How many rectangles will fit about a point when tessellating the plane? How do you know?
Angles around a point = 360°
Each angle of a rectangle is 90°
So number of rectangles that can fit a point is 360/90=4
Thank you!
To determine how many rectangles will fit around a point when tessellating the plane, we need to consider the concept of symmetry and the properties of rectangles.
A rectangle can be defined as a quadrilateral with four right angles. It has two pairs of parallel sides, and opposite sides are equal in length. When we tessellate the plane with rectangles, we want to arrange them in a way that covers the entire plane without any gaps or overlaps.
Around a point, we can visualize the placement of rectangles by considering the rotational symmetry of a rectangle. A rectangle has a rotational symmetry of 180 degrees, meaning that if we rotate the rectangle by 180 degrees, it will look the same. This symmetry allows us to determine the possible arrangements of rectangles around a point.
When we tessellate the plane, we can start by placing a rectangle centered around the point. Then, we can rotate this rectangle by 180 degrees and place it again, creating one full rotation around the point. Since one full rotation equals 360 degrees, and a rectangle has a rotational symmetry of 180 degrees, we can fit two rectangles around a point.
Therefore, when tessellating the plane with rectangles, we can conclude that two rectangles will fit around a point. By considering the concepts of symmetry and rotational symmetry, we can arrive at this answer.