Math 181.S96, Construction: The Oriented Square
ANIMATE:
The construction, animated at the rate of one frame per second.
THE STEPS: The construction, step-by-step.
- Step 01
: Given an orientation and a length.
- Step 02
: Make a circle of any convenient radius.
- Step 03
: Using one of the intersections of the circle and the line as a center,
draw another circle of a convenient radius.
- Step 04
: Using the other intersection as a center,
draw another circle of the same radius as in Step 03.
- Step 05
: Draw a line through the intersections of the circles of Steps 03 and 04.
This is perpendicular to the given orientation, bisecting the given length.
NOTE THE VESICA PISCIS.
- Step 06
: Draw a circle of the given length.
- Step 07
: Draw a square in the circle of the given length, using the
cross of Step 05.
- Step 08
: Now bisect the NorthEast side of the square. Begin
with a circle of a convenient length at the North end.
ANOTHER VESICA PISCIS.
- Step 09
: Draw a circle of the same size at the South end.
- Step 10
: Using the intersections of these two circles,
draw the perpendicular bisector of the NorthEast
side of the square.
ANOTHER VESICA PISCIS.
- Step 11
: Here is a cleaner view of the construction so far.
Using the midpoint of the NorthEast side and the
center point, set the compass for the next circle.
- Step 12
: Now draw the circle inscribed in the square.
- Step 13
: Transfering half the length of the NE side of the square
to the other three sides, draw the horizontal square inscribed
in the circle inscribed in the inclined square.
- Step 14
: Connect the corners of the square in the circle in
the square in the circle! (This step is optional,
but traditional.)
- Step 15
: With constructions removed, here is the desired
square of the given length and orientation.
Revised 14 April 1996.
