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Nicaragua is the most triangular country in the world
Underperforming, the U.S. comes in only 157th out of 196 in global triangularity ranking.
- Sierra Leone is the world's roundest country and Egypt the squarest. But you knew that.
- Bet you didn't know which is the world's most triangle-shaped country.
- That is until now, because someone's figured out that it's... Nicaragua!
Circles, squares and triangles
The flag of Nicaragua. Coincidentally or not, it features a... triangle.
So you like triangles. And you know how to hold a tune. Then, like Alt-J, you could write a song about how "triangles are (your) favorite shape". But what if you're left-brained rather than right-brained, and prefer maps and maths over notes and lyrics?
We feel we've hit upon a pretty good description of Tom Alps. With a name like that, he can't not be geographically inclined. And for proof that he knows his numbers and likes his triangles, look no further than the latest entry on Tom's Data Blog, titled "What is the Most Triangular Country?"
It's not the first question that we'd expect to see flowering in that weird and wild frontier zone between abstract mathematics and applied geography. Nor the second one. No, those would be, respectively: What is the Roundest Country? And What is the Squarest Country?
If we had to take a guess, the answers to those two would be: Lesotho, and Turkey. Turns out we would be wrong on both accounts – because those questions have already been answered. As we discussed some time ago, Sierra Leone is the roundest country in the world, and Egypt is the squarest one (see #926). And, weirdly, the Vatican is both the world's fourth roundest and second most rectangular country.
Ranked: the world's squarest (left) and roundest (right) countries.
Credit: G. Ciruelos, D. Barry.
As it turns out, Lesotho is only the 36th roundest out of a total of 206 countries and territories, and Turkey only the 15th boxiest. So we were off by quite a bit. But ask us which is the most triangular nation on earth, and we can't even picture a likely candidate.
This is where Mr Alps's mathematical skills kick in. Inspired as he was by the pioneering work by Gonzalo Ciruelos (on sovereign circularity) and David Barry (on state-based squareness), he decided to test the world's countries and territories for their conformity to the third-most-basic geometrical shape.
As he writes on his blog, "the first step is to define mathematically what 'triangularity' means." For the full methodology, check Mr Alps's blog. And let's skip to the juicy bits. Out of the 196 countries listed in the Encyclopaedia Britannica, the most triangular country is...
(ripping open envelope)
And yes, now that you mention it – we see it too.
Triangles on flags
The five most triangular countries in the world: Nicaragua, Bosnia, Namibia, Mauritania and Bolivia.
Credit: Tom's Data Blog
On the 'triangularity' index devised by Mr Alps, which indicates maximum similarity between a country and a triangle, the Central American nation scores 0.918672. That is slightly better than the runner-up, Bosnia-Herzegovina. Although now that you mention it, that is a very triangular-looking country, too.
In fact, the Bosnians thought so themselves. The country's national flag features a triangle as an approximation of the nation's geographic shape. Weirdly, the Nicaraguan flag also features a triangle. By accident or design?
Mr Alps plotted the triangularity of each country. "This shows that there is a quite gentle decrease in triangularity over the first 150 countries, followed by a sharp drop-off, seemingly due to countries that have multiple parts."
The least triangular country? The Marshall Islands. "Hardly surprising, considering the country is a collection of tiny islands spread over a large area of ocean."
For the least triangular country that isn't a group of islands, we have to move up 16 places in the ranking to Vietnam at #180. The United States is also among the world's poorest performers when it comes to triangularity, stuck in 157th place between Laos and Mexico.
What is human dignity? Here's a primer, told through 200 years of great essays, lectures, and novels.
- Human dignity means that each of our lives have an unimpeachable value simply because we are human, and therefore we are deserving of a baseline level of respect.
- That baseline requires more than the absence of violence, discrimination, and authoritarianism. It means giving individuals the freedom to pursue their own happiness and purpose.
- We look at incredible writings from the last 200 years that illustrate the push for human dignity in regards to slavery, equality, communism, free speech and education.
The inherent worth of all human beings<p>Human dignity is the inherent worth of each individual human being. Recognizing human dignity means respecting human beings' special value—value that sets us apart from other animals; value that is intrinsic and cannot be lost.</p> <p>Liberalism—the broad political philosophy that organizes society around liberty, justice, and equality—is rooted in the idea of human dignity. Liberalism assumes each of our lives, plans, and preferences have some unimpeachable value, not because of any objective evaluation or contribution to a greater good, but simply because they belong to a human being. We are human, and therefore deserving of a baseline level of respect. </p> <p>Because so many of us take human dignity for granted—just a fact of our humanness—it's usually only when someone's dignity is ignored or violated that we feel compelled to talk about it. </p> <p>But human dignity means more than the absence of violence, discrimination, and authoritarianism. It means giving individuals the freedom to pursue their own happiness and purpose—a freedom that can be hampered by restrictive social institutions or the tyranny of the majority. The liberal ideal of the good society is not just peaceful but also pluralistic: It is a society in which we respect others' right to think and live differently than we do.</p>
From the 19th century to today<p>With <a href="https://books.google.com/ngrams/graph?year_start=1800&year_end=2019&content=human+dignity&corpus=26&smoothing=3&direct_url=t1%3B%2Chuman%20dignity%3B%2Cc0" target="_blank" rel="noopener noreferrer">Google Books Ngram Viewer</a>, we can chart mentions of human dignity from 1800-2019.</p><img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDg0ODU0My9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY1MTUwMzE4MX0.bu0D_0uQuyNLyJjfRESNhu7twkJ5nxu8pQtfa1w3hZs/img.png?width=980" id="7ef38" class="rm-shortcode" data-rm-shortcode-id="9974c7bef3812fcb36858f325889e3c6" data-rm-shortcode-name="rebelmouse-image" />
American novelist, writer, playwright, poet, essayist and civil rights activist James Baldwin at his home in Saint-Paul-de-Vence, southern France, on November 6, 1979.
