Math: Circles
Many natural and human objects are circle-shaped. Students will come to understand that the two basic dimensions of a circle are its circumference and its diameter. Using real life examples students will be shown how the basic geometric objects are useful in everyday life.
A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius.
This lesson is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that 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 calculus of variations. Annulus: a ring-shaped object, the region bounded by two concentric circles. Arc: any connected part of a circle. Specifying two end points of an arc and a center allows for two arcs that together make up a full circle. Centre: the point equidistant from all points on the circle. Chord: a line segment whose endpoints lie on the circle, thus dividing a circle in two segments.
Through relatable examples and relatable narration, the video explores the fundamental dimensions of a circle. With clarity and simplicity, the concepts of circumference and diameter are unveiled. Students are guided to understand how these geometric properties not only define circles but also play a crucial role in problem-solving and design.
Real-life applications take center stage as young learners witness how these basic geometric objects are pivotal in everyday scenarios. From the formation of pizza slices to the creation of merry-go-rounds, students grasp the practicality of circles in a tangible and exciting way. (4:34)
Properties of Circles
A circle is a two-dimensional, closed shape that has no edges or corners. It can be thought of as the set of all points in a plane that are equidistant from a single point called the center. The distance between any point on the circle and its center is known as the radius of the circle. The circumference of a circle is its perimeter, which is equal to 2π times the radius. A diameter is any line segment connecting two points on a circle that passes through its center. Circles can also be defined using equations, such as x2 + y2 = r2, where r is equal to the radius of the desired circle.