The ceiling light fixtures in the Texas Ballroom at the Hyatt Regency Austin have an interesting geometry. Each one consists of four concentric cylinders.
The configuration suggests a variety of mathematical questions concerning, say, relative area or volume.
Even more intriguing, however, are the rings of lights between the cylinders. One light sits in the center circle, eight in the first ring, ten in the second ring, and sixteen in the third. Is there a pattern?
We have the sequence: 1, 8, 10, 16, which suggests the following question: If the fixture were to have a fourth ring, how many lights would it contain?
Neil Sloane's On-:Line Encyclopedia of Integer Sequences is one source of possible answers. Querying the database, however, produces just one result for the string 1, 8, 10, 16. These are four consecutive numbers representing the absolute difference between the sum of the odd digits and the sum of the even digits of the nth prime, starting at n = 19. The next number in this sequence is 5, and that doesn't make sense in the context of the light fixtures.
So, is there a pattern, beyond the notion that the number of lights should increase as you move away from the center? What would be a plausible number for the fourth ring?
Photos by I. Peterson