Credit: Ralph Gatti/AFP via Getty Images
The future of dignity<p>Around the world, people are still working toward the full and equal recognition of human dignity. Every year, new speeches and writings help us understand what dignity is—not only what it looks like when dignity is violated but also what it looks like when dignity is honored. In his posthumous essay, Congressman Lewis wrote, "When historians pick up their pens to write the story of the 21st century, let them say that it was your generation who laid down the heavy burdens of hate at last and that peace finally triumphed over violence, aggression and war."</p> <p>The more we talk about human dignity, the better we understand it. And the sooner we can make progress toward a shared vision of peace, freedom, and mutual respect for all. </p>
With just a few strategical tweaks, the Nazis could have won one of World War II's most decisive battles.
- The Battle of Britain is widely recognized as one of the most significant battles that occurred during World War II. It marked the first major victory of the Allied forces and shifted the tide of the war.
- Historians, however, have long debated the deciding factor in the British victory and German defeat.
- A new mathematical model took into account numerous alternative tactics that the German's could have made and found that just two tweaks stood between them and victory over Britain.
Two strategic blunders<p>Now, historians and mathematicians from York St. John University have collaborated to produce <a href="http://www-users.york.ac.uk/~nm15/bootstrapBoB%20AAMS.docx" target="_blank">a statistical model (docx download)</a> capable of calculating what the likely outcomes of the Battle of Britain would have been had the circumstances been different. </p><p>Would the German war effort have fared better had they not bombed Britain at all? What if Hitler had begun his bombing campaign earlier, even by just a few weeks? What if they had focused their targets on RAF airfields for the entire course of the battle? Using a statistical technique called weighted bootstrapping, the researchers studied these and other alternatives.</p><p>"The weighted bootstrap technique allowed us to model alternative campaigns in which the Luftwaffe prolongs or contracts the different phases of the battle and varies its targets," said co-author Dr. Jaime Wood in a <a href="https://www.york.ac.uk/news-and-events/news/2020/research/mathematicians-battle-britain-what-if-scenarios/" target="_blank">statement</a>. Based on the different strategic decisions that the German forces could have made, the researchers' model enabled them to predict the likelihood that the events of a given day of fighting would or would not occur.</p><p>"The Luftwaffe would only have been able to make the necessary bases in France available to launch an air attack on Britain in June at the earliest, so our alternative campaign brings forward the air campaign by three weeks," continued Wood. "We tested the impact of this and the other counterfactuals by varying the probabilities with which we choose individual days."</p><p>Ultimately, two strategic tweaks shifted the odds significantly towards the Germans' favor. Had the German forces started their campaign earlier in the year and had they consistently targeted RAF airfields, an Allied victory would have been extremely unlikely.</p><p>Say the odds of a British victory in the real-world Battle of Britain stood at 50-50 (there's no real way of knowing what the actual odds are, so we'll just have to select an arbitrary figure). If this were the case, changing the start date of the campaign and focusing only on airfields would have reduced British chances at victory to just 10 percent. Even if a British victory stood at 98 percent, these changes would have cut them down to just 34 percent.</p>
A tool for understanding history<p>This technique, said co-author Niall Mackay, "demonstrates just how finely-balanced the outcomes of some of the biggest moments of history were. Even when we use the actual days' events of the battle, make a small change of timing or emphasis to the arrangement of those days and things might have turned out very differently."</p><p>The researchers also claimed that their technique could be applied to other uncertain historical events. "Weighted bootstrapping can provide a natural and intuitive tool for historians to investigate unrealized possibilities, informing historical controversies and debates," said Mackay.</p><p>Using this technique, researchers can evaluate other what-ifs and gain insight into how differently influential events could have turned out if only the slightest things had changed. For now, at least, we can all be thankful that Hitler underestimated Britain's grit.</p>
We’ve mapped a million previously undiscovered galaxies beyond the Milky Way. Take the virtual tour here.
See the most detailed survey of the southern sky ever carried out using radio waves.
Astronomers have mapped about a million previously undiscovered galaxies beyond the Milky Way, in the most detailed survey of the southern sky ever carried out using radio waves.
A new study shows our planet is much closer to the supermassive black hole at the galaxy's center than previously estimated.
Credit: NAOJ<p><em>Arrows on this map show position and velocity data for the 224 objects utilized to model the Milky Way Galaxy. The solid black lines point to the positions of the spiral arms of the Galaxy. Colors reflect groups of objects that are part of the same arm, while the background is a simulation image.</em></p>
Apple sold its first iPod in 2001, and six years later it introduced the iPhone, which ushered in a new era of personal technology.