Making symmetric designs

Now that we can spot symmetry, let's make it. Given one half of a design, can we draw the other half? Can we design a symmetric rangoli from scratch? Yes , and it is great fun.

What is this?

To draw the mirror image of a half-given shape:

1. Identify the line of symmetry (it is given).
2. For each point on the original half, find the same distance on the other side of the line of symmetry.
3. Mark that mirror point.
4. Join the mirror points in the same order as the original.

The mirror image is like what you see in a mirror placed along the line of symmetry. Every point is the same distance from the mirror, but on the other side.

For drawing rangolis with symmetry:

1. Draw the line(s) of symmetry first.
2. Sketch a design on one side only.
3. Copy it to the other side(s).

For a 4-fold rangoli (like a typical square rangoli), draw a square with both diagonals and both midpoint lines. That gives 4 lines of symmetry. Draw a pattern in one of the 8 wedges and copy it to all the others.

This is exactly how artists make complex-looking patterns with simple repetition. Madhubani paintings, kolam designs, and mehndi all use this trick.

Worked examples

Example 1. Half a butterfly is drawn to the left of a vertical line. To draw the other half:

• Pick each point on the left half.
• Measure how far it is from the line.
• Mark the same distance on the right side.
• Join the points the same way.

Example 2. Half a heart shape is drawn. To complete:

• The straight side of the half is along the line of symmetry.
• Mirror every curve to the other side.

Example 3. Make a 2-fold symmetric design.

• Draw a vertical line on a paper.
• Sketch a leaf shape on the left side.
• Carefully mirror every point to the right.
• The result has line symmetry along the vertical line.

Try it

1. Draw a half-flower on the left of a line. Complete the right half by mirror reflection.
2. Draw a triangle on one side of a vertical line. Mirror it to the other side.
3. Make a symmetric design using a single horizontal line.
4. Make a symmetric design with 2 lines of symmetry (cross-shaped lines).
5. Design a 4-fold rangoli inside a square using both diagonals.

Hands-on

Paper-fold cut-out. Fold a paper in half. Draw a half-shape touching the folded edge. Cut along the curve. Open it , you have a perfectly symmetric shape.

Mini rangoli. Take a sheet of paper. Draw two lines crossing in the middle (vertical + horizontal). In one of the four quarters, draw any small design. Carefully copy it into the other three quarters, mirroring each time. Colour and admire.