Symmetries of a Circle

Transcript

Symmetries of a CircleLet’s look at a circle We will discuss it’s Rotational and Reflection Symmetry both Let’s do it one by oneWe will discuss it’s Rotational and Reflection Symmetry both Let’s do it one by one Rotational Symmetry (Turning) When we rotate a circle around its center, it always "coincides with itself". Unlike a square (which only looks the same at 90^∘,180^∘, etc.), it doesn't matter what angle you rotate the circle by. A 1^∘ turn, a 30^∘ turn, or a 145^∘ turn all result in the circle looking identical to how it started. Thus, we can say every angle is an angle of symmetry. Since the angles can be decimal also, this means circle has infinite angles of symmetry Reflection Symmetry (Line Symmetry) Imagine a diameter, which is a line segment that passes through the center of the circle and connects two points on its rim. If we fold along this diameter, we find that the circle is symmetric along the diameter Thus, Diameter is a line of symmetry Since we can draw a diameter at any angle, we can conclude that "Every diameter is a line of symmetry!". This means the circle also has infinite lines of symmetry.