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William Jones: The First Math Teacher to Use Pi

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Eighteenth-century mathematician William Jones had a problem with pi—namely, it didn’t exist yet. At the time of his working and teaching in the field of mathematics, there was no term for the ratio of a circle’s circumference to its diameter, despite the value’s importance to even the most basic study of geometry. In his 1706 book, Synopsis Palmariorum Matheseos, or A New Introduction to the Mathematics, he made a modest proposal: that the universal constant be known as pi, and thus was mathematical history born.

Before being ascribed a modern name, pi existed under the guise of a bulkier, more antiquated phrase: quantitas in quam cum multiflicetur diameter, proveniet circumferencia—Latin for “the quantity which, when the diameter is multiplied by it, yields the circumference.” While descriptive, the collection of words required to denote pi before “pi” did not lend itself to clear or efficient discussion of the concept. Prior to Jones publishing his bold decision, fractions like 22/7 or 355/113 often served to fill in for the mysterious constant, but gave the erroneous impression that the number was a rational one, which can be fully expressed by one whole number divided into another—an assumption that had not yet been disproved, but with which Jones firmly disagreed. For this reason, only an idealized symbol would suffice to represent the concept, and so the Welshman turned to the Greek alphabet.

π, written in Roman letters as “pi,” is the Greek equivalent to our letter ‘p’. For this reason, 17th-century mathematician William Oughtred used π to denote the “periphery,” or the circumference of any given circle—a value that changed as the circle changed. Jones borrowed this earlier logic and applied it to his theory of an irrational, but universal constant value for the circle’s circumference-to-diameter ratio. Johann Lambert’s definitive proof in 1761 that π was an irrational number justified Jones’s earlier instinct, and once Swiss mathematician Leonhard Euler began to use and widely disseminate the symbol π in correspondence with his contemporaries, π was here to stay.

In honor of William Jones, unsung hero of pi, throw on one of these two new mental_floss t-shirts and have a moment of silence for the man responsible for turning pi from a letter into a number.

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Watch How Computers Perform Optical Character Recognition
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Optical Character Recognition (OCR) is the key technology in scanning books, signs, and all other real-world texts into digital form. OCR is all about identifying a picture of written language (or set of letters, numbers, glyphs, you name it) and sorting out what specific characters are in there.

OCR is a hard computer science problem, though you wouldn't know it from its current pervasive presence in consumer software. Today, you can point a smartphone at a document, or a sign in a national park, and instantly get a pretty accurate OCR read-out...and even a translation. It has taken decades of research to reach this point.

Beyond the obvious problems—telling a lowercase "L" apart from the number "1," for instance—there are deep problems associated with OCR. For one thing, the system needs to figure out what font is in use. For another, it needs to sort out what language the writing is in, as that will radically affect the set of characters it can expect to see together. This gets especially weird when a single photo contains multiple fonts and languages. Fortunately, computer scientists are awesome.

In this Computerphile video, Professor Steve Simske (University of Nottingham) walks us through some of the key computer science challenges involved with OCR, showing common solutions by drawing them out on paper. Tune in and learn how this impressive technology really works:

A somewhat related challenge, also featuring Simske, is "security printing" and "crazy text." Check out this Computerphile video examining those computer science problems, for another peek into how computers see (and generate) text and imagery.

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Can You Solve This Fish Riddle?
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Transporting cargo by boat doesn’t usually require solving tricky brainteasers. That’s not the case with this fishy riddle from TED-Ed.

For this scenario, imagine you're a cargo boat director who’s charged with shipping several tanks of rare fish to an aquarium. The tanks are tossed overboard during a rough storm and it’s your job to retrieve them. There’s a mini-sub onboard that might be of assistance, but there’s a problem: You only have enough fuel for it to make one quick trip. Before launching your rescue mission, you need to figure out exactly how many tanks fell into the water and where they landed.

After referring to sonar data, thermal imaging, and your shipping notes, you come up with this list of information to help narrow down your search.

1. There are three sectors where the cargo landed.

2. There are 50 animals in the area, including the lost fish and deadly sharks.

3. Each sector contains between one and seven sharks and no two sectors have the same amount of sharks.

4. The tanks each have the same amount of fish.

5. There are 13 tanks at most.

6. The first sector has two sharks and four tanks in it.

7. The second sector has four sharks and two tanks.

So how many fish are there? If you came up with 39, you’re right. There can only be 39 fish spread out across 13 tanks, which means there are three fish in each.

In case you’re feeling more confused now than you were before, you can refer to TED-Ed’s full explanation in the video below.

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