The other night my husband was away and I decided to take kids to a restaurant. While waiting for a three-person table to free up, my son has asked me, "Why there are no triangular tables? Why should three people be sitting at a four person table with one empty spot?"

Great question, I think. What do you think are the advantages and disadvantages of triangular tables?

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## 3 comments:

Great question from you son!

Triangular table advantages:

(1) everyone gets their own side

(2) it's different and unique

(3) the table has half the area of a square table with the same side lengths, so less clean-up

but...

(1) only half the area for placing food (so there is considerably less space per diner)

(2) the distance between diners is much smaller than for a square (and probably uncomfortable for everyone). [Assuming the triangle is equilateral and the diners each sit in the middle of their side, they are only sidelength/2 apart, whereas people facing each other on square a table are sidelength apart.]

I like the idea for its uniqueness, but I don't think we'll be seeing them in restaurants.

Great answer.

I would like to add one more advantage and one more disadvantage to Kim's list.

Advantage: triangles are used extensively in computer graphics to approximate smooth surfaces in a simple and cheap way. Take any surface (for example a face) and divide it recursively into triangles till each triangle is flat. You will get a multitude of triangles but it is easy to define them. Much easier than describing the curves of the face. Similarly, our triangular tables could be used to assemble many different shapes. For example, six triangles with all equal sides could be put together into a hexagon that will comfortably sit 6 people, or the same six triangles could be elegantly arranged in a chain with some random curves, creating a unique cool monster table sitting up to 14 people.

Disadvantage: a friend of mine that stopped by last night reminded me that people rarely appear in a restaurant in odd numbers. Much more frequently we could expect two, four or six people in a group. In fact my friend went on to suggest a "discrimination of odd number" in our environment. After you had one child, people are starting to ask you about your plans for a second. You are also likely to be asked whether you expect any company, when lunching or dining alone or in a group of three. But this sound as a beginning of another story or puzzle. New one tomorrow!

Consider what happens when tables are put together at restaurants: 2 sqaure tables seat 6, 3 seat 8, each time tables are put togther, 2 sides (2 seats) are lost, and the table's capacity is gained, yielding +2 seats per table for squares. For trianlge, each new table yields +1 seat. A party of 10 would require 9 tables. That would make the manager very unhappy to seat 1 party of 10 instead of 9 parties of 3 (but the dishwasher would like it).

The smallest circumferance (seats) to area (space consumed on the restaurant floor) atio is found in the circle, making it most ideal for tables (all else being equal), and teh triangle has the greatest ratio (making it the worst choise). Hexagons may be a better non-standard table shape.

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