For some of us, Christmas is a spectator sport. But I had a great time this year, vegging in front of my computer and watch all my friends on Facebook scurrying around getting ready for the holiday. By far, the best show this year was provided by my friends the Joneses, who got a little geeky when it came to setting up their Christmas tree.

It started on Sunday, when Mike, a computer guy, and son Nick, a 17-year-old homeschooler and engineering student at a local community college, posted the photo above of the two of them "using higher math to figure out how to get the tree into the tree stand." ("Beats lifting it up," cracked one friend of theirs.) The tree was sold as 11 feet high, but was probably a little taller, as mom Terri explained. In the end, the angel topper had to be tucked into the branches.

But even once they figured out how to trim the trunk, the math didn't stop there. Terri described the Jones Tree Lighting Technique:

I come from a family tradition of "Needs more lights!" Apparently it started with my parents' first Christmas together. Mom sent Dad out for more lights three times. My mom's idea is that you run lights out each branch, then back to the trunk, then out the next branch, spiraling down the tree. ... The result is a tree that glows from within, not just points of light on the surface. My father was, I'm pretty sure, incredulous their first Christmas together.

When we moved into this house, we calculated how tall a tree we could fit in the living room, and it was 11+ feet. When you light one of those with C7s it makes the living room nice and cozy. And the next step is to put on a lot of shiny balls that reflect the lights for added brilliance. Then the fancy ornaments. You can read by it when we're done, and I will.

So Mike and Nick got to work figuring out the "conical volumes to determine whether we have enough lights based on how much volume each light will have to fill." Nick called it "treegonometry." Here's Mike's explanation:

We figured that each light would have to be some distance away from every other light to allow us to decorate the whole tree with X number of lights (bulbs). If that distance exceeded the space between the lights on the strings then we couldn't decorate the whole tree. Thus we formulated the following: approximate volume of the tree divided by the number of lights on hand. This results in a unit of distance per bulb.

The problem with our technique was we assumed a spherical cow -- that is, we did not allow for all of reality in our calculations -- the density of our specific tree, or our specific style of decorating. A better method would combine the following information:

• The mass and density of the tree
• Information from previous Christmases on how many lights per feet per volume was required to produce satisfactory results.

Combining the number of lights and the length of the string would give better consistency (and allow calculations about how many strings to buy); the mass/density calculations would provide more accurate volume of the tree. A denser tree will, of course, require more lights -- this would accommodate that.

Going even further would involve approximating the actual routing of the lights on the tree based on the Jones Method of Tree Lighting. The mapping could estimate the minimum distance to cover the tree as well as adjust the density of the route (how close it comes to overlapping itself) based on tree density and lumens per distance of the light string.

Or, in Nick's TLDR summary: "Our number was wrong, so we had to buy more lights. But if we were geekier we might've gotten better results!"

Then came the discussion of why the Joneses need to buy more lights every year, since as Terri says "It is very strange, as we ... almost always have the same size (giant) tree, and somehow run out of lights about 3/4 of the way down and have to buy more every Christmas." A wormhole in the shed was proposed as a possible explanation.

Other Facebook spectators wondered about the other implications of using so many lights. One worried about the fire hazard. Terri responded:

[T]he key to fireproofing is to cut the tree on Xmas eve or the day before, and keep it well watered, and get it out of the house in about 14 days. With truly fresh trees, we've never had a problem. When we stopped using the old C6s for the twinkle lights, that made a huge difference.

However, Mike did add:

All I can say is, thank God for LEDs. One year we had good old incandescent C6s on the tree. I noticed after a couple of days that it was warmer in the living room than anywhere else in the house. A little math told us we were dumping about 2.5kW of electric heat into the room.

Apparently that's a lot, as one friend replied, "Two thousand five hundred watts? You've been showing your tree to orbiting astronauts?"

But the final result, as all their friends on Facebook agreed, was spectacular.

With the decorating done, Terri was able to sit and read by the light of the tree, while Nick worked on deriving the formula for volume of a cone. As Christmas approached, he was trying to use the method of disks to integrate and find the volume, although "I was all for doing a triple integral in cylindrical coordinates."

Truly, a geeky, geeky Christmas!

For more treegonometry, check out the work of the "maths" students at the University of Sheffield.