How many lights should go on a Christmas tree?
“A good rule of thumb is 100 lights for every foot-and-a-half of tree,” according to Lowe’s. But Better Homes & Gardens recommends using three 100-light sets for every foot of a tree’s height. And Real Simple suggests 100 lights for every foot.
Since there’s no consensus about just how many lights is right, trimming a tree can be daunting for novice decorators. It’s even given headaches to mathematicians like Troy Henderson, a professor at the University of Mobile’s College of Arts and Sciences in Alabama. Last year, he developed what he describes as a hack to perfectly light a Christmas tree. By thinking of a holiday evergreen as an inverted cone, Henderson used the mathematical concept known as the conical helix to determine the right number of lights for his tree. He explained:
“Our Christmas tree is 3½ feet wide at its base and 8 feet tall. When using 75 feet of lights, the vertical spacing between rotations is about 7 inches. This ensures that if we begin wrapping the lights in a conical helix pattern beginning at the bottom of the tree and vertically space the lights by about 7 inches between successive rotations, the strands of lights will terminate precisely at the top of the tree.”
Henderson has made his Christmas tree light-spacing formula available to the public, and Dominik Czernia and Álvaro Díez, physics doctoral candidates studying in Poland and Turkey, respectively, have expanded on the mathematician’s work. They feature their approach on a web tool called the Omni Calculator. The free calculator factors in tree lights and ornaments and provides users with step-by-step computation and visualization. To use it, you’ll need to know some basic information, such as your tree’s height and bottom diameter, the length and spacing of the light strands, and the diameter of the ornaments you plan to use.
So who’s most likely to use a Christmas tree calculator? Is it designed for the math-and-science crowd or for anyone who wants a perfectly decorated tree? I interviewed Czernia and Omni Calculator Project founder Mateusz Mucha about the tool.
Who knew that decorating a Christmas tree even stumps physicists? What prompted you all to develop a web tool that could simplify this process for everyone?
We had been wondering how many lights and ornaments make a Christmas tree so beautiful. To our surprise, it was impossible for us to make at least some rough estimations. With the help of Dr. Henderson’s formula, we developed our intuitive tool with visualization of your perfect tree with lights and baubles. The best thing about it is the simplicity — all you need to enter are your tree’s dimensions.
The conical helix is the key to the calculator. Can you describe how this pattern works in more detail?
We surely can all agree that when we look at the Christmas tree, its shape reminds us of a cone, a pyramid with a circular base. So what does the conical helix have in common with a cone? Imagine you’ve got a ribbon that you attach to the top of a cone. Then start wrapping it around the cone, moving downwards until you reach the base. The curve formed by the ribbon is a conical helix.
Using the conical helix pattern, it’s helpful to look at a Christmas tree from the top while decorating it. Why is that?
One of the aesthetic factors that please most people is uniformity. The best way to check it is to look at a Christmas tree from the top so you can see every single ornament on it. Do they look uniformly distributed from that point of view? Perfect! That’s what we’re aiming for. This is another unique feature of a conical helix; it gives us excellent uniformity.
An efficiently decorated tree might even help cut down on electricity costs. That’s amazing.
It surely could help. The larger number of lights naturally translates into higher power consumption. However, we don’t want to resign from the lights entirely; they’re one of those things which bring a magical Christmas atmosphere. What we can do, though, is plan in advance how bright our Christmas tree should be to buy light strands of appropriate length.
This allows us to avoid the situation in which the light strand is too long, and we hide it somewhere in the tree foliage or leave it trailing on the floor. But still, these redundant lights will use electricity and generate costs! A well-decorated tree has uniformly distributed lights around; thus, it looks as pretty as we wanted, and simultaneously, the length of strands is perfectly adjusted to the Christmas tree’s dimensions.
Who’s the target audience for the Omni Calculator? Is it mostly math-and-science types, or have normies expressed interest?
Omni Calculator is used both by geeks and people who aren’t as confident with math, but it’s actually the latter group we think about the most. People have thousands of decisions to make that they should base on numbers. But they don’t think in terms of math formulas, don’t have the time, or just don’t feel like making this effort. And they end up making bad decisions. It’s our goal to make this process easy, fast, and kind of fun so that people are more likely to do the math.
On the Omni Calculator site, there’s a funny gif of Monica from Friends. She turns a Christmas tree around to show off her expertly decorated side of the tree and to hide the very messy side her friends decorated. Do you think Monica would use your calculator?
Sure, but it’s actually Joey and Rachel who could get the most value out of it. Chandler suffers through Excel every day, so he’d be capable. Ross would somehow make the tree about dinosaurs, and Phoebe would try to save the tree and homeless squirrels instead.
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