How many rectangles will fit about a point when tessellating
the plane? How do you know?
Four rectangles can touch a point. The corners occupy 90 degrees and there are only 360 degrees available.
Why does a regular pentagon not tessellate the plane?
To determine how many rectangles will fit around a point when tessellating the plane, we need to understand the concept of tessellation and the properties of rectangles.
Tessellation refers to the process of covering a plane with congruent copies of a shape without any overlaps or gaps. In this case, we are considering rectangles as the shape for tessellation.
To find the number of rectangles that can fit around a point, we need to analyze the arrangement of rectangles in the tessellation pattern. We can start by considering a single rectangle around the point.
In order for rectangles to tessellate the plane, they must fit together without gaps or overlaps. To achieve this, each side of a rectangle must align with a corresponding side of adjacent rectangles. This alignment creates rows and columns of rectangles around the point.
Looking at the arrangement, we notice that two rectangles can fit along one side of the point. Similarly, two rectangles can fit along the other side. Therefore, the total number of rectangles that fit around a point in a tessellation is the product of the number of rectangles on each side.
By multiplying the number of rectangles on each side, we get the formula:
Number of rectangles = (number of rectangles on one side) * (number of rectangles on the other side)
This formula applies to any point in the tessellation pattern. Hence, the number of rectangles that will fit around a point when tessellating the plane can be determined by counting the number of rectangles on each side of the point and multiplying those values together.