Category Archives: Columns

A Trip to MoMath

By: Gabriela Godlewski (CE ‘19)

The National Museum of Math is open everyday, except for Thanksgiving, 10 a.m. to 5 p.m.  Below: the front doors to the museum. Photos by Gabriela Godlewski (CE ‘19).
The National Museum of Math is open everyday, except for Thanksgiving, 10 a.m. to 5 p.m. Below: the front doors to the museum. Photos by Gabriela Godlewski (CE ‘19).



A trip to any museum is always a fun time. In most museums, the fun comes from the peace of exploring exhibits and learning about different forms of art or past events from an objective stance. Then there are the museums that require you to delve directly into the exhibits, learning and exploring exhibits through interaction, a category in which The National Museum of Math falls into. Located in the Flatiron District in Manhattan, The National Museum of Math, popularly known as MoMath, consists of two floors demonstrating many different mathematical concepts in fun and creative exhibits dedicated to teaching math through immersion.

The opening of MoMath was in response to the closing of the Goudreau Museum of Mathematics in Science and Art. It was the only museum dedicated to math in the United States of America. Unfortunately, due to lack of funding, the Gourdreau Museum closed in 2006. A group of interested parties (the “Working Group”) met in August 2008 to explore the creation of a new museum of mathematics — one that would go well beyond the Goudreau in both its scope and methodology. The group quickly discovered that there was no museum of mathematics in the United States, and yet there was incredible demand for hands-on math programming. The group, led by Glen Whitney, began work to create a new math museum, and MoMath, the National Museum of Mathematics, opened its doors in 2012. Since then, the museum has been entertaining and educating people of all ages in complicated mathematical concepts, including, but not limited to, curvature, cross-sections, and the Mobius strip.

As an engineering student trained in calculus and physics, the MoMath appealed to me in that it was said to show exhibits that demonstrated many familiar mathematical and physical concepts. Tired of the 2D, non-immersive illustrations in Thomas Calculus, 12th Edition, I decided to pay the museum a visit and see the exhibits for myself. I was hooked from the moment I opened the pi-handled doors. Inside was a colorful playground of exhibits that drew me in immediately. In the very center of the first floor was a racecar track in the shape of a Mobius strip, demonstrating how a seemingly two-sided surface is actually one whole surface.

Next to the racecar track was another exhibit where you could ride two tricycles with square wheels on a track made up of catenary curves. Sound impossible? The tricycles were specially built so that one side of the square wheel was equivalent in length to the arc of the catenary curve it was riding over, showing the creativity and endless possibilities of math. These were only two exhibits out of many, with each exhibit demonstrating a new, formerly difficult concept in a simple and creative way.

My personal favorite was a sculpture made up of colorful spheres connected to each other. If you touched a sphere, it glowed and played a note or a chord, harmonizing with any nearby spheres you touched after. The math and robotics in these cool and immersive exhibits was as impressive as the simple physical demonstrations of everything Professor Vulakh taught me before.

Overall, my trip to the MoMath was very enjoyable. I liked seeing the museum I’ve heard so much about firsthand. It was also fascinating to see how much thought and creativity was put into each exhibit in order for all of them to flawlessly demonstrate a different mathematical concept as simply and as pleasantly as possible. However, despite the fact that I was enjoying myself and that I was surrounded by people of all ages, the exhibitions were designed more for children. Although I did have fun, such a museum would be made more enjoyable accompanied by friends who like both math and fun. I recommend this museum as the perfect study break with friends. It’s a nice walk or short train ride away, and you’re not wasting time there as you’re simultaneously learning and having fun.◊

Corrections (March 12, 2017): There were some inaccuracies about the history of MoMath, which have been amended. Also, the tricycles do not ride on cylinders; they ride on catenary curves.

