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Geometric Constructions
Published in Ken Morling, Stéphane Danjou, Geometric and Engineering Drawing, 2022
The length of the circumference of a circle is πD or 2πR, where D is the diameter and R the radius of the circle, π is the ratio of the diameter to the circumference and may be taken as 22/7 or, more accurately, as 3.142.
Rotational Motion
Published in Daniel H. Nichols, Physics for Technology, 2019
The unit radians may be unfamiliar. It has its origin in nature. Take any circle and place a string around it to measure its circumference. Then measure its diameter. Divide the circumference by the diameter, and the number 3.14159…, which is written as π, will result.
Learning linear equations: capitalizing on cognitive load theory and learning by analogy
Published in International Journal of Mathematical Education in Science and Technology, 2022
Similarly, the level of element interactivity for the equation of V = lwh would be lower for a learner who has prior knowledge and understanding of the formula of the area of a rectangle – that is: A = lw where lw represents a surface area or cross-section of the volume. Why this is the case? Simply for the fact that cognitive load theory (Sweller, 2005, 2012; Sweller et al., 2011) would inform and advise us to treat lw as a single unit if we have prior knowledge (schema) for the area of a rectangle (A). By identifying the relation between multiple interactive elements in the domain, it is sufficed to rationalize that a lower-level schema (i.e. area of a rectangle: lw) could assist a person in his/her acquisition of a higher-level schema (i.e. volume of a rectangle prism: lwh), which then would reduce the burden of the working memory load. From this description, as a point of summation, we could consider the following logical sequence to depict the capitalization of lower-level schemas. The formula of a circumference of a circle c = 2Πr may be reduced to c = Πd, where d = 2r (i.e. prior knowledge or low-level schema).