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Math at Work Monday: Mary Helen the History Museum Curator

I’ve known Mary Helen Dellinger my whole life. That’s because she’s my cousin, born a whole two months before I was (a fact she never let me forget when we were kids). Growing up in Virginia as we both did, it was darned near impossible to avoid a history lesson at every turn. And while I never really caught the bug, Mary Helen got it bad.

She’s been a history museum curator for 22 years now, the last year in a new position as curator for the City of Manassas Museum System, where she has overseen exhibits that include photographs of the Civil War and a collection that features a rare, surviving “John Brown Pike,” or spear, with which abolitionist Brown had intended to arm sympathizers in an aborted raid at Harper’s Ferry.

Yeah, this is cool stuff. And much to Mary Helen’s chagrin, her job includes quite a bit of math. She’s not shy about expressing her disdain for the Queen of Sciences, but like most grownups, she has learned to get along just fine.

Can you explain what you do for a living? 

There are two major aspects to my with the Manassas Museum System. First, I am in charge of maintaining the Museum’s collection of objects. This includes meeting with prospective donors and accepting new donations for the collection, making sure the collection is properly stored and that a proper environment is maintained at all times (stable temperature and humidity at acceptable levels), and that adequate security is always in place. There is a lot of paperwork that goes along with this – Deed of Gift forms for donors, thank you letters, conservation reports, tax forms for those objects that are really valuable. Everything has to be photographed and entered into the Museum’s collection database. The entire collection numbers over 10,000 pieces – most of it in off site storage. Much of the work I described above is backlogged from the past eight years, so there is always something to keep me busy.

The second aspect of my job is running the Museum’s exhibition program. Exhibit schedules are usually created 2-3 years out. So right now, I am scheduling shows for 2015. For exhibits that we do “in-house” I select objects from our collection and negotiate loans from private collectors and other museums. I also have to write labels, work with exhibit designers and (if necessary) conservators, and do things like select paint colors, make object mounts, etc. – basically come up with the look and feel of the gallery space. The final step in all of this is the installation process – which is the most fun of all.  It’s a very creative process and neat to see it all come together in the end. On occasion, I will rent a traveling exhibition that was put together by another museum. When I do that, it is just a matter of unpacking it and installing it.

When do you use basic math in your job? (And what kind of math is it?) If you can offer a very specific situation when math is important, that would be great.

Math is very important when creating any exhibition. First, I have to keep in mind what the square footage is in the gallery, and how much space the objects in the exhibits will take up. This includes spaces on the floor, inside cases, and on the walls. Large objects take up lots of floor space but also cover the wall space behind them. Cases have to hold the objects AND the labels. Framed pieces go on the walls. My design must include measurements of all the major components that include height, width and depth. This allows me to make sure everything will fit and yet allow space for visitors to move through the exhibit. During the design process we are constantly measuring, re-measuring and moving things around to get the most out of the space. For complicated exhibits we use floor plans and sketch in everything including measurements to help us understand the relationships between the pieces and if we are leaving enough space. You don’t want to get to installation and realize you don’t have enough room for a key piece of the exhibit. There is some geometry involved here (understanding angles and lines) but most of it is basic addition, subtraction, etc.

Secondly, each exhibit has an individual budget that I am responsible for creating at the outset of the project. I have to include designer time, materials, the cost of creating graphics, prepping the gallery space, etc. Each budget has a contingency built in for those unexpected things that inevitably crop up. I have to carefully track expenses to make sure I don’t overrun my budget.

In addition to the exhibitions, I am in charge of the annual budget for my part of the department. In fact, we are in the middle of creating the budget for FY 2014 right now. Using last years’ budget as a base, I have to project (using the aforementioned two-year exhibition schedule) how much money I am going to need in the next fiscal year. This requires me to know how much contractors charge per hour and how many hours I am going to need them, the cost of supplies, shipping schedules, etc. The math used here is addition/subtraction/multiplication/division – but it can be complicated because you are working with a lot of assumptions.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

I use calculators when doing the budget. For exhibit design, we use basic rulers and calculators. Nothing fancy.

How do you think math helps you do your job better?

Math enables me to design exhibits that are affordable, and work within the spaces that we have.

How comfortable with math do you feel? Does this math feel different to you? (In other words, is it easier to do this math at work or do you feel relatively comfortable with math all the time?)

I have NEVER been comfortable with math, not even today, 22 years into my career. Budgets, especially, make me nervous because if we don’t get it right, that will impact future expenditures and our ability to do other projects. So while the math I use in my job is familiar to me, because it is something I do every day, I don’t think I will ever be comfortable with it.

What kind of math did you take in high school? Did you like it/feel like you were good at it?

In high school I took Algebra I and II (barely passing both) and Geometry (did okay in this). I absolutely hated math, and only took it because I had to. Despite my best efforts, going to all the extra tutorials, studying every night, etc. I never could get it. The abstract concepts were not something I could ever wrap my mind around. Put me in a history class with definable dates, facts, and people to learn about and I was fine. I never had to “show my work” in history.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pick up using the skills you learned in school?

The math skills I learned in elementary/high school are enough for me to do my job. I have not had to learn anything new.

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In Math for Teachers

The Cult That Changed Geometry

While the development of numbers continued for many, many centuries, even before the discovery or invention of zero, the Greeks were responsible for a long, long period filled with mathematical advances. By 600 B.C., a fellow named Thales of Miletus brought Babylonian mathematical discoveries to Greece, which were used to calculate distance and other measurements.

