Tessellation Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyDoes an equilateral triangle tessellate the plane? Justify your answer using the interior angle.
Solution
- 1 Interior angle of equilateral triangle: .
- 2 — exactly triangles fit around each vertex with no gap or overlap.
Answer
Yes; equilateral triangles tessellate because of them meet at each vertex to form exactly .
Because divides exactly six times, six equilateral triangles can always be arranged around any vertex point without gaps or overlaps. This makes the equilateral triangle one of only three regular polygons that tessellate alone.
About Tessellation
A tessellation is a pattern that covers an infinite plane with repeated geometric shapes, leaving no gaps and having no overlaps.
Learn more about Tessellation →More Tessellation Examples
Example 1 medium
Explain why regular hexagons tessellate the plane but regular pentagons do not.
Example 2 hardA proposed semi-regular tiling places [formula] triangles and [formula] squares at every vertex. Ver
Example 4 mediumA tiling uses regular octagons and squares. One proposed vertex arrangement has [formula] octagon an