Sometimes when things get a bit overwhelming it’s good to turn to numbers and highways. As mentioned in earlier posts, I maintain a rather cursory yoga routine for both health/exercise and grounding. The number **108** comes up fairly often in cycles of repetition and I have been curious about its significance. Long before it was featured on *Lost*, 108 prominently figured in Hinduism as the number of beads on a *mala* and in other contexts, and through Hinduism finds its way into Buddhism. 108 has several interesting purely mathematical properties. My favorite is its being the *hyperfactorial* of 3. The hyperfactorial is the product of consecutive integers, each raised to itself as an exponent:

1^{1} x 2^{2} x 3^{3} = 108

Among the more random properties is being the sum of 9 consecutive integers:

**8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 = 108**

9 is of course a divisor of 108, as in **9 x 12 = 108**. And both 9 and 12 appear in the above series.

More significantly, 108 degrees is the angle of a vertex a regular pentagon, and 108 degrees can also be used to derive the *golden ratio*.

The relationship to the golden ratio would seem to be an interesting one, until one remembers that the representation of angles as degrees is itself arbitrarily based on the number 360. The 3π/5 radian representation is more significant in this regard.

And what about fun with highways numbered 108? Here in California, state highway 108 runs from the Central Valley town of Modesto northward and eastward across the Sierra via the Sonora Pass (north of Yosemite) to meet US 395 on the eastern side of the Sierra.

[*Photo by jodastephen on flickr. (License CC BY-ND 2.0)*]

While I have not driven CA 108, I am sure I have crossed its path on CA 120 on the way to Yosemite. From the picture above, it looks like it would be a nice drive, particularly in the summer. The eastern side of the Sierra has that stark, desolate quality, in comparison to the heavily wooded slopes on the western side. They are both quite beautiful, but the eastern side tends to speak to me more.

In New York, Route 108 is a short highway on Long Island. In fact, it is very short, a little under two miles total. It’s southern terminus is the picture below.

[*Photo by dougtone on flickr. (License CC BY-SA 2.0)*]

Route 108 southbound crosses into Nassau County, but soon curves away back into Suffolk. Soon after, the two-lane road continues into Trail View State Park, where the route becomes desolate, passing two local ponds.

It is interesting how the word “desolate” can come up for both highways, with very different connotations.

Fun with numbers, and highways.

Like that middle picture – very long road and nice view. 🙂

Always nice to come here and learn something

and see something interesting 🙂

Your topics about math are always interesting!!

Interesting how two very different highways on opposite coasts have more in common than just their number. Thanks for explaining more about the mathematics of 108.