But the big player in Greece was Pythagoras. (Yes, you should recognize that name.) Born in 580 B.C. in Samos, he met old-man Thales when he was but a young lad. Perhaps Thales convinced him to travel to Egypt so that he could learn the mathematics of the Babylonians. At any rate, when Pythagoras returned from his journey, he settled in Croton (which is on the eastern coast of Italy) and this is where things get strange — at least by our modern standards.

Pythagoras established a philosophical and religious school that was made up of two societies: the akousmatikoi (hearers) and mathematikoi (learned). And while his followers look much like a cult to us, Pythagoras was in fact developing the world’s first intentional, philosophical society. Members — both men and women — were intent on living a contemplative and theoretical life, and as such divorced themselves from the culture at large, becoming completely devoted to philosophical and mathematical discovery.

But in order to do this, they had to follow a very strict set of rules, which included vegetarianism, giving up all personal possessions and absolute secrecy. And then there are the really strange orders: do not pick up something that has fallen; do not touch a white rooster; do not look in a mirror beside the light.

That’s not all. Mysticism infused almost all the Pythagoreans did, which led to some really off-the-wall mathematical ideas, like their understanding of numbers.

  1. Nothing exists without a center, and so the circle is considered the parent of all other shapes. It was called the monad or “The First, The Essence, The Foundation, and Unity” — or according to Pythagoras, “god and the good.”
  2. The dyad was a line segment and considered to be the “door between One and Many.” It was described as audacity and anguish, illustrating the tension between the monad and something even larger.
  3. And then there’s the triad, which of course represents the number 3. Continuing in their pseudo-anthropomorphism of numbers, the triad is considered the first born, with characteristics like wisdom, peace and harmony.

I could go on. Seriously. But while the ideas of the Pythagoreans were kind of kooky, this band of deep-thinking brothers and sisters advanced mathematics in some pretty significant ways. First of all, they began classifying numbers as even and odd, prime and composite, triangular, square, perfect and irrational. Through their strange ideas of numbers, they popularized geometric constructions. They are also attributed with the discovery of the five regular solids (tetrahedron, hexahedron, octahedron, iscosahedron and dodecahedron).

But their biggest discovery is the theorem named for Pythagoras. The Pythagorean Theorem states that the in a right triangle, the square of the longest side is equal to the sum of the squares of the remaining two sides. In other words:

This is more than just a silly formula you needed to memorize in high school. Carpenters use it to be sure that they have right angles (in other words that their door frames, decks, and walls are “square”). It’s useful to find the diagonal of a television set (which is how those contraptions are measured for some reason), if you only know its length and width. And it’s the basis of a great deal of additional math discovery, like the distance formula and various area formulas.

It’s a big, honkin’ deal. And in some ways, we’re lucky it survived the secrecy of the Pythagoreans. Pythagoras wrote nothing down. (If tin foil had been invented, he might have been wearing a hat of the stuff.) But despite its closed society, this cult of nutty mathematicians and philosophers is considered one of the most important influences in all of history.

What do you remember of Pythagoras from your high school geometry class? Have you used the Pythagorean theorem in your everyday or work life? If so, how?

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In Math for Teachers

A Mathematical Time Machine

Was mathematics invented or discovered?

(I’ll give you a second or two to really think about that.)

Most non-mathematicians have never really given that question much thought. Math has just always been there. An isosceles triangle has always had two congruent sides, and 3 + 8 has always equalled 11. But the reality is this: since the beginning time, human kind has struggled to find ways to describe its world. And one important outcome of this struggle is what I call the language of mathematics. Whether math was invented or discovered, the people involved were fascinating and scary and funny and sometimes sad. And that’s why I’ve decided to devote the remainder of November to the history of mathematics. Here are a few of the stories I hope to share with you.

1. There was the 1st Century Roman who, while taking a bath, figured out the idea of displacement. What did he do? Well, naturally, he shouted “Eureka!” and went running down the streets in his birthday suit. (Or so the story goes.)

2. Then there was the 5th century, mystical cult that demanded complete loyal and secrecy from its members. And by the way one of its members discovered one of the most useful and important facts about right triangles.

3. In the 1600s, the surrogates of two mathematicians — one in England and the other in Germany — held heated debates over who had actually invented (or discovered) calculus.

4. A child prodigy born in 1777 was confounding his teachers and managing his father’s business accounts at the tender age of five. He went on to make a staggering number of contributions in number theory, statistics and algebra, including normal distribution and the bell curve. He also apparently chose work over being at his wife’s deathbed, saying, “Ask her to wait a moment; I’m almost done.”

5.  A girl (gasp!) made significant contributions to the fields of abstract algebra and physics in 19th and 20th century Germany.

6. After cracking World War II German codes for the Brits and playing a major role in the birth of computer science, one fellow was arrested for the crime of homosexuality, chose chemical castration over prison and is said to have killed himself by cyanide poisoning at the age of 42.

Clearly, the history of mathematics is full of comedy and tragedy. The stories weave in and out of major world developments and the histories of other sciences. At the least, some of these stories are entertaining. Others help us make connections between ideas that lead to our own personal revelations. Still others remind us that while these contributions have provided the underpinning of how we understand our world today, the people behind them were just that — people.

So climb aboard this mathematical time machine. I’m still trying to decide whether to take it chronologically or by subject or perhaps even with a more random approach. Let’s just see what happens, shall we?

Do you have a question about the history of mathematics? If so, please share it in the comments section. I’m happy to take suggestions of topics I should consider.

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