Recreate this design using only a ruler and compass —

Question

Homi · Accepted Answer

Understand the Question

To recreate the floral/curved pattern inside a square using only a ruler and compass:

Construct a square $ABCD$ .
Locate the midpoint of each side ( $P, Q, R, S$ ) using perpendicular bisectors.
Using each midpoint as a center and half the side length as radius, draw inward-facing semicircles on each side.

Step 1 · Draw a Square

Draw a square with any convenient side length and label its vertices $A$ , $B$ , $C$ , and $D$ . Diagram 1

Step 2 · Find Midpoints of the Sides

Construct the perpendicular bisector of each side using a compass:

With compass width greater than half of $AB$ , draw arcs from $A$ and $B$ above and below the line.
Join the intersection points of the arcs to locate the midpoint $P$ on $AB$ .
Repeat this process to find:
- Midpoint $Q$ on side $BC$
- Midpoint $R$ on side $CD$
- Midpoint $S$ on side $DA$

Step 3 · Draw the Semicircles

Set the compass radius equal to half the side length of the square (radius $= AP$ ):

With center $P$ , draw a semicircle connecting $A$ and $B$ facing inside the square.
With center $Q$ , draw a semicircle connecting $B$ and $C$ facing inside the square.
With center $R$ , draw a semicircle connecting $C$ and $D$ facing inside the square.
With center $S$ , draw a semicircle connecting $D$ and $A$ facing inside the square.

Step 4 · Highlight the Boundary

Trace and colour the boundary of the four semicircles using a coloured pencil to complete the design.

Answer

The design is constructed by drawing inward semicircles on all four sides of square $ABCD$ centered at their respective midpoints $P, Q, R, S$ with radius equal to half the side length.

Common Mistakes

Inward vs. Outward Semicircles: Drawing the semicircles facing outward from the square rather than inward toward the center.
Incorrect Radius: Changing the compass width between drawing different semicircles. Ensure the radius remains constant at $\text{radius} = \dfrac{1}{2} \times (\text{side of square})$ .
Inaccurate Midpoints: Estimating the midpoints with a ruler instead of constructing exact perpendicular bisectors with a compass.

Question 4

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