and it mainly distributed in Neogene oil and gas reservoirs. The trap types are mainly structural traps, lithologic traps and composite traps. In addition, the pre-Neogene bedrock oil and gas reservoirs also show a good exploration prospect. The resource prospecting indicates that Niigata Basin, Ulleung Basin and kitakami Basin are the main target areas for future exploration and development.©2023 China Geology Editorial Office.

Extension of Pick’s Theorem to Spherical Geometry using Girard’s Theorem

In this article, Pick’s theorem is extended to three-dimensional bodies with two-dimensional surfaces, namely spherical geometry. The equation for the area of a polygon consisting of equilateral spherical triangles is obtained by combining Girard’s theorem used to find area of any spherical triangle and Pick’s theorem used to find area of a simple polygon with lattice point vertices in Euclidian geometry. Vertices of the polygon are represented by integer points. In this way, an equation to find area of a spherical polygon is presented. This equation could give an idea to be applied on cylindrical surfaces, hyperbolic geometry and more general surfaces. The theorem proposed in this article which is the extension of Pick’s theorem using Girard’s theorem seems to be a special case of a more general theorem.

Tersembunyi di Balik Keramaian: Eksplorasi Sisi Lain Pasar Gede Hardjonagoro Kota Surakarta 1998-2001

Pasar Gede Hardjonagoro or better known as Pasar Gede, is a market located in Surakarta City. Pasar Gede itself is included in the category of the golden triangle area which is included in a strategic area. Traders in this market come from various regions and also ethnicities. As one of the parent markets, Pasar Gede is not only used by traders. Many other parties play a role in it, such as porters. Its existence also celebrates market activity. Not only as a place to buy and sell, Pasar Gede is also a place that provides night entertainment. Markets with activities that are quite dense and open for 24 hours can be a crime target. The research aims to find out the other side of Pasar Gede which is rarely known to the general public. The method used is the historical research method. Data collection is done by searching for primary sources and secondary sources. Primary sources in can be from newspapers and interviews. Secondary sources are obtained from articles, theses and books. The results of this study show that people who work in Pasar Gede come from various ethnicities and have a harmonious relationship. Trading in Pasar Gede is not only crowded with buying and selling activities, but there is also interaction and cooperation carried out by porter, cleaners, and security. People who work in Pasar Gede come from various ethnicities and have a harmonious relationship.&#x0D; Keywords: Pasar Gede, Trader, Porter

Climate Justice in Coral Reef Management: Learning from the Savu Sea Marine National Park Area

This study focuses on analyzing climate justice in the management and assessing the protection model of coral reefs in the Savu Sea Marine National Park (MNP) to realize climate justice sustainably. The research method used a normative-empirical research method with a flow model of data analysis, which examines the implementation or enforcement of favorable legal provisions and written literature or documents associated with specific legal events in society. The research results indicate various potential coral reef resources in Sawu Sea MNP, one of the world’s coral triangle areas. In addition, several local wisdom owned by the community around the coast utilizing fishery resources, especially coral reefs, such as Tasaeb Talas, Kowa Hole, Panadahi, and Liku Ketuga.

Anterolateral surgical triangle of the cavernous sinus: a cadaveric study of neurosurgical importance.

The anterolateral triangle around the cavernous sinus is a surgical skull base triangle used as a neurosurgical landmark essential to skull-based surgeries. There are few reports of its measurements with little attention paid to anatomical variations. A total of 15 adult human cadaveric skulls were dissected to expose the anterolateral triangle on both sides. The triangle was defined and measurements of the three borders were taken precisely and the area of each triangle was calculated using Heron's formula. On an average, the length of the anteromedial border is 11.4 (+ 2.2mm); the length of the posteromedial border is 8.7 (+ 2.6mm); the length of the lateral border is 13.06 (+ 2.6mm) and the area of the anterolateral triangle is 48.05 (+ 17.5mm2). Concise understanding of anterolateral triangle is essential to skull-based surgeries; comprehending its anatomy helps with better surgical planning and provides insight into local pathology.

