Top View [Puzzle]

If the first image below is a side view, and the second image is the front view (as viewed from the arrow). What’s the top view of this object?

[Source: Rob Eastaway]

The Wrath of Khan

The global impact of forest re-growth in even the long-lasting events [such as Black Death] was diminished by the continued clearing of forests elsewhere in the world. But in the case of the Mongol invasions […] re-growth on depopulated lands stockpiled nearly 700 million tons of carbon absorbed from the atmosphere. This is equivalent to the world’s total annual demand for gasoline today. [Source]

Pi Day Paradox

Here’s the infamous “proof” that shows that  π is equal to 4.

The zig-zagged polygon, whose perimeter always remains 4, does appear to approach the circle as we repeat these steps to infinity. Ergo, π is equal to 4!

The problem, as Vi Hart explains in this amusing math doodle video, is that while the area of the polygon does approach the area of the circle, the actual perimeter of the polygon is much larger than the circumference of the circle. Confused? Think of it this way: if you put a jumbled up 10 feet long rope into a 1 foot long container, you wouldn’t say that the rope is now 1 foot long, would you? You would take out the rope, and extend it fully to measure its actual size.

See some more discussion here. Also, here’s another video that “proves” — using a similar approach — that π is equal to 2, and the square root of 2 (another one of my favorite irrational numbers) is also equal to 2!

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By the way, if π were actually equal to 4, all circles would be squares. What a terrible world that would be! Similarly, if π were equal to 3, all circles would be hexagons. (For a hexagon, the ratio of its circumference to its diameter is equal to 3.)

Oh, and happy pi day! Don’t forget to have some delicious pie, and as you eat it, marvel at the glory of this magnificent, transcendental, and most importantly, irrational number.

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Previously on this blog: Proof Without Words IV, Happy Pi Day 2013, 3.14, A Sanskrit Mnemonic for π, Happy Pi Day!, A Mathematical Conundrum.

Ghosts of Evolution

[HT: brain pickings]

One Trillion

One hundred dollar bill ($100)

Ten thousand dollars ($10,000)

One million dollars ($1,000,000)

One hundred million dollars ($100,000,000)

One billion dollars ($1,000,000,000)

One trillion dollars ($1,000,000,000,000)

That escalated quickly, huh?!

[Source]

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Previous “Sense of Proportion” posts: I, II, III, IV, V, VI, VII.

Counterfeit Coin [Puzzle]

There are 12 coins, one of which is a counterfeit. The false coin differs in weight from the true ones, but you don’t know whether it’s heavier or lighter. Find the counterfeit coin using three weighings in a pan balance.

[From Futility Closet]

No Alternative

The “pulping” of Wendy Doniger’s The Hindus: An Alternative History by Penguin is yet another blow to the freedom of expression by the religious radicals and fundamentalists who take offence at the drop of a hat. The instances of such attacks — started in 1989 when the Indian government banned Satanic Verses — have increased dramatically in recent years, and the offence-mongers’ purview has expanded from books to movies, artists, and even celebrities. This is not surprising. When a society obliges to a culture of mutual intolerance by capitulating to those who are easily offended, it results into an if-them-then-why-not-us race, with every faction of society vying appeasement for their injured self-esteem.

I read this book back in 2009. Although the size and scope of this epic was prohibitive (with more than 700 pages), I found Doniger’s vantage refreshing and thought-provoking. The book offers an alternative history of the Hindu religion, looking through the prism of scriptures and tales, zooming into the role of women, members of the lower caste, and animals. It’s a story about the alternative people and characters. Her rationale is to provide an auxiliary viewpoint to show that the so-called marginalized groups (women and Pariahs) actually did have substantial contribution to the development of Hindu tradition. The book is a “celebration of diversity and pluralism, not to mention the worldly wisdom and sensuality, of the Hindus “.

By renouncing such scholarly work, the Hindu radicals are not only attacking the liberal values of our society, but (ironically) also weakening the pluralistic nature of Hindu tradition. It doesn’t surprise me that this regressive act is braced by the right-wing Hindus that are often politically motivated. What troubles me more is the passive support from the moderates. “Yes, I believe in freedom of speech as well, but we have to draw the line somewhere”, “We need to be careful about hurting other (religious) people’s sentiments”, “No one gets away with an offensive book about Muslims, then why shouldn’t we protect Hindu sentiments as well?” are some common responses to this controversy by the religious moderates. It’s dismaying to see a rather large section of the Indian society supporting (however passively), and hence fortifying, the spirits of offence-mongers.

A culture with no space for alternative interpretations and ideas is a culture of putrid orthodoxy. We must not succumb to these regressive forces that are destructive to an open society. 

Belphegor’s Prime

1000000000000066600000000000001  is a palindromic prime number, which contains the number of the beast (666) surrounded by thirteen zeros on each side. The number is called Belphegor’s prime, after the demon (depicted below) with the same name.

[Source]

Periodic Table of Dots

Simple, minimalist, and elegant. From here.

Happy Thanksgiving!

Here’s a little turkey-day trivia:

• When Europeans first encountered this bird, they mistakenly identified it as guinea-fowl, which were also known as turkey fowl because they were imported to Europe through Turkey.
• In Turkish, the bird is known as hindi, which means “from/related to India.”
• In Hindi, the bird is called peru, which is a borrowed word from Portuguese language.
• The Portuguese word peru refers, obviously, to the country Peru.

Had the Peruvians called the bird american, the circle would have been complete.

[Source: Wikipedia, HT: @manish_vij]