How often have you been eating a meal in one of life's
eating establishments, and thought, "I wish my napkin was more
aesthetically sized."?
I thought so, which is why I bring you 5 easy steps to make your eating experience that little bit more perfect.
- Start with a square portion of the napkin.
+-----------+
| |
| |
| |
| |
+-----------+
- Divide the square in half.
+-----+-----+
| | |
| | |
| | |
| | |
+-----+-----+
- Draw a diagonal across one of half of the square.
+-----+-----+
| | / |
| | / |
| | / |
| |/ |
+-----+-----+
- Use the diagonal as the radius of a circle, and complete an arc to the baseline of the square.
+-----+-----+-
| | / | \
| | / | \
| | / | \
| |/ | |
+-----+-----+------+
- Complete the rectangle from this point on the baseline.
+-----+-----+------+
| | / | \ |
| | / | \ |
| | / | \|
| |/ | |
+-----+-----+------+
You now are the proud owner of a napkin that is a
golden rectangle. What a pleasure wiping your mouth will be.
But, I hear you ask, how do you know that this is a golden rectangle? Well, dear reader, read on.
Lets say the original square was x by x. Given that, the length of the diagonal can be found using the school boy favourite, Pythagoras:
c2 = a2 + b2
x2
= - + x2
4
__________
| x2
c = | - + x2
\| 4
_____
| 5x2
c = | ---
\| 4
With that said, the bottom edge of the golden rectangle is:
_____
x | 5x2
- + | ---
2 \| 4
_____
x + \| 5x2
-----------
2
x ( 1 + √5 )
-------------
2
So, if we now consider this in terms of the ratio of short to long edge we have:
x ( 1 + √5 )
x : ------------
2
1 + √5
1 : ------
2
Which, my fellow geometrist, is the golden ratio.