Table of Contents: Volume 17; Issue 02; February 2025

No scientific theory lasts forever, but specific research and discoveries continuously build upon each other. The three classic ancient Greek mathematical challenges likely referring to are “Doubling The Circle”, “Trisecting An Angle” & “Squaring The Circle”, all famously proven Impossible under strict compass-and-straightedge constraints, by Pierre Wantzel (1837) using field theory and algebraic methods, then also by Ferdinand von Lindemann (1882) after proving π is transcendental. These original Greek challenges remain impossible under classical rules since their proofs rely on deep algebraic/transcendental properties settled in the 19th century. Recent claims may involve reinterpretations or unrelated advances but do overturn these conclusions above. Among these, the "Squaring The Circle" problem and related problems involving π have captivated both professional and amateur mathematicians for millennia. The title of this paper refers to the concept of "constructing a regular triangle that has the exact area of a given circle," or “Triangling the Circle”. This research idea arose after the “Squaring The Circle” problem was studied and solved and published in “SJPMS” in 2024.This paper presents an exact solution to constructing a regular triangle that is concentric with and has the same area as any given circle. The solution does not rely on the number π and adheres strictly to the constraints of Euclidean geometry, using only a straightedge and compass. The technique of “ANALYSIS” is employed to solve the “Triangling the Circle” problem precisely and exactly with only a straightedge and compass, without altering any premise of the problem. This independent research demonstrates the solution to the challenge using only these tools. All mathematical tools and propositions in this solution are derived from Euclidean geometry. The methodology involves geometric methods to arrange the given circle and its equal-area regular triangle into a concentric position. Building on this method of exact “Triangling A Circle,” one can deduce an equivalent problem to formulate a new mathematical challenge: "Hexagoning A Circle" (i.e., constructing a regular hexagon that has the same area as a given circle, using only a straightedge and compass).

Introduction-Inflammatory bowel disease (IBD) is constituted by ulcerative colitis and Crohn’s disease. In western countries, both have almost equal representation but in India, predominantly ulcerative colitis is seen. Ulcerative colitis affects large bowel whereas Crohn’s disease can be seen throughout gastro-intestinal tract but both of them can have extra-intestinal involvement of skin and hairs, symptoms of which can start before, simultaneously or later in the course of IBD. Case Series- Our instituteis tertiary care centre and thus we get plenty of referrals including suspected cases of IBD. Hence, there is good load of IBD patients who come for regular follow up for last many years. We analysed 100 males and 100 females of confirmed IBD who were on regular follow up for many years for hair loss. Out of 100 males, 28 (28%) had hair loss whereas out of 100 females, 40 (40%) had hair loss during course of this disease. Conclusion-The treating gastroenterologist and physicians should be extra vigilant for extra-intestinal manifestation of IBD which include hair fall also, which has huge cosmetic value, especially in young patients which constitute major percentage of IBD.

The misuse of dowry-related laws by some individuals in India has emerged as a significant concern. While dowry is a deeply entrenched social issue, laws such as Section 498A of the Indian Penal Code and the Dowry Prohibition Act were introduced to protect women from harassment and exploitation. However, there have been growing reports of these laws being misused by women to file false dowry cases against their spouses and in-laws. This trend, though not widespread, has raised questions about the balance between safeguarding women's rights and preventing the misuse of legal provisions. False dowry cases can lead to severe consequences for the accused, including social stigma, financial losses, and mental anguish. Judicial systems have recognized this issue, with courts emphasizing the need for careful scrutiny of complaints and discouraging frivolous litigation. However, the misuse of laws should not overshadow their importance in protecting genuine victims of dowry harassment. A multifaceted strategy is needed to address this problem, which includes enhancing systems for early detection of false complaints, encouraging gender-sensitive education, and increasing public understanding of legal provisions. Simultaneously, it is imperative to guarantee that legitimate victims continue to obtain the necessary help and legal protection. India can maintain justice and prevent the abuse of dowry-related laws without reducing their ability to solve the underlying issue by promoting a more equitable and balanced judicial system.

Orthopedic correction of skeletal Class III malocclusion in a growing individual is crucial as it can circumvent future surgical procedures. Further, as surgery is done only at a later stage, early treatment helps to avoid the ill effects produced by the facial disfigurement on the patient’s social life. This case report describes the treatment of a child aged 12 years who had a skeletal Class III malocclusion. The treatment plan involved the use of a reverse pull headgear (facemask) and multibracket appliance therapy resulting in successful correction of the malocclusion. The treatment results were highly satisfactory resulting in improved facial esthetics, a skeletal Class I with a dental Class I molar and canine relationship, an ideal overjet and overbite. Thus, if it is done in properly selected cases, alleviates the need for surgical intervention in futue. The patient is being monitored until the end of growth to ensure the stability of treatment results.

