Project Maths Online

Numbers 1

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Geometric Construction of √3

• Draw line segment [AB] of length 1 unit
• Construct a circle with a centre at A and a radius of [AB]
• Construct another circle with a centre at B and a radius of [AB]
• Mark the intersections of the two circles C, D
• Draw the line segment [CD]
• |CD| = √3

Proof:

• [CD] is the perpendicular bisector of [AB]
• |AE| = |EB| = ¹⁄₂
• |AC| = |BC|
• |AE|² + |EC|² = |AC|² Pythagoras
• (¹⁄₂)² + |EC|² = 12
• ¹⁄₄ + |EC|² = 1
• |EC|² = ³⁄₄
• |EC| = √³⁄₄
• |EC| = ^√3⁄₂
• |CD| = 2|EC|
• |CD| = 2 (^√3⁄₂)
• |CD| = √3