Bounded by the statements of Feynman and Galileo, I describe certain tricks that can be useful for the teaching of physics. In particular, I describe the calculation of the center of mass (centroid) of an arc of circumference and a circular sector. For this purpose, I also use Pappus's theorems. An Appendix is available with Archimedes' method to…

Keto-enol tautomerization is paramount to understanding the mechanisms involved in many organic reactions and biochemical transformations. Isomerization of an enol to a carbonyl compound is typically introduced during the discussion of the acid-catalyzed electrophilic addition of water to alkynes. The tautomerization of carbonyl compounds to enol…

Computational thinking (CT) is becoming increasingly important for K-12 science education, thus warranting new integrations of CT and science content. This intervention study integrated CT through unplugged, or handwritten, algorithmic explanations of natural selection. As students investigated natural selection in varying contexts (specific and…

Ion transport, involving the diffusion and migration of ions within the electrolyte, stands as a fundamental concept in electrochemistry and serves as the driving force for electrochemical reactions. Electric double layers are critical in the fields of electrochemical energy storage and chemical conversion, constituting a central focus of…

The study and analysis of enzymatic reactions are essential for characterizing various biological systems. As part of these procedures, it is important to understand how to quantify the biological activity of these proteins in terms of enzymatic activity. This work proposes a general equation for determining enzymatic activity based on…

Enrico Fermi is remembered for his many contributions to theoretical and experimental physics, but from an educational point of view he also popularized the use of the kind of questions we now call "Fermi problems" (or "Fermi questions"). Fermi problems (FPs) are back-of-envelope problems that arose from the need to make order…

In this article we find the thermodynamics of some large N particles systems and some small N particles classical systems using micro canonical ensemble. Small N particle systems are seldom done in textbooks, since statistical mechanics(SM) systems work for large N systems. We show that small N systems will help the students to get an insight…

Valence shell electron pair repulsion theory (VSEPR) as explained in most textbooks predicts that substituents bonded to a central atom in AX[subscript n]E[subscript z][superscript c] species (A = main-group central atom, X = substituent, E = lone pair on central atom, c = charge) will change their X-A-X angles to bend away from the lone pairs.…

Background/purpose: Computational Thinking is a content that has been integrated into primary education curricula in several countries. Its proper integration into education is not limited to its inclusion in the educational curricula, and teachers and pre-service teachers must develop the necessary knowledge to integrate it into their practices…

Synthesis of (Z)-alkenes is challenging because the (E) stereoisomers are usually more stable. Energy transfer photocatalysis has emerged as an efficient strategy for (E) [right arrow] (Z) alkene isomerization. We report the development of an advanced undergraduate laboratory experiment that introduces students to contemporary organic…

The relativistic addition of velocities is usually introduced early in the study of Einstein's special theory of relativity. The equations are simple enough, but randomly chosen velocities lead to unwieldy calculations that can dishearten the student. This paper presents tables of velocity components in two dimensions, composed of five or fewer…

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into…

It is difficult for an instructor to just make up valid numbers for B[subscript x], B[subscript y], B[subscript z], E[subscript x], E[subscript y], and E[subscript z] in the creation of homework problems and test questions calculating the Poynting vector. In this paper, 25 examples are given of the electric and magnetic fields of electromagnetic…

This short paper presents an educational approach to teaching three popular methods for encoding DNA sequences: one-hot encoding, binary encoding, and integer encoding. Aimed at bioinformatics and computational biology students, our learning intervention focuses on developing practical skills in implementing these essential techniques for…

Background/purpose. 21st-century skills are essential across all aspects of life in the modern era. Pre-service elementary school teachers must also develop computational thinking skills as part of the problem-solving process--one of the most critical 21st-century competencies. These skills are critical in science learning and serve as fundamental…