How to Construct a Golden Rectangle

Step-by-Step Guide

1. 1

   Step 1: Draw a square.

   Let us name the vertices of the square as A, B, C and D.
2. 2

   Step 2: Locate the mid-point of any one side of the square by bisecting it.

   Let us pick the side AB and call its mid-point as point P. , Since P lies on the side AB, the opposite side shall be the side CD.
   
   Let's choose to connect P with C. , Draw a large arc towards the side BC. ,,,, You just drew a Golden Rectangle AQRD.
   
   Erase any extraneous constructions if you so wish.
   
   You may verify that the ratio of the measure of the shorter side of the rectangle (QR or AD) to the measure of its longer side (AQ or RD) is very close to 1:1.618.
3. 3

   Step 3: Connect the mid-point P to a corner of the opposite side.

4. 4

   Step 4: Place the tip of the compass on P and set its width to match the distance PC.

5. 5

   Step 5: Extend the side AB to cut the arc at some point (say Q).

6. 6

   Step 6: Draw a line parallel to the side BC

7. 7

   Step 7: passing through the point Q.

8. 8

   Step 8: Extend the side DC to meet the parallel line at some point (say R).

9. 9

   Step 9: Congratulations!

Detailed Guide

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