Circles and the three types of symmetry
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This document discusses circles and the three types of symmetry. It defines a circle as a closed loop where every point is equidistant from the center. Circles have properties like a center, radius, diameter, circumference, and area. It also discusses chords, tangents, and secants of a circle. Finally, it explains that a circle has all three types of symmetry - reflectional symmetry across the x-axis, y-axis, and rotational symmetry around the origin - as demonstrated by the equation x^2 + y^2 = r.
Circles and the three types of symmetry
- 1. Circles and the Three types of Symmetry By Andrew Lee
- 2. Symmetry • The correspondence in size, form and arrangement of parts on opposite sides of a plane, line, or point; arranged reciprocally or correspondingly.
- 3. What is a Circle? • “A line forming a closed loop, every point on which is a fixed distance from a center point.” • Has no edges. • Sum of angles inside is 360` • "The set of all points equidistant from the center". This assumes that a line can be defined as an infinitely large set of points.
- 4. Properties • Center = A point inside the circle. All points on the circle are equidistant (same distance) from the center point. • Radius = The radius is the distance from the center to any point on the circle. It is half the diameter. • Diameter = The distance across the circle. The length of any chord passing through the center. It is twice the radius. • Circumference = The circumference is the distance around the circle. • Area = Strictly speaking a circle is a line, and so has no area. What is usually meant is the area of the region enclosed by the circle. • Chord = A line segment linking any two points on a circle. • Tangent = A line passing a circle and touching it at just one point. • Secant = A line that intersects a circle at two points.
- 6. A circle that has all three types of Symmetry • Solution: - Use the equation x^2 + y^2 = r - x and y being a point on the circle and the r being the radius. note: when x or y is replaced by a (-x) or (-y) it will still remain the same, because (-x)^2 is equal to x^2. - it has to be symmetric with respect to the x-axis, y-axis and origin.