As the calendar year draws to a close, I often think about using Geometiles to build a representation of the number corresponding to the upcoming year. Our soon to end 2025 was a square number, which lent itself to a very elegant representation as 2025=45×45. That was a tough act to follow, so for 2026, I decided to switch numeral systems altogether and go with Roman numerals. This provided me with an opportunity to construct my first letter “M” with Geometiles, and I was thrilled with the result:
I used scalene right triangles, isosceles right triangles, equilateral triangles, rectangles and squares to build this letter. In other words, all the Geometiles shapes except pentagons were necessary. To the best of my knowledge, Geometiles is the only construction system that makes it possible to build an “M” like this.
The origins of Roman numerals are somewhat obscure, but one thing is certain: they have been in use at least since the time of the ancient Rome. In Roman numerals, each letter represents a numerical value as follows:
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
You may have seen a string of these letters written on older buildings. To translate the Roman numeral into our standard Hindu Arabic numerals, one adds the numbers from left to right as long as the number on the right is less than or equal to the number to its left. Otherwise, if the number on the left is smaller than the number on the right, you subtract it from the number on the right. For example:
MVIII
stands for 1008, but
MIX
stands for 1009. The I is in front of the X, IX represents 10-1=9
Now you can see that
MMXXVI stands for 2026.
Besides adding an air of class to old buildings, Roman numerals are also used in movie title credits in order to make it difficult for the viewers to know when the movie was made– so they don’t decide that the movie is too old to watch. There is a funny example of a simple Roman numeral math mistake that resulted in much larger monetary losses. The movie in question is “The Last Time I Saw Paris” starring Elizabeth Taylor.
If you look at the line under the word “Saw” you will see
COPYRIGHT MCMXLIV
Those Roman numerals stand for 1944. In fact, the movie was made in 1954, so it should have read
COPYRIGHT MCMLIV
Copyrights are typically valid for 28 years, and this mistake took 10 years off this number. So the copyright expired in 1972 instead of 1982. MGM must have thought that it had 10 more years, so it did not renew the copyright in 1972. As a result, the movie ended up in public domain, causing MGM to lose a lot of money in royalty. MGM seems to have done well for itself despite this financial hit, but the rest of us might take this story as a lesson to be careful with numbers!
This could be a great activity to start the year in a classroom or a math club! You could build 2026 with your students in either Hindu Arabic numerals or Roman ones– or both! The letter “M” is especially fun to build. Here are some videos about building it.