Question

Construct a square root spiral with pythagoras formula

Answer 1

To represent √2 on a number line.

Draw a line OX on the tracing paper. Mark point O on one end and mark points 0, 1,2, 3, … at equal distances of 1 unit by paper folding.

Fold the paper along the line that passes through the point marked ‘1’ and perpendicular to the line OX, i.e., fold the paper in such a way that point ‘O’ coincides with point ‘2’. Make a crease and unfold it. From the point marked ‘1’, draw a line of length 1 unit moving along the crease. Mark the point as M such that PM = 1 unit. Join OM, clearly OM= √2 units.

Fold the paper along the line ( fold on point M in such a way that point O joined with any point lie on OX,) that passes through point M and perpendicular to OM at M. Make a crease and unfold it. From the point M, draw a line of 1 unit moving upward, along the crease. Mark the point as N such that MN = 1 unit. Join ON, where ON = √3.

Keep this process continuously to get √4, √5, √6, ……….

Answer 2

$\sqrt{4 \sqrt{5 \sqrt{6} } }$