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A quick look at the usage of geometrical terms that make interesting literal sense and figurative sense in English language

Whenever we talk about people below the poverty line in India, the phrase “square meal" turns up. We say that they cannot afford even one square meal a day. Now why do we call it a square meal? From its context, we might think that a square meal must be a barely satisfying, insufficient meal. But my dictionary says otherwise. The phrase is defined as a substantial, nourishing meal. The origin is supposed to be from the practice in the Royal Navy of serving meals on square wooden plates. But this origin is not supported by evidence.

Now square is a geometrical term that has in different phrases acquired figurative meanings. But in such usage it can have opposite meanings. “We have squared the official" can mean we have bribed him. But if you say, “His dealings are on the square", it means he is honest, straightforward. “Fair and square" has a positive meaning too. This phrase was first used by Francis Bacon in an essay in 1604.

Circle is another equally popular term from geometry. Perhaps the best known use as an idiom is in “full circle". Shakespeare has this phrase in King Lear: Edmund the villain says “The wheel is come full circle and I am here." His villainy has come full circle and he acts too late for redemption.

“Vicious circle" is a situation in which you solve one problem and find that a second problem has to be faced. Solving that leads you again to the first problem. You are trapped between these situations. You raise the wages and then the prices go up; then you have to raise the wages again, and prices go up again. It is a vicious circle.

A common complaint we hear from discussion groups is this: “This discussion is getting us nowhere. We are just going round in circles." The idea of a square and a circle are used together in a couple of idioms. We speak of a square peg in a round hole, referring to someone who does not fit into the group he is in, and remains an outsider.

An idiom that is interesting both in its literal sense and figurative sense is “squaring the circle". This is a task in geometry that aims at constructing a square that has the same area as a given circle. Leading mathematicians were fascinated by the challenge of this problem. Soon they realized that it has no solution. The calculation involves the value of “pi", and this value goes on into an infinite number of decimal places.

Srinivasa Ramanujan, the celebrated Indian mathematician, attempted the task, and was able to find a value of “pi" correct to eight decimal places. In another construction, he found that for a circle of diameter 8,000 miles, the error in the length of the side of the square was only a fraction of an inch.

In metaphorical terms, someone who is attempting an insoluble task is said to be squaring the circle. “To increase taxes and at the same time cut down aid is the same as squaring a circle."

In the last few years, there has been talk of the “bottom of the pyramid". It was originally used by Franklin D. Roosevelt to refer to the “forgotten man at the bottom of the pyramid". In 2004 professor C.K. Prahalad wrote The Fortune at the Bottom of the Pyramid. “The bottom of the pyramid is the largest, but poorest socio-economic group. In global terms, this is the 4 billion people who live on less than \$2.50 per day" (Wikipedia). This phrase is used in particular by people who recommend that this group, instead of being seen as victims of circumstances, should be seen as promising entrepreneurs.

V.R. Narayanaswami is a former professor of English, and has written several books and articles on the usage of the language. He looks at the peculiarities of business and popular English usage in his fortnightly column.

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