Math 181.S96, Construction: The Silver Section
ANIMATE:
The construction, animated at the rate of one frame per second.
THE STEPS: The construction, step-by-step.
- Step 01
: We begin with a square.
- Step 02
: Draw a diagonal line through the corners.
- Step 03
:Draw the other diagonal.
- Step 04
: The crossing of the two diagonals locates the
center of the square.
Draw the circle centered at the SW corner and
passing through the center of the square.
- Step 05
: Draw the circle centered at the NW corner and
passing through the center of the square.
- Step 06
: Draw a line across the square, connecting
the two points where the construction circles
intersect the sides of the square.
- Step 07
: Here is the (vertical) silver section line!.
- Step 08
: Repeat the construction,
using the SW and SE corners of the square.
This is a horizontal silver section.
- Step 09
: Here are the two silver sections, one horizontal, the
other vertical.
- Step 10
: Suppose the size of the original square
(magenta) is one.
- Step 11
: Then the size of the (yellow) square cut out
by the two silver section lines is one half.
- Step 12
: Now lets start all over again,
within the yellow square.
- Step 13
: The green square has half the area of
the yellow square, and thus, one fourth
the area of the magenta square.
- Step 14
: The corner of the green square is in
the center of the original square.
- Step 15
: Four green squares exactly fill
the original square.
Revised 08 April 1996.
