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The circle and its properties
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
A circle is one of the fundamental shapes of geometry; it consists of all the points that are equidistant from a central point. Knowledge of calculations involving circles is needed with crank mechanisms, with determinations of latitude and longitude, with pendulums, and even in the design of paper clips. The floodlit area at a football ground, the area an automatic garden sprayer sprays and the angle of lap of a belt drive all rely on calculations involving the are of a circle. The ability to handle calculations involving circles and their properties is clearly essential in several branches of engineering design.
Fundamentals
Published in Michael Hann, The Grammar of Pattern, 2019
A circle is thus an enclosed space, created by a line composed of a series of points in the same plane, with each point in the series positioned at an equal distance to a central stationary point (Rich 1963, p. 68, Jacobs 1974, p. 420, Hann 2012, p. 33). The line created from the set of points is known as a circumference, and a part of the circumference is known as an arc. A line between any point on the circumference and the centre is known as a radius (plural radii). A line joining two points on the circle is a chord. A diameter is a chord which passes through the centre of a circle. A centre, circumference, arc, chord, radii and diameter are shown in Figure 2.22 (adapted from Rich 1963, p. 68).
Geometry, areas and volumes
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
The part of a circle between 2 radii is known as the sector. If the sector is smaller than the semi-circle then it is called a minor sector, otherwise it is called a major sector (Figure 6.6b). ∠AOB in a minor sector is less than 180°, whereas in a major sector this angle is greater than 180°.
Describing the geometric difference of architectural forms in three primary shapes of circle, triangle and square
Published in Journal of Asian Architecture and Building Engineering, 2022
By definition, a circle is the locus of all points equidistant from a central point. It encloses the most space inside the shortest perimeter of all shapes and is considered perfect and compact by definition. Schneider (1995) traced ancient philosophers who believed that the circle represented the number one. Ching (2007) appreciated the circle in architecture as a centralized, introverted form that is usually stable and self-centring in its environment. Vartanian et al. (2013) showed that curvilinear contour activated the brain region more strongly responsive to objects’ reward properties and emotional salience than rectangular shapes through an fMRI experiment in neuroscience.
Teaching the circle equation using a practical mathematical problem
Published in International Journal of Mathematical Education in Science and Technology, 2022
In different countries, usually the topics on circle equation are taught in the upper secondary school through abstract materials. For example, in the Malaysian curriculum, this topic is taught for foundation or pre-university-level students. A circle is a geometric shape, consisting of all points in a plane that is a given distance (value of the radius) from a given point (centre of the circle). The following equation introduces a circle with the centre and the radius ;