Morning Mathematical Monsters & Maniacs!
(Today’s post is sponsored by the letter “M”)
Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.
And what better way to start your week, then by discussing math Monday morning?
Recently we’ve had a lot of talk about Shelbyville and the Lemon of Troy episode. So this week, we’re going to look at a numeric system that pops up in that episode, Roman numerals.
In Season 6, Episode 24 Lemon of Troy, Bart and Milhouse are chatting while Mrs. Krabappel writes Roman numerals on the board.
Mrs. Krabappel: “Class, please! If you don’t learn Roman numerals, you’ll never know the years certain motion pictures were copyrighted.”
Nelson [bursting in to the classroom]: “Everybody come quick! Something’s happened. No time to explain.”
Mrs. Krabappel [as the kids run out after Nelson]: “No, children, no. Your education is important. Roman numerals, et cetera. Whatever. I tried!”
Later in the episode, Bart hides from the Shelbyville kids behind a door at the zoo labeled, “Danger: Tiger Feeding Area.” Inside are twelve doors numbered in Roman numerals I through XII. Bart reads a note: “Caution: Exit through Door 7 only. All other rooms contain man-eating tigers.”
Bart: “Roman numerals?! They never even tried to teach us that in school…. OK, think, Bart. Where have you seen Roman numerals before? I know: Rocky V. That was the fifth one! So, Rocky 5 [points to V], plus Rocky 2 [points to II], equals Rocky 7 [points to VII], Adrian’s Revenge!”
The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, employ seven symbols, each with a fixed integer value, as follows:
The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day. For our American readers, Roman numerals come back into fashion every early February when the Super Bowl comes around.
The original pattern for Roman numerals used the symbols I, V, and X (1, 5, and 10) as simple tally marks. Each marker for 1 (I) added a unit value up to 5 (V), and was then added to (V) to make the numbers from 6 to 9:
I, II, III, IIII, V, VI, VII, VIII, VIIII, X.
The numerals for 4 (IIII) and 9 (VIIII) proved problematic (among other things, they are easily confused with III and VIII, especially at a quick glance), and are generally replaced with IV (one less than 5) and IX (one less than 10). This feature of Roman numerals is called subtractive notation. The numbers from 1 to 10 (including subtractive notation for 4 and 9) are expressed in Roman numerals as follows:
I, II, III, IV, V, VI, VII, VIII, IX, X.
The system being basically decimal, tens and hundreds follow the same underlying pattern. This is the key to understanding Roman numerals. Thus 10 to 100 (counting in tens, with X taking the place of I, L taking the place of V and C taking the place of X):
X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C.
Note that 40 (XL) and 90 (XC) follow the same subtractive pattern as 4 and 9, avoiding the confusing XXXX and LXXXX.
By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus (modern day Portugal and Spain), by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient Arabic equivalents was quite gradual, and Roman numerals are still used today in certain contexts.
Roman numerals play another important role on The Simpsons, when they make an appearance every October in the Treehouse of Horror episodes.
Now we know more about one of the older, yet still used, numeric systems. Are you familiar with all 7 symbols of the Roman numeral system? Do you have trouble with Roman numerals? Bart managed to add Rocky V and Rocky II to get Rocky VII; but what would have happened if the exit was out of door 9? Would he have been eaten? Sound off in the comments below. You know we love hearing from you.