Miles of Movies: Logan

By: Miles Barber (CE ‘18)

In a world of uplifting, happy-ending, fast-paced superhero films, Logan takes a different approach. It presents its titular character as a dark, depressed man who’s lived for two hundred years, watching other mutants like him rise and fall, and watching people he’s cared for get killed because of him. To Logan, the world is a painful place, and there isn’t much to make him care about living. Charles Xavier is one of the few people he takes care of—until he meets Laura, a young Hispanic girl that he must take to the Canadian border.

This film is half road-trip, half bloody action. There are no bright colors or super heroes. The opening ten to twenty minutes set the tone perfectly: heartbreaking, realistic and believable. They also provide some backstory about Laura and make the main characters feel authentic.

The special effects, sound design, and cinematography are all great in this film. Hugh Jackman plays Logan well and has for the past seventeen years. Dafne Keen, who plays Laura, isn’t given a whole lot to do until the last act of the film, but really brings it then. As far as I know, she’s never been in a film before, so I’m interested to see where she goes from here.

Logan’s character arc develops strongly in the first two acts of this film (introduction and road-trip), but it does not play out well in the third act. As a “road trip” movie, you might expect this film to be formulaic. And it is but not in a way that I particularly like.

For a dark movie like this to work, you need the main character to be either likable, relatable, or sympathetic. After all that Logan has been through in the previous X-Men films, he should at least be sympathetic. But in the third act, he isn’t. He just goes back to being a stubborn, cranky guy who doesn’t want to do anything or help anyone. And that took me out of the movie.

Overall, Logan is a new tone for a superhero film. It features a different world for mutants without hope or purpose. The first two acts are strong in setting up the tone, characters, and story. There are some truly heartbreaking moments here, but the third act made Logan unlikable again—which was disappointing. I would still recommend this film, but just know that it is a bloody mess and isn’t terribly uplifting or fun like a typical superhero film. ◊

Grade: B+


Oli’s Sweet Mess: Van Leeuwen

Olivia Heuiyoung Park (ME ‘19)

Hey there! This is Olivia, and I’d like to welcome you to Oli’s Sweet Mess! Each issue, I’ll be documenting my adventures in the city by featuring one or two dessert shops. If you have any suggestions, feel free to reach out to me!

For my first “Oli’s Sweet Mess”, I thought it would be most fitting to feature none other than “Van Leeuwen,” my favorite artisan ice cream parlor of all time! As a lactose intolerant ice cream lover, Van Leeuwen is the perfect place for me. They have both amazing classic and vegan ice cream flavors, with phenomenal seasonal flavors such as: rose jam cardamom cake, labneh (yogurt-cheese) with pistachio & candied orange, and banana cream pie. A scoop costs $5.50 (or $6 for vegan flavors), but it’s totally worth the price!

The ice cream is super rich and flavorful, and you can even try as many flavors as you want before deciding on a flavor! It’s very close to Cooper actually—located on 2nd Avenue and 7th Street. It is a perfect spot for hanging out with friends, treating yourself, or even studying! They have limited seating, but the store itself has the perfect atmosphere to grab a warm drink and to study (yes they have free Wi-Fi). Also, the workers are all very friendly and fun.

Van Leeuwen was created by three friends in a small kitchen in Brooklyn in 2007 and now has several locations and trucks in New York and California. The store offers amazing ice cream with optional toppings, house made sundaes, Toby’s Estate coffee and espresso, Rishi Organic teas, house made pastries with plenty of vegan options, and more! The only downfall is that the East Village location doesn’t have a bathroom, but hey, everything else about this place makes up for it. You can even buy hand packed pints at the store, or for a cheaper price at a grocery store nearby!