Lophomonas blattarum infections are very rare in human. However, in the world the major infections of L. blattarum occurred in China, 94.4%. The differentiate between this infection and the other pulmonary infections are very difficult because of the similar symptoms. Here we reported a case of L. blattarum infection confirmed by bronchoalveolar lavage fluid smear on the microscopic observations. The patient was a 40-year-old male farmer was admitted via OPD in GMC and associated Hospital, Badaun (UP) on 29 September, 2024. We briefly reviewed on this infection which is reported in the world during the recent 15-20 years. On the basis of epidemiology, diagnostic, and treatment of this disease we discussed the case to provide a better understanding of recognition, diagnosis, and treatment of L. blattarum infection.

Breast cancer has been considered as the most common type of cancer among the women. The age-adjusted incidence rate is approximately 25.8 per 100,000 women, with a mortality rate of 12.7 per 100,000 women. This means that about 1 in 29 Indian women are at risk of developing breast cancer during their lifetime. Breast cancer happens when cells in the breast start to grow out of control. Physical signs that breast cancer is developing include changes to the skin on the breast, nipple discharge, and a new lump on or around the breast area. Breast cancer is the uncontrolled growth of cells in the breast tissue. It usually begins in the milk ducts or milk-producing glands. Two major etiologic factors in pathogenesis of breast cancer are: Hormonal and genetic. Breast cancer is so prevalent; knowing the steps to help prevent or detect it is important. Vitamin D, a group of fat-soluble vitamins renowned for their role in preserving the balance of calcium and phosphorus. or people with cancer, a form called vitamin D3 (cholecalciferol) is preferred over vitamin D2 (ergocalciferol) as it is better able to raise and sustain vitamin D levels. Some researchers contend that maintaining optimal vitamin D levels may not only prevent breast cancer but also slow disease progression in those with cancer by delaying changes that lead to metastasis.

Introduction: An inflammatory condition called rheumatoid arthritis (RA) results in persistent joint inflammation, which is painful and incapacitating. There are no racial or ethnic disparities in the prevalence of RA, which is believed to be between 1% and 2% worldwide. Inflammation is indicated by elevated blood levels of the C-Reactive Protein (CRP), which can be used to identify and track the illness. RA patients often experience a heavy burden of pain, disability, and limited activities, all of which have an impact on their health-related quality of life. Given the rising prevalence of RA worldwide, it is necessary to evaluate the efficacy and safety of medications and offer appropriate treatment to enhance patients' quality of life. Methodology: This was a prospective study conducted in orthopaedic OPD of ESIC Model Hospital Bari Brahamna in Jammu district. All the subjects (n=100) meeting the inclusion and exclusion criteria were briefed about the purpose of the study and the informed consent was obtained. The subject’s demographic details and responses were collected. All the enrolled patients were assessed at the time of starting the treatment, then at 2nd month and 5th month. The collected data were entered in microsoft excel and appropriate descriptive analysis was performed. Results: A total of 100 samples were enrolled in the study based on inclusion and exclusion criteria. Out of which 50% of the participants were on Methotrexate (MTX) and the other 50% were on Tofacitinib. Majority of the subjects in the study were women (79%) and men (21%) . On comparing the effectiveness of both Methotrexate and Tofacitinib, it was found that the rate of reduction of CRP levels and ESR was better with Tofacitinib in comparison to Methotrexate. Conclusion: From this study, Tofacitinib concludes to be more effective than Methotrexate with regard to its ability to decrease CRP levels and ESR in high disease activity patients.

The United Nations (UN) peacekeeping is one of the most important and long-lasting initiatives of the organization. It is based on international rules, principles, and decision-making processes that have been developed since the late 1940s. Peacekeeping has become a key part of the UN’s identity, representing its dedication to maintaining global peace and security. Over the years, UN peacekeeping has grown into one of the most well-known and respected functions of the organization. It is a symbol of the UN’s efforts to resolve conflicts and help countries recover after wars. So far, the UN has carried out over 120 peacekeeping missions in more than 50 countries across Africa, the Americas, Asia, Europe, and the Middle East. These missions have played a crucial role in resolving conflicts, maintaining peace, and assisting nations in rebuilding after violence. This study aims to explore the evolving future roles of United Nations (UN) peacekeeping missions.

The higher fertility rate of Muslims than Hindus gives birth to social tensions and political concerns in India. The government of India followed ante-natal population policies where Muslims are not the exception. In India, a large section of the common people believed that the religion Islam had a significant positive role in the higher fertility rate of Muslims. Even a rumour had been believed by a section of Indian people that soon Muslims will be exceeding Hindus by number in India. Therefore, it is important to identify the views of Muslim religious leaders on the uses of various modern family planning methods to control the fertility rate of Muslims. Qualitative interviews were conducted with 180 local Muslim religious leaders whose ages ranged from 27 – 72 years. The local Islamic religious leaders are selected for an interview through multi-stage purposive convenience sampling. The result shows that all the Muslim religious leaders considered permanent methods of contraceptives i.e., sterilization (Both male and female sterilization), and abortion is strictly prohibited in Islam. However, there is controversy among the leaders regarding the use of various temporary modern contraceptives. The study also suggests that Islamic religious leaders are more comfortable with the word 'birth spacing' instead of 'birth control'.