What is ethnomathematics?
Ethnomathematics is the study of the maths that people use in their own culture and daily work. Farmers measure fields, weavers count threads, builders mark out rooms, and artists draw patterns. Each group has its own tools and words, but the ideas (shape, number, symmetry, ratio) are shared by all. No single culture "owns" maths. Many cultures found the same ideas on their own, and learned from each other.
Three moves: slide, mirror, turn
A symmetry is a move that leaves a pattern looking the same. Start with one motif (a small shape) and use three moves:
- Slide (translation): move the shape along a line without turning it. Repeating a slide makes a border or a frieze, like the strip on a temple wall.
- Mirror (reflection): flip the shape across a line. A shape with a mirror line (line of symmetry) has two matching halves. A regular polygon with n sides has n lines of symmetry.
- Turn (rotation): spin the shape about a centre. If it fits itself n times in one full turn, its order is n and each turn is 360° ÷ n. A square has order 4 (90°). A regular hexagon has order 6 (60°). A rosette in a kolam or a carved ceiling often has 6, 8 or 12 petals.
Tiling floors and screens, and proportion in buildings
A tiling (tessellation) covers a floor with copies of shapes, with no gaps and no overlaps. Around each corner the angles must add up to 360°. A square has 90°, and 4 fit (4 × 90° = 360°). A regular hexagon has 120°, and 3 fit. An equilateral triangle has 60°, and 6 fit. A regular pentagon has 108°, and 360 ÷ 108 is not a whole number, so pentagons alone leave gaps.
Builders also use proportion. Many traditional buildings are designed from one basic unit, and every other length is a simple multiple of it (such as 1:2 or 3:4). A stone jaali uses repeating shapes to let in air and light while giving shade. Arches and domes use curves to carry weight. Which ratio a famous building uses is often debated, so measure before you claim.
Try it: find the moves around you
Draw one L-shape on squared paper. Slide it 5 times to make a border. Mirror it to make a pair. Turn it 4 times about a corner to make a pinwheel. Then in the 3D lab, change the number of turns from 2 to 8 and write down the angle for each. Next, look at a real floor or screen at home and name the moves you can spot.
Key formulas and definitions
- Angle of one turn for n-fold symmetry = 360° ÷ n
- Regular polygon with n sides: n lines of symmetry, order of rotation n
- A tiling needs the angles at a point to add up to 360°
- Regular shapes that tile alone: triangle (6 at a point), square (4), hexagon (3)
- Interior angle of a regular n-gon = (n − 2) × 180° ÷ n
Worked examples
1. What is the order of rotation of a square? What is the angle of one turn?
A square fits itself 4 times in a full turn, so the order is 4. One turn is 360° ÷ 4 = 90°.
2. A carved ceiling has a rosette of 12 identical petals. What is the angle between neighbouring petals?
360° ÷ 12 = 30°.
3. Can regular pentagons cover a floor alone? Use angles.
Interior angle of a regular pentagon = (5 − 2) × 180° ÷ 5 = 108°. At a corner we need a whole number of pentagons to give 360°, but 360 ÷ 108 = 3.33. It is not whole, so there will be a gap or overlap. They cannot tile alone.
4. A floor is made of 16 motifs in a 4 by 4 grid. Each 2 by 2 block is one pinwheel. How many pinwheel blocks are there?
16 ÷ 4 = 4 pinwheel blocks. The same block is slid to make the whole floor.
5. How many lines of symmetry does a regular hexagon have?
A regular n-gon has n lines of symmetry. A hexagon has 6.
Common mistakes
- Mixing up a slide and a turn. A slide never changes the direction the shape points. A turn does.
- Thinking a mirror copy is the same as a turn. A mirror copy is flipped, so a left hand becomes a right hand, and no turn can do that.
- Believing any regular shape can tile a floor. Regular pentagons and octagons leave gaps unless mixed with other shapes.
- Saying "ethnomathematics is only old or village maths". It is simply maths done within a culture, and it includes modern work too.