Hexagons in a Honeycomb
Bees build hexagonal cells that tile the comb with no wasted space.
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Three hexagons meet at every corner: 3 × 120° = 360°, so the comb has no gaps. Scientists still wonder how bees make such regular cells.
Explain which regular polygons tile the plane using the angles at a corner, and meet tilings in art and in beehives.
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Copies of one shape spreading in every direction with no gaps.
Squares clearly tile the plane. So do equilateral triangles and regular hexagons.
Test each regular polygon's angle against 360°.
Problem. Are there regular polygons other than squares that can tile the plane? (Textbook p. 161)
Bees build hexagonal cells that tile the comb with no wasted space.
Three hexagons meet at every corner: 3 × 120° = 360°, so the comb has no gaps. Scientists still wonder how bees make such regular cells.
Questions about tiling the plane.
How many squares meet at each corner of a square tiling?
Find tilings around you and describe them.
Textbook p. 162. Find two tilings in daily life: floor tiles, a brick wall, a jaali screen, a honeycomb, a paving pattern…
For each one, name the shape or shapes, count how many meet at each corner, and check that the angles add up to 360°.