HSC Higher Mathematics 1st Paper Note 4th Chapter Circles. A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the center; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the center is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior. In everyday use, the term “circle” may be used interchangeably to refer to either the boundary of the figure or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc. A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using the calculus of variations.
HSC Higher Mathematics 1st Paper Note 4th Chapter Circles
The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy, and calculus.
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