Category Archives: Science Communication

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The Mathematically Perfect Couch

Anyone who has participated in the urban ritual of moving big things through small doorways understands the unique struggle of moving sofa couches. Luckily, mathematicians have found the answer to the woes of furniture movers.

“No John, twist it MY clockwise but push to YOUR left.” | Philip Lee Harvey, Stone, Getty Images

This problem was first formalized in the 1960’s by Leo Moser: what is the largest sofa that can fit around a hallway corner?

Of course, an experienced mover will tell you to stand the sofa on one end, but in what came to be known as the moving sofa problem, we imagine a really, really heavy sofa that is impossible to lift, tilt, or even squish.

Though the problem is simple to understand, it has remained unsolved for over half a century.

First, mathematicians realized the simplest shape to get around a corner doesn’t need to be rotated: a square. If we think of each side of this square as being 1, it has the area=1.

Next, mathematicians understood they could use rotation to help solve the problem and showed a half-circle with an area of about 1.5 would squeeze through the corner.

Square Sofa | Dan Romik

Half-circle Sofa | Dan Romik

By combining these shapes, John Hammersley designed a sofa in 1968

 

That random couch in your grandparents’ basement | Ronald Crufke, August 2010 Ugliest Couch, Norwood Mall

Hideous. No, the Hammersley Couch actually looks like this, with an area of  2.2, more than double the square sofa! He considered this solution to be the best possible.

Hammersley Sofa | Dan Romik

However, in the 1990’s the mathematician Joseph Gerver dropped a bombshell. He toppled Hammersley’s record sofa with complex mathematics, creating a truly marvellous eighteen sided couch. Prepare yourself, this is the most beautiful sofa thus-known to humankind.

The 18-sided Gerver Sofa | Weburbia, Wikimedia Commons

Okay, that may have been an exaggeration. By slightly modifying Hammersley’s Couch design, Gerver was able to increase the area by a whopping 0.5%.

But in mathematics, only one example of something contrary to the rule is enough to disprove the previous finding.

But there’s a common problem with all of these couches – they only turn one direction! What happens if you live somewhere that has both left and right 90° turns?

Unfortunately for Ross, his friends were not mathematicians that could help him derive the optimum couch shape for optimum pivotability | tenor

Enter Dan Romik, a prolific mathematician at the University of California, Davis. Using similar techniques to Gerver, he recently found the likely optimum shape for this unique version of the moving sofa problem.

Romik’s ‘ambidextrous’ sofa | Dan Romik

Romik’s results not only look like a cool modern design for two chairs attached by a table, they also led to surprisingly simple solutions to complex mathematical problems. However, there are still many questions left open in his paper – no one has proved the optimum shape.

Often with difficult mathematical problems, new fields must be developed in order to solve them definitively. There is still much left unproven in mathematics.

– Braydan Pastucha

Acne Medication Responsible for Infant Deaths and Teen Suicides

With promising results of clear skin and boosts of self confidence, many choose to commit to the Accutane (a drug to be taken daily 4-6 months as acne treatment). As heroic as the drug may sound as advertised by pharmaceuticals, researchers have found alarming side effects of Accutane users, including bowel disease, birth defects, depression, and suicide.

Image from: http://www.etrebelle.com/wp-content/uploads/2016/06/Acne.jpg

Acne is reported to be the most commonly seen skin disease amongst teenagers with an average of 4 in every 5 teens suffering from constant breakouts. Although most common treatments are sold as over-the-counter drugs, patients who suffer from severe acne are often referred by dermatologiests to go on Accutane.

Image from: http://www.njlawjournal.com/image/EM/NJ/accutane-Article-201412301735.jpg

It was reported that 43% of pregnant women on Accutane treatments have babies suffering from fetus defects and deaths. After Accutane was identified as the most toxic drugs for embryos, Britain introduced laws that require women to undergo abortion when pregnancies occur during Accutane treatments.

Another equally or rather more serious side of effect of Accutane is suicide. Researches have shown that Accutane users have approximately 21% decrease in orbitofrontal cortex activity (region of the brain responsible for cognitive decision making). This may explain the 11% suicidal rates amongst accutane users.

Image from: http://mypregnanthealth.com/wp-content/uploads/2014/02/Why-is-My-Belly-Button-Painful-During-Pregnancy.jpg

Is it worth it? Even with all the known side effects and precautions of Accutane, doctors are prescribing these pills to more and more patients. Most teens often resort to Accutane as a solution due to embarrassment and lowered self confidence caused by acne. However, non-medical methods including drinking sufficient amounts of water and having quality sleep is not only effective, but also risk free. On top of that, as a society we can eliminate discrimination towards those with acne to avoid embarrassment and loss of self confidence.

 

Lisa Liang

Earth, It’s Time For Your Injection

When pollution in Beijing became so bad that poisonous smog formed and remained for several days, China finally realized that climate change is a real threat. However, the effects of climate change isn’t isolated to just China, it affects the rest of the world as well. Personally, I prefer my regular Summer weather to be warm and not scorching hot, but in 20 years I may have to live with unbearably hot afternoons. A recent breakthrough involving the storage of carbon dioxide (CO2), one of the main greenhouse gases in the Earth’s atmosphere, by injecting it into the ground has caught my attention.

A study by Matter in Iceland used a method where they separated CO2 gas from the atmosphere and inserted it in the rock near volcanoes. The study found that the CO2 that was injected in these areas reacted with the volcanic material to form new materials such as limestone. The carbon is trapped in the form of new material and does not reenter the atmosphere, therefore reducing the amount of greenhouse gases in the Earth’s atmosphere.

The general process behind how greenhouse gases work to trap energy that is released by the Earth. From Wikimedia Commons.

What does a greenhouse gas do exactly? The Earth radiates its own energy outwards and some of it escapes into the depths of space. However, most of the energy hits a greenhouse gas molecule such as carbon dioxide (CO2), causing the energy to be shot out randomly in any direction. This means that the energy could potentially be redirected down back to the Earth, trapping the energy and causing the temperatures to rise as a result.

Graphs showing the change in amounts of different greenhouse gases across a period of time from 1975 to 2015. From Wikimedia Commons.

What does this mean for the rest of the world? If this method proves to be viable in all regions that have access to a volcano, then perhaps a worldwide collaboration involving the injection of carbon could be discussed. As more carbon is removed from the atmosphere and stored in the ground, lower amounts of energy will be trapped by greenhouse gases which may allow the Earth to slow down its current warming trend. However, not all countries will be able to readily use this method due to its high cost, but perhaps future advancements in technology will lower these costs so that it becomes viable for any country to perform.

I think our current year round weather is great in Vancouver. However, as the amount of greenhouse gases increases, it’s going to make the Summer season much harder for me to enjoy. Therefore I’m personally hoping that this research gains more recognition so more studies can be performed on the long term viability of its findings.
Angus Lee