This paper investigates the constructability of angles multiples of 3 within the framework of Euclidean geometry. It makes a significant contribution by presenting the first geometric construction for all such angles, offering a rigorous solution to a longstanding geometric problem. The paper reaffirms the efficacy of Euclidean geometry in providing precise constructions and robust proofs for these angles, demonstrating the enduring strength of Euclidean principles from classical to modern times. The presented workflow goes beyond Euclidean geometry to examine non-Euclidean methods, particularly analytical approaches, revealing misconceptions that compromise the genetic and geometric rigor of Euclidean principles. The paper exposes incongruities when algebraic proofs related to angle constructability are applied to the Euclidean system, emphasizing the misalignment of fundamental geometric concepts. A notable result in the paper is the construction of a angle, introducing the “ angle chord” as a novel geometric property. This property challenges assumptions made by non-Euclidean methods and highlights the nuanced geometric properties crucial for rigorous constructions. The paper refutes the fallacy of relying solely on algebra for solutions to angles multiples of , emphasizing the necessity of embracing Euclidean geometry for geometric discoveries. The paper underscores the merits and resilience of Euclidean geometry, showcasing its independence and depth across historical and modern perspectives. The newly presented geometric construction not only resolves a longstanding question but also emphasizes the intrinsic strength and uniqueness of Euclidean principles in contrast to alternative methodologies.

Student engagement in educational activities is essential for achieving desired learning outcomes. Despite this, little is known about the engagement patterns of nursing students from diverse or disadvantaged backgrounds. A mixed method study was conducted to explore engagement patterns within and outside the classroom but not during clinical placements. Students were asked what engagement means to them and what influences their engagement. Students were also asked how many hours they engaged in each of their undergraduate subjects and the reasons for this. The study was conducted at an Australian education provider. All students (n = 240) enrolled in the Bachelor of Nursing course were invited to participate. Lecture attendance was high at the start of the semester, fluctuated weekly and declined as the semester progressed. Students averaged between 3.5 and 4.4 hours of engagement per subject per week. They defined engagement as actually coming to class and a commitment to learning. Students were engaged by new, interesting content and disengaged by repetitive or complex content and poor tutoring. Most students want to engage but are distracted by intrinsic and extrinsic factors. Research should explore how to best assess students without the concurrent academic workload interfering with their studies.

In contemporary society, a marked decline in humanity's intrinsic values has become a point of lamentation for many observers. This is particularly evident when one considers the recognition often bestowed upon individuals of dubious character, while those who embody exemplary virtues are frequently overlooked or forgotten. In this context, this paper seeks to pay rightful tribute to David Kwadwo Boadu—the Renaissance Man of Kyekyeku—a figure whose remarkable life reflects a profound dedication to multiplicity and benevolence. This study delves deeply into his multifaceted contributions spanning various domains, including his roles as a husband, father, farmer, herbalist, midwife, hunter, catechist, musician, builder, arbitrator, counsellor, and cacao merchant. Each of these roles highlights essential themes of generosity and diversity, serving to illustrate how such attributes shape both an individual's identity and their contributions to the broader society. Utilising qualitative approach that involved interviews and employing the Streamwrite methodology—an innovative art-based approach designed to engage with the complexities of human experiences—this study underscores the critical importance of recognising individuals who exemplify these virtues as key to restoring the eroding humaneness in our communities.

The purpose of the study was to examine teachers’ intrinsic and extrinsic motivation in leadership for learning (LfL) in Aboabo Educational Circuit (AEC) in the Ashanti Region of Ghana. The study employed an explanatory correlational quantitative research approach. The population of the study consisted of ten (10) headmasters and forty-two (42) teachers in public Junior High Schools (JHS) of Aboabo Educational Circuit. Convenience, purposive and quota sampling techniques were used to select schools, headteachers and teachers for the study. The main instrument used for data collection was questionnaire. Spearman’s rank order correlation was used to analyse research hypotheses 1 and 2; Wilcoxon test was also used to analyse research hypothesis 3. The study revealed that intrinsic teachers’ motivation is negatively related to Leadership for Learning within the AEC. The study also indicated that extrinsic teachers’ motivation has an insignificant positive association with Leadership for Learning within the AEC. The study also concluded that there is a significant difference between Intrinsic Teacher Motivation (ITM) and Extrinsic Teacher Motivation (ETM) in AEC. Therefore, ITM and ETM plays minimal or no role within AEC. It is recommended that the officers within AEC must not focus only on high pupils’ academic achievement at the detriment of taking appropriate steps to make classroom teaching interesting and attractive. It is also recommended that School Management Committees within AEC must in their small way do their best to boost the extrinsic motivation of teachers within the circuit.