I have two names. I can make a good tiling pattern. I am symmetrical in two ways. All my corners are the same size, and I have two pairs of equal sides.
What am I?
Answer (3)
Rectangle.
A rectangle can also be called a quadrilateral, the two length sides are the same and the two height sides are the same. All the angles are 90°, and tiling patterns need to be something that tessellates, and rectangles tessellate.
The shape in question is either a rectangle or a square, both of which have two pairs of equal sides, four equal angles, and are capable of bilateral symmetry. They can create a tessellation pattern when repeated without gaps or overlaps, which fits the student's description of the shape.
The shape described in the question appears to have two pairs of equal sides, four equal angles (implying that all corners are the same size), and two directions of symmetry (also known as bilateral symmetry), enabling it to create a good tiling pattern.
These characteristics define a shape known as a rectangle. A rectangle can tile a plane without any gaps or overlaps, which in mathematical terms is referred to as tessellation. Rectangles and squares are common forms in tessellations due to their simple side-to-side and top-to-bottom fit which give the pattern a sense of regularity and cohesion.
Furthermore, the phrase 'I am symmetrical in 2 ways' suggests that the shape has two axes of symmetry, which is true for rectangles (each axis running through the midpoints of opposite sides). However, it can also apply to a square, which is essentially a special type of rectangle with all four sides of equal length. A square also fits the description and has even more symmetry due to its equal sides and angles - it has four axes of symmetry and rotational symmetry.
The answer is a rectangle, which is a quadrilateral with two pairs of equal sides and four right angles. It has symmetry along both its vertical and horizontal axes, making it ideal for tiling patterns. Overall, it fits all the characteristics described in your riddle.
;
