Computer Assignment: Construction of a Golden Rectangle

Goal: Construct a golden rectangle

Step 1: Build a unit segment labelled AB

Step 2: Draw a line with two points labelled CD, this line should be horizontal or close to it inorder to match the diagrams provided.

Step 3: Construct a line perpendicular to line CD passing through point C( you may use the Construction Menu for perpendicular lines on this assignment )

Step 4: Construct a circle with a centre at point C with a unit radius ( length of segment AB )

Step 5: Construct Points of Intersection with the circle on line AB. These points are labelled Eand F on my sketch.

Step 6: Construct Points of Intersection with the circle on the line made in step 3. These pointsare labelled G and H on my sketch.

Step 7: Using what I labelled as point F construct a perpendicular line to CD passing throughpoint F.

Step 8: Using the point of intersection I labelled as G construct a perpendicular line to the linemade in step 3 passing through G.

Aside: What is the name of the shape defined by the points CFIG?

Step 9: The two lines made in the last two steps should intersect. Construct a point atintersection for these two lines. I labelled as I.

At this point you should see a square. Hide the lines that were constructed in steps 3 and 7.

Step 10: The top of the square is defined by two points the vertices G and I. Construct thesegment GI. Whilst that segment is selected construct the midpoint of that segment by using theConstruction Menu, and the Midpoint option. You may wish to build the segments CG and FI tohelp you see the square.

Step 11: Select the midpoint from step 10 and F. Construct a Circle by Centre and Point.

Step 12: The circle constructed in step 11 should intersect the line that helps define the top of thesquare twice. You will need to construct those points of intersection. I labelled these points as Land K

Step 13: Using K construct a perpendicular line to the line on which the point lies. This lineshould intersect the line which defines the lower side of the square.

Step 14: Construct the point of intersection described in step 13. I labelled this as M.

Step 15: Construct segments CG, GK, KM, and MC. Hide everything else except the segmentAB. Measure the length of one of the long sides then one of the short sides. Go to the MeasureMenu and choose Calculate. A window should appear on your screen. Move your pointingdevice to the first measurement that you made (the long side) and click on this. Next go to thedivision symbol in the box and click on it. Now move your pointing device to the secondmeasurement that you made (the short side) and click on it. You have just made a ratio of thetwo sides, next click on the OK button in the widow on the screen. You may change yourrectangle by playing with the segment AB. What happens to the ratio?

Save this as grec. Designed by David Jay Hebert, PhD