Next time when you’re craving something sweet, cold, or even just a quick cup of joe, give Van Leeuwen a try! I promise you’ll fall in love with the store as quickly and deeply as I did! ◊

Buy High, Sell Low: Risk

By: John Doe

Hello Readers. Below is a new column with the goal of educating Pioneer readers in matters of investment. This column will cover topics that translate well from math and science classes at The Cooper Union to real applications in financial markets.
Risk is a difficult thing to define. For most people, the risk of making a decision is the possible negative impact of the choice. In terms of investment, the risk is the total loss possible from that decision. Some people use volatility as a measurement of risk, volatility being the standard deviation or variance of an investment return.
The standard deviation of a set is well known to all engineering students at The Cooper Union. If we look at the close prices of Apple (NYSE: AAPL) and Microsoft (NYSE: MSFT) every week over the past month and tabulate the average and standard deviation (see Figure 1), we can see in this definition of risk, AAPL is a “riskier” investment than MSFT.
However, this definition of risk is extremely lacking in utility. For example, look at the prices for AAPL and MSFT; while the AAPL prices continue to rise, MSFT hovers around the average and not rising or falling. Now, investors are not distressed by rising prices; in fact they find it very good! So how can we define risk to be more useful for evaluating investment options?
In 1987, there was a particularly nasty stock market crash where overvalued investments corrected to very low prices. Most investors did not have a way of numerically understanding the possible losses associated with investing in the stock market bubble and lost a lot of money. Investment banks and financial institutions sought out statistical ways of determining—to a percentage certainty—how much money could be lost in a crash. It turns out this method is very simple to understand. Say we aggregate the daily returns of AAPL and MSFT into buckets and plot a histogram of the number of days each bucket of returns occurred for the last 5 years.
Figures 2 and 3 are the normal distributions of the daily returns of AAPL and MSFT—Cooper students are very familiar with the physics of normal distributions. Since we order the returns from worst to greatest, we want to look at the left tail of this distribution. This allows us to make a very useful statement: With a 99.92% confidence, an investment in AAPL will, at worst, absorb a daily loss of 13.2% and MSFT can incur 12.1%. Now, it is very clear that AAPL is riskier than MSFT with a 99.2% confidence interval.
This method has its faults, it makes two basic assumptions: (1) that past performance is predictive of future performance and (2) that the distribution of returns is normal. These are very basic statistical mistakes in finance, and so the value at risk (VaR) estimate, like the one done above, must be considered alongside other measures of risk. There are ways to make VaR more effective which will be covered in the next installment of “Buy High, Sell Low.” Happy investing, everyone! ◊

Figure 1: A comparison of the average and standard deviation of Apple and Microsoft for the month of February.
Figure 1: A comparison of the average and standard deviation of Apple and Microsoft for the month of February.


Figure 2: The daily returns of Apple for the past five years.
Figure 2: The daily returns of Apple for the past five years.


Figure 3: The daily returns of Microsoft for the past five years.
Figure 3: The daily returns of Microsoft for the past five years.


Archi-Skate One

By Austin Richard Mayer (Arch ‘18)

Photo provided by Austin Richard Mayer (Arch ‘18).

The Cooper Union sits in what might be considered the cradle of NYC skateboard territory. Our next few issues will profile the building elements that compose our own campus skate park. First up we have east coast powerhouse Ishod Wair performing a 50-50 grind on the Foundation Building’s access ramp handrail. The ramp, designed by John Hejduk and Edwin Aviles, was installed in 1992 to allow wheelchair access and heavy freight loading into the building. Drawings made by Steven Hillyer were granted approval from the Landmark Preservation Committee to construct this addition to the portico of our 1859 historic brownstone. The ramp-side space created is a tiny thread of juxta-temporal urban fabric with a mood all its own, enjoyed by those who frequently and infrequently hang out within it. In conclusion, I suggest that this element can be read as a lil tongue sticking out the side of a lil mouth. ◊

Miles of Movies: The Lego Batman Movie

By Miles Barber (CE ‘18)

The Lego Batman Movie is about Lego Batman who goes around Gotham City saving the day, fighting criminals, and above all, working alone. Much to the dismay of Alfred, his caretaker, and even The Joker, who just wants to be Batman’s arch-enemy, Batman just doesn’t care about anybody but himself. So when he accidentally adopts the orphan Dick Grayson, Batman must grapple with his fear of family and what that might mean for both him and his image.
I was skeptical about this film, which seemed like it would be just a sillier version of the previous Lego Movie, but in fact, I was surprised. The Lego Batman Movie is just as good as The Lego Movie, playing a lot of the same beats but taking its focus away from the story and onto Batman. In fact, the entire film revolves around Batman’s inner struggle with having people around him to care for. There are a lot of moments when you really feel for Batman and what it’s like to be admired by so many people but unable to connect to any of them.

