How to construct a square root n with an iterative structure of a geometric artboard

If there is a segment ab=1, how to iterate the performance length of the segment effect? The specific steps are as follows:

1. Construct point A, "transform"-"translate", set the translation distance to 1 centimeters in the pop-up dialog box, angle is 0°, get point C, construct Ray AC. Draw the moving point B on the Ray AC, construct the segment AB, hide the point C and Ray AC; measure the length of the segment AB to get the measure.

Construct a segment AB and measure its length

2. Construct Point D near B to construct segment ad. The perpendicular of the D-structured segment ad over point. Select Point D and Segment AB length measures, "construct"-"Draw circle with center and radius", get intersection of circle and perpendicular line E, construct segment ae and DE. Select the segment AE, construct the midpoint F.

Construction segment AD, AE, and de examples

3. New parameter K, value 3, unit none. New parameter n, value 1, unit none. Establish the calculation "n+1". Using the Text tool, enter the text in theblanks "": Use the symbol notation to enter the square root format, in the "?" , click on "N+1" to calculate the value and introduce a dynamic computed value, shown as"".

New parameter k, n and calculate value

4. Select "" and point F, hold down SHIFT and click "Edit"--"merge text to points." Hide Point F, Circle and vertical, select Point D (original image), parameter n (original image) and parameter K (iteration depth), hold SHIFT key, "transform"-"depth iteration". Click on the point e, n+1, in the "Structure" to cancel the generation of data tables, and finally click the "Iteration" button.

Select point D and Parameter n, K perform iterative operations

5. Select Point D and Point B, "edit"-"merge Point", point D disappears, only point B. Change the size of the parameter k, you can change the number of iterations, the horizontal direction to change the position of point B, you can change the size of the graphic.

Merge point D and point B complete iterative fabrication

In this paper, The iterative method of non-free point of the geometric artboard is explained by constructing the geometry sketchpad, in fact, the iteration of the series can be realized by using the geometric sketchpad.