Construction Methods in Śulba-Sūtras

Transcript

Construction Methods in Śulba-SūtrasLong before plastic rulers and metal compasses, ancient Indian mathematicians (from the Vedic period) needed to build fire altars with perfect shapes. They wrote their rules in texts called the Śulba-Sūtras (which means "Rules of the Cord" or Rope). All the construction methods in the Śulba-Sūtras make use of a different kind of compass from what you would have used — a rope. A rope can be used to draw circles or arcs. It can also be stretched to form a straight line. Let’s look at how we Construct Perpendendicular Bisector using Ropes Construction of the Perpendicular Bisector using a rope (Kātyāyana-Śulbasūtra ) Instead of a compass, they used a long rope and two pegs (sticks) in the ground. Set the scene: Imagine two sticks stuck in the ground at points 𝐗 and 𝐘. Prepare the rope: Take a long rope and fold it exactly in half to find its middle. Mark this middle point. Tie the two ends of the rope to the sticks at X and Y . Stretch it Up (Point A): Pull the middle of the rope tight towards one side (upwards in the diagram) until the rope is straight and tight like a triangle. Mark this point on the ground as 𝐀. Stretch it Down (Point B): Pull the middle of the rope tight towards the other side. Mark this point as B. The Result: Draw a line connecting 𝐀 and 𝐁. This line 𝐀𝐁 cuts right through the original line XY. It crosses exactly in the middle and stands at a perfect 90^∘ angle.