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The circle and its properties
Published in John Bird, Basic Engineering Mathematics, 2017
Find the area of a circle having a circumference of 60.0 mm Circumference,c=2πrfrom which radius,r=c2π=60.02π=30.0πArea of a circle=πr2i.e.area=π30.0π2=286.5mm2 $$ \begin{aligned}&\text{ Circumference}, c = 2\pi r\\&\text{ from} \text{ which} \text{ radius}, r = \frac{c}{2\pi } = \frac{60.0}{2\pi } = \frac{30.0}{\pi }\\&\text{ Area} \text{ of} \text{ a} \text{ circle} =\pi r^{2}\\&\text{ i.e.}\quad \mathbf area = \pi \left({\frac{30.0}{\pi }} \right)^{2}\,{=}\,\boldsymbol{286.5\,\mathbf{mm}^{2}} \end{aligned} $$
Students’ mathematical reasoning on the area of the circle: 5E-based flipped classroom approach
Published in International Journal of Mathematical Education in Science and Technology, 2023
Mehmet Demir, Yılmaz Zengin, Şule Özcan, Selin Urhan, Nazlı Aksu
In the context of geometry, Duval (1998) argues that the cognitive processes underlying the students’ reasoning should be examined to determine the difficulties they experience. Circle is one of the concepts with which students have difficulties in geometry (Akyuz, 2016; Ansong & Wiafe, 2021; Diana et al., 2020; Ertem-Akbaş & Cancan, 2020; Putriani & Rahayu, 2018). The students encounter the difficulties in the topics of the circle, circumference of the circle, and area of the circle at the secondary school level. In addition, research shows that they have difficulty in defining the concepts of circle and circular region (Sudihartinih & Purniati, 2019; Tsamir et al., 2015; Ünlü, 2022). Another difficulty experienced by the students is that they cannot distinguish between the area and circumference of the circle (Rejeki & Putri, 2018). Diana et al. (2020) stated that the students struggled to use the formula and to explain how to calculate the circumference or area of the circle when its radius or diameter is provided. It was also revealed that the students had difficulties with the following concepts: the degree and radian in the problems related to the geometric figures drawn in a circle, the interior, exterior, central and peripheral angles, and drawing a circle with the equation given (Ertem-Akbaş & Cancan, 2020). As claimed by Rejeki and Putri (2018) problems with complex context should be used more to enable students to better understand the area of the circle.
UAV manipulation by hand gesture recognition
Published in SICE Journal of Control, Measurement, and System Integration, 2022
Shoichiro Togo, Hiroyuki Ukida
Step 3.1. The range of motion of the hand can be fixed. Therefore, we set “the hand detection region,” and the right hand position is searched with in this region. We assume that the hand detection region satisfies following conditions. The hand detection region is shown in Figure 3(b): Inner area of a circle whose centre is and its radius .Eliminate the area where y-coordinate is upper than .Eliminate the area of “Not used detection region” where it includes human’s head in Figure 1.
Calculus of pasta, sausages, and bagels: can their surface areas be derivatives of their volumes?
Published in International Journal of Mathematical Education in Science and Technology, 2020
For a right cylinder with changing radius and fixed length L such as the situation illustrated in Figure 1, we start with the circle of radius r (Figure 1(a)). When the radius is extended from to , the area of the circle changes by . If we neglect higher powers of , we arrive at relationship (4). But this is just with respect to the cross-section of a right cylinder (parallel to its base), and if we consider this change over the entire length, L, the increment of volume of the cylinder is , and the derivative of is equal to the lateral area of the cylinder − not the total surface area (5). This is reasonable because the increment in cylinder volume is the result only of extending the lateral surface.