The self-aware humor and cultural references in The Lego Movie are all back for this film. What worked really well in The Lego Movie works even better here as this film brings back all of Batman’s villains and then some, making fun of everything Batman. The slapstick comedy that was everywhere in the previous film is toned down a little bit in this film to make way for more Batman-related humor. The Joker’s relationship with Batman is hilarious and the other villains tie in pretty well. Even Sauron is in this film! How did they manage to get that to work?

A big change in this film is the animation. It’s still mostly Legos, but there is a distinct camera now, giving a feeling of a live-action film. The lighting effects are really great this time around, and there are some wide shots of Batman flying that look gorgeous. The color scheme is different too, focusing on blacks and reds in contrast to the colorful feel of the previous film. All of these changes make you forget that you’re watching a movie animated from Lego blocks. So much of The Lego Movie revolved around building things with Legos, but almost nothing in The Lego Batman Movie required them.

Overall, The Lego Batman Movie is a worthy follow-up to The Lego Movie. It keeps the same amount of humor but changes it up a little. The story itself is centered around Batman, which makes for good character development but a bit of a forgettable story. I really enjoyed the change in animation style, even though it begs the question, “why even bother making it a Lego Movie?” I really had a blast with this film and would definitely recommend it to anyone looking for a good time or just feeling a little lonely; you’ll finish the movie with a smile on your face. ◊

Grade: A-

Miles of Movies: The Edge of Seventeen

by Miles Barber (CE ’18)

The Edge of Seventeen is about Nadine (Hailee Steinfeld), a high school junior who suffered a huge loss in the family a few years ago. She’s bitter and annoyed at how life has turned out and resents her brother Darian (Blake Jenner) who just seems unfairly perfect. and now feels betrayed by her only friend Krista who seems to be prioritizing other people. Throw in a hilarious teacher, Mr. Bruner (Woody Harrelson) and some real emotion and you have a stellar coming-of-age story that is pleasantly surprising.

I wouldn’t call this film a comedy, but there is a lot of humor, especially from Woody Harrelson. The situational awkwardness of so many of the scenes is also funny. Nadine is a pretty awkward person, but one of the characters in this film, Erwin, is hundreds of times more awkward. Usually I don’t like awkward humor but it works in this film because Nadine’s self-loathing is driven by her awkwardness.

The performances are really good too. Hailee Steinfeld has only really had smaller roles since her fantastic performance in True Grit, playing smaller characters in often mediocre movies. I’m so glad this film lets her really shine. Blake Jenner is really good as her brother too, giving a layered character some really powerful scenes towards the end. Even Woody Harrelson’s character works on multiple levels.

What I’m really getting at here is that the writing in this film is pretty stellar. Not a single line of dialogue felt like it was fake or written for a movie. All of the characters had depth beyond what you might expect in a comedy or even your standard coming-of-age film.

Unfortunately, the film isn’t without some flaws. Though I love the writing of the dialogue, the story is just a little messy in the middle of the film. There are just a few too many stories and characters set in motion for everybody to get enough time to shine. A lot of time is given to Erwin while less time was given to Krista, who should have been a little more central to the story. Still, it’s impressive enough as it is that all of these characters have real depth.

Overall, The Edge of Seventeen delivers a solid coming-of-age story with layered characters, clever dialogue, and some real emotion towards the end. When characters feel something, you feel it too. Even though Nadine is such a bitter person, you feel for her pain and the seeming hopelessness of her situation and ultimately relate to her. ◊

Grade: A-