OGBN O09V Multi-modal Approach with Fluorescence Imaging, Intraoperative Ultrasound and Laser Lithotripsy in the Laparoscopic Management of Complex Large Bile Duct Stones

Abstract Background Choledocholithiasis is a common condition with various presentations. There are several approaches through which this can be managed. This presentation aims to explain novel techniques and various modalities in managing complex bile duct stones successfully with minimal invasive approach. Methods This video presentation depicts the procedure performed for large CBD stones with the use of indocyanine green (ICG) and intraoperative ultrasound (IOUS). The patient is a 61 year old gentleman presented with abdominal discomfort and deranged liver functions. Cross sectional imaging showed 2 large CBD calculi and attempt at endoscopic retrograde cholangio-pancreatigoraphy (ERCP) failed due to large impacted stones. Decision was made to proceed to single stage laparoscopic cholecystectomy and common bile duct exploration with use of ICG, IOUS and laser lithotripsy to achieve successful clearance of CBD. Results At laparoscopy, the CBD and common hepatic artery were identified with ICG and IOUS. A vertical choledochotomy was performed and choledochoscopy undertaken. Attempts to retrieve the stone with extraction basket were not successful. Laser lithotripsy was used to break the stones into smaller fragments which were subsequently retrieved using atraumatic graspers and extraction wire. Post operative period was uneventful and the patient was discharged home on day 2. Face to face follow-up at 6 weeks confirmed good recovery. Conclusions Laparoscopic management of complex CBD stones is challenging. Despite advances in endoscopy intervention, the role of surgery is irrefutable. Advanced laparoscopic skills and experience in bile duct exploration with advanced minimally invasive instruments and equipment are critical to achieve optimal patient outcomes, and mitigated the chances of conversion to open surgery which its associated morbidity. This presentation demonstrates a safe technique while working in the hostile area of the inflamed hepatocystic triangle and an alternative method in the retrieval of large common bile duct stones following failed ERCP.

Activity Reduction as Resilience Indicator: Evidence with Filomena Data

We explore how different socioeconomic groups adapt to the snowstorm Filomena that occurred in Madrid in 2021. A reverse interpretation of the resilience triangle is proposed, where smaller triangle areas indicate less resilient populations continuing to travel despite disruptions, while larger demand losses indicate greater adaptability. Using Google Popular Times data, the study measures activity levels in neighborhoods, focusing on essential and non-essential trips. Vulnerable groups with lower incomes show limited adaptability, resulting in a smaller reduction in commercial activities compared to affluent neighborhoods. The study emphasizes the significance of considering demand adaptability and socioeconomic factors in assessing resilience.

AN AREA OF RIGHT TRIANGLE FOR TRIGONOMETRY

In this paper, we shall investigate formula of tangent function through determination of area of right triangle and rectangle. The consequence of this formula is used to obtain the other two trigonometric function, i.e. sine and cosine functions. Moreover, we also reprove Pythagorean theorem.

Validation of a surgical difficulty grading system in laparoscopic cholecystectomy for acute cholecystitis.

The surgical difficulty of laparoscopic cholecystectomy (LC) for acute cholecystitis varies from case to case, and appropriate intraoperative evaluation would help prevent bile duct injury (BDI). We analyzed 178 patients who underwent LC for acute cholecystitis. Expert surgeons and trainees individually evaluated the surgical difficulty. The inter-rater agreement was analyzed using Conger's κ and Gwet's agreement coefficient (AC). Furthermore, we analyzed the predictive surgical difficulty item for performing subtotal cholecystectomy (STC). Regarding the inter-rater agreement between expert surgeons and trainees, 15 of the 17 surgical difficulty items had a Gwet's AC of 0.5 or higher, indicating "moderate" agreement or higher. Furthermore, the highest and total surgical difficulty scores were deemed "substantial" agreement. Scarring and dense fibrotic changes around the Calot's triangle area with easy bleeding with/without necrotic changes were predictive of whether STC should be performed. This surgical difficulty grading system is expected to be a tool that can be used by any surgeon with LC experience. STC should be performed to prevent BDI according to the changes around the Calot's triangle area.

Molecular identification of Dwarf Bees Apis florea species discovered on the Golden Triangle area, Red Sea, Egypt

Molecular identification of Dwarf Bees Apis florea species discovered on the Golden Triangle area, Red Sea, Egypt