Tag Archives: science

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

Menopause: Why Do Humans Experience It?

It has always been a mystery as to why humans go through menopause. Chimpanzees and bonobos, whom we share 99% of our DNA with, are still able to reproduce throughout their entire lifespans while humans in their latter part of their lives become infertile. What then, are the reasons for humans becoming infertile as they get older?

Recently BBC and the Atlantic has published an article that can potentially explain the cause of menopause. Menopause is actually a unique trait shared by only three species: humans, killer whales, and pilot whales. Scientists have made many predictions as to why humans may experience menopause, but these predictions end up being extremely difficult to test. One possible explanation for menopause is the Grandmother Hypothesis. The Grandmother Hypothesis suggests that humans have given up their reproductive potential to focus more on caring for their children and grandchildren. In order to prove this hypothesis, we must prove that children are more likely to survive when their grandmother is present compared to when she isn’t. Dr. Lummaa from the University of Turku has published a study that shows that children are 12% more likely to survive adulthood if their grandmother is present.

Elderly Woman Image by Kawahara via Flickr

With the help of advanced technology, humans nowadays are able to live longer than ever, and women often outlive the lifespan of the female reproductive system. However scientists are still finding it. This hypothesis is near impossible to test because humans’ current fertility rate patterns are different from the fertility patterns of our ancestors.

Surprisingly, if we investigated other species that also experience menopause, we could possibly relate this information back to the human species. Darren P. Croft, an animal behaviorist at the University of Exeter, used years of data to reveal why killer whales potentially experience menopause. It became clear that from an evolutionary standpoint, it is a disadvantage for the mother and daughter killer whales to be impregnated at the same time. When both the mother and daughter killer whales reproduce during the same period, the newborns of the older generation have a higher chance of dying, approximately 1.7 times more likely as opposed to the younger generation. According to Croft, “this new research shows that old females go through the menopause because they lose out in reproductive competitive with their own daughters.” This research on killer whales provide us with an explanation for menopause that may possibly apply to humans.

Killer Whales: One of the three species that goes through menopause
image by Grit via Flickr

All in all, it remains a mystery as to why humans go through menopause. Although there are many existing hypotheses that may potentially explain menopause, nothing has been scientifically proven. However, we can gain insight into why humans experience menopause through observing other species.

-Andrew Ting

The Zika Virus: Are we done with it yet?

Zika virus transmission. Imagine courtesy of World Health Organization (WHO).

In April 2015, an epidemic of the Zika virus disease took Brazil by storm , quickly spreading through South America and parts of North America. The disease was relatively unknown but it was associated with causing microcephaly, a brain defect where a baby’s head is significantly smaller than normal in fetuses of pregnant women with the Zika virus. As time passed with nearing proximity to the 2016 Summer Olympics in Rio de Janeiro, the possibility of contracting the disease caused so much concern that many athletes withdrew from competition.

But the Zika virus is not new.

It was first discovered in 1947 in monkeys of the Zika Forest in Uganda. Since then, there have been small outbreaks in the equatorial Africa and Asia. Unfortunately, due to the mild symptoms of the disease and it’s similarities to dengue, yellow fever and chikungunya, it was often overlooked and underreported until its recent outbreak.

The virus is mainly spread by mosquitoes of the Aedes genus common, namely A. aegypti and A. albopictus. Transmission to a fetus during pregnancy increases the risk of many birth defects such as microcephaly in the newborn child. If that doesn’t sound scary enough, it can also be spread from sexual activity and blood transfusions!

Microcephaly in newborn infants as a result of the Zika virus. Image courtesy of the Boston’s Children’s Hospital.

So what are the symptoms? Infections from the Zika virus will only display mild symptoms at most, including fever, rash, joint pain, pinkeye (conjunctivitis), muscle pain and headache. Symptoms typically subside after a week. Travellers and pregnant women who have recently visited affected areas should be tested for the disease.

The Zika virus is no longer an epidemic by the World Health Organization (WHO) as of November 2016 and it seems like something of the past. But why should we still be concerned about it?

Sadly, just because it is no longer an epidemic doesn’t mean that you shouldn’t be worried. Right now there is no cure for the Zika virus. Vaccines are being developed as we speak, but they probably won’t be available for another 10 years. For now all we can do is take precautions against mosquito bites and avoid travelling to places affected by Zika, especially if you are pregnant.

The problems Zika poses are far from solved. The Zika virus outbreak highlights the just one of the detrimental effects that poor sanitation has on our population. If we don’t solve the problem of managing mosquito populations and inventing new vaccines, we will have persisting human vulnerabilities to mosquito-spread diseases. We will always be at risk of infection to a disease we haven’t cured.

In the meantime, be mindful of your travel plans and check out this video on the Zika virus!

  • Florence Ng