Stretching the Rope
Marking a perpendicular bisector on the ground with a rope, as in the Śulba-Sūtras.
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With the rope's two halves pulled tight, the marked point is exactly as far from one peg as from the other.
Draw a right angle at a point on a line or through a point outside it, and see how the Śulba-Sūtras did it with a rope.
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Make O the midpoint of a segment, then build its bisector.
To draw 90° at a point O on a line, find a segment of the line that has O as its midpoint. Its perpendicular bisector passes through O.
Two perpendicular constructions, step by step.
Problem 1. Construct a 90° angle at a point O on a line. (Textbook p. 141, Figs. 6.2–6.3)
Questions about constructing right angles.
To draw 90° at a point O on a line, the first step is to…
Vedic altar builders made perpendiculars with a rope and pegs.
Mathematicians in many ancient civilisations knew exact ways to construct perpendiculars. In India, the earliest known texts with these methods are the Śulba-Sūtras: geometry texts of the Vedic period about building fire altars. They are part of one of the six Vedāṅgas ('limbs of the Vedas').
Marking a perpendicular bisector on the ground with a rope, as in the Śulba-Sūtras.
With the rope's two halves pulled tight, the marked point is exactly as far from one peg as from the other.
Justifying Kātyāyana's method with equal distances.
Problem. Justify why AB in Fig. 6.4 is the perpendicular bisector of XY. (Textbook p. 142, Q1)
Think of another way to make a 90° angle with a rope.
Math Talk, Textbook p. 142, Q2. Can you think of a different method to construct a 90° angle at a given point on a line, using a rope?
Pegs, loops, folding, stretching…
Use equal distances.