Mathematics : Geometric constructions

Geometric square root construction (spiral of Theodorus)

Geometric construction of square root af a number with spiral of Theodorus of Cyrene (or spiral of Pythagoras or spiral of Einstein)

: S T E P S    O F   C O N S T R U C T I O N :

1. Construct an isosceles right triangle (with base and height (legs or catheti) = 1 → hypotenuse = square root of number 2 (Pythagoras theorem));

[Plane geometry, Pythagoras theorem  -  (local-Formule)]

2. Construct a circle with the center = one endpoint of the hypotenuse and radius = 1;

3. Construct a straight line perpendicular to the hypotenuse passing for one his endpoint (point = center of circle 2.);

[Geometric constructions, Perpendicular to a line segment through one of its endpoints  -  (locale-Formule)]

4. Fix the intersection points with the circle 1. and the straight line 2.;

5. Construct the new right triangle (passing for one point of 4. and the endpoints of the hypotenuse of the right triangle 1.;

6. Repeat 2. and 5. for all new right triangles constructed;

: G I F : GEOMETRIC CONSTRUCTION : Square root construction (spiral of Theodorus)