Let me ad my 2 cents into how to draw line with length SQRT(3) units. 1. Draw square rectangle with sides equal to 1 unit. 2. Draw any diagonal of that rectangle. Accordingly to Pythagorean theorem length of diagonal will be SQRT(1^2 + 1^2) = SQRT(2) units. See http://en.wikipedia.org/wiki/Square\_root\_of\_2 Notice that we just draw line with length measured as irrational number SQRT(2) units. 3. Draw perpendicular with length 1 unit to the one end of the above diagonal. You can do it by using caliper. 4. Draw line from another end of diagonal to the free end of above perpendicular. Accordingly to Pythagorean theorem length of this line will be SQRT(SQRT(2)^2 + 1^2) = SQRT(3) units. Therefore, we draw line with length measured as irrational number SQRT(3) units. We also can do it using caliper and drawing circle and hexagon. See http://en.wikipedia.org/wiki/Square\_root\_of\_3