Numbers 1
Page: 5 of 6
Geometric Construction of √2
- Draw line segment [AB] of length 1 unit
- Construct a perpendicular line, m, to [AB] at B
- Construct a circle with a centre at B and a radius of [AB]
- Mark the intersection of the circle and the line m at C
- Draw the line segment [CA]
- |AC| = √2
Proof:
- |AB| = |BC| = 1
- |AB|2 + |BC|2 = |AC|2 Pythagoras
- 12 + 12 = |AC|2
- 2 = |AC|2
- √2 = |AC|