I like watching HGTV, I really do. There is a calm that comes over me when I'm fed the easily digested format of 3 out 3 in each and every program they put out (3 homes to pick out from, 3 tiles to choose from, 3 problems that will be solved).
The number 3 is a magical number in the design world; 3 vases, 3 color choices, 3 windows. I even use the number 3 trick when presenting clients options of tiles, colors, etc., it's enough to show diversity, yet not too much that it overwhelms them. Flipping through random furniture store catalogs most of the spaces have some sort of 'casual' feel to them. If you look closely, you'll notice many spaces have an odd number of pillows on the beds, an arrangement of 3 cups on table, these little things make you feel at "home".
There is the saying 'three's a crowd', so why the number 3 in design?
I don't think that there is a clear cut answer to this, I can only try and give my take on it.
From the beginning of time, there was a need to define aesthetics in a certain way, one aspect was the use of theGolden Ratio , which in very layman terms is devision of space to 1/3 and 2/3.
This creates a bit of an imbalance yet not a complete upset of space.
In the Jewdeo-Christian cultures the number 3 stars in many ways, the 3 fathers, the 3 archangels,triptychpaintings at the alters. You see, we humans like things a bit messy, we like to round up some of the sharp edges of the corner. If there are only 2 vases on the fire place mantel, it will look balanced, it will look solid, static completely forgettable, and boring. We need to create a visual interest, something to draw the eye to, because if it's not balanced, we are intrigued. Any odd number would create this kind of visual upset, but most of us have small spaces and even smaller budgets.
Next time you arrange your dinning table, try putting 3 glasses of water with some flowers in them, I think the reactions you'll get will be great!