On the War in Vietnam, and its Memorial

Vietnam Veterans Memorial

This is a starkly geometrical monument to the tens of thousands of American fighting men and women who died in the Southeast Asian theater of war, from 1957 to 1975.

At first, it just looks like a long, black, polished granite V or chevron half-buried in the ground. When you get closer, you begin to see that each of the stone panels has names that were carefully carved into the stone, five names per line, in no immediately obvious order.

But the names are in fact carefully catalogued in chronological order by date of death (or initial injury/wound/disappearance). The order starts in panel 1E, just to the right of the center bend, and continues to the right as you face the wall, up until the single line of names on panel 70E, for May 25, 1968, and then continuing with another single line of names on panel 70W, also for 5/25/68, and continuing from left to right up to panel 1W.

If you want to look up a person who died in that war, you can look their name up alphabetically online or in a printed directory that is the size of a large old-fashioned telephone book. There you can find their branch of service, rank, casualty date, state of origin, and a code giving the panel and line number on which his name is engraved.

Math connection:

1. How many names are carved on the wall?
2. What was the midpoint of the war, as far as US combat deaths are concerned?

The second question is by far the easiest to answer: it was May 25, 1968, because the panels on the left of the vertex are virtually identical to the ones to the right of the vertex in terms of numbers of names.

The first question is a bit harder.

It was suggested by an elementary-school child that one could simply think of each half of the V as a triangle; if we were to use our imagination and flip, slide, or rotate one side above the other one, we would get a rectangle. Then, count the number of lines of names in the tallest panel, multiply by the number of panels, and then by five (because there appear to be five names per line, no matter how long or short the names) and we should have a pretty good estimate.

Here’s the idea:

Using that rule, the tallest panel that is all names (no extra inscriptions) has 137 lines of names. The shortest panel has a single line of names. There are 70 panels to the east, and 70 to the west. Re-arrange them to make a rectangle, and we have 70 panels with about 138 lines of names, each with 5 names per line. Multiply all that and we get 48,300 names.Unfortunately, this number is much too low: more than 55,000 American service personnel died in Vietnam.

What went wrong?

Let’s look at the wall again, more carefully.

Each side is in fact NOT a triangle. They are quadrilaterals. The bottom edge makes a bend at about panel 20, a little bit to the right of the head of the man in blue looking at the wall. It’s easy to miss.

If you spend some time counting and recording the number of lines on a sample of panels, you will notice that the number of lines does not go up uniformly.

I carefully counted and recorded the number of lines of names for about a few dozen panels, and found that my data, when graphed, looked more like this:

(By the way, I didn’t count every single line in all of those panels, except for the ones to the right of panel 30. I found patterns that allowed me to figure out how many names there were in panels 3 through 17. How did I do it?)

But how do we calculate the total number of names now?

My original triangle was easy enough, but the new, green triangle was pretty difficult to measure the area of, so I decided to cut the figure up differently, as shown here:

We have a light blue trapezoid (or close enough) on the left, which will be matched with another trapezoid rotated from the west side, producing a rectangle whose base is 20 panels long and that is about 137+128 lines tall; so it has 20 times 265 lines of names, or 5300 lines of names.

The darker blue triangle will be matched with its twin, also rotated from the west side, to produce a 50 by 128 rectangle with 6400 lines of names.

That’s a total of 11,700 lines of names.

Five names per line give 58,500 American military deaths from the Vietnam War.

Which is quite close to the official figure of 58,272 names.

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Obviously there was more than one country involved in this war. If you want to see memorials to the Vietnamese, Cambodians, Laotians, South Koreans, Australians, and other nationalities, both fighters and civilians, who were killed in that same conflict, you will need to look elsewhere, overseas.

Estimates of the number of Vietnamese, Laotian, and Cambodian killed during and right after the war vary widely and are not very accurate. It is safe to say that several million Southeast Asians were killed during the war and its aftermath.

If one were to build a memorial to all those Southeast Asian casualties with the names spaced in the same way as in this one, how large would that memorial need to be?

For scale: If we begin counting at 1960 and end at 1980, that’s about 20 years, or 240 months. If three million Southeast Asian combatants and civilians were killed during that period, then that means that about 12,500 Vietnamese, Cambodians and Laotians were killed by bombs, bayonet, napalm, bullets, knives, drowning, and so on, each and every single month. In four months, that’s about 50,000 dead, which is pretty close to the total number of American combat deaths for the entire war.

Two hundred forty months divided by 4 months gives 60, which means that one would need approximately sixty memorials the size of this one to honor the memories of the millions of Southeast Asian civilians and fighters killed during and after the Vietnam War.

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Post script:

While touring this memorial on Saturday, November 9, 2013 (i.e. two days before Veterans Day / Armistice Day) with four other math teachers, I was shown a couple of features I hadn’t noticed before:

1. Every ten rows, in every second panel, there is a dot; this makes it much easier to count the total number rows in each panel.
2. A few lines of names actually do have six names. It does not happen very often, but is definitely enough to throw the count off by a bit.

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Some grim calculations in honor of today being Veterans Day (actually, the 11^th day of the 11^th month of 1918 was the day that an armistice (a cease-fire) was proclaimed to stop the fighting on the Franco-German front during World War One.

58,000	Rough estimate of US war dead in Vietnam theater
1,218,000	square feet at 3 fet by 7 ft per coffin
43,560	one acre (in square feet)
28	acres neded to bury all American Vietnam War dead
2,000,000	rough number of Vietnamese, Cambodian and Laotian war dead
42,000,000	square feet at 3 fet by 7 ft per coffin
43,560	one acre (in square feet)
964	acres neded to bury all Southeast Asian Vietnam War dead
1.51	number of square miles needed

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And here is what I just wrote on the time line of a colleague, who had the bad fortune to get drafted during Vietnam and served over there:

“As someone who lived through the Vietnam War era dreading the day when I would be ordered by my draft to report for induction in a war that I knew for a fact was completely unjustified, I am sorry that you and your buddies were drafted and had to fight and risk or lose [your] lives over there and fight against one side in a civil war. (Some wars are justified, many wars are not.) I am glad that my lottery # ended up being a little too high to get called up. I did my best to try to stop the war… I suspect that our efforts, along with the [much more important] actions of many soldiers etc who saw no point in the war, may have saved a lot of lives in getting the US out of there. In any case, I’m glad you made it back safely, Ben.”