A Brief Guide to the Great Equations: The Hunt for Cosmic by Robert Crease

By Robert Crease

Listed here are the tales of the 10 preferred equations of all time as voted for by way of readers of "Physics World", together with - accessibly defined the following for the 1st time - the favorite equation of all, Euler's equation. each one is an equation that captures with appealing simplicity what can merely be defined clumsily in phrases. Euler's equation [eip + 1 = zero] was once defined by way of respondents as 'the so much profound mathematic assertion ever written', 'uncanny and sublime', 'filled with cosmic good looks' and 'mind-blowing'. jointly those equations additionally volume to the world's so much concise and trustworthy physique of data. Many scientists and people with a mathematical bent have a smooth spot for equations. This ebook explains either why those ten equations are so appealing and demanding, and the human tales at the back of them.

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To provide the proof of a rule therefore involves a different perspective on mathematics than just stating the rule. For a proof is not an assertion of authority but an acknowledgement of intellectual democracy. It does not simply pass on a piece of wisdom from one’s precursors as a tour de force of intellect, a stroke of genius. ’ Instead, the proof of a result says that the journey is something anyone can take, in principle at least, thanks to the matrix of mathematical definitions and concepts that we already possess.

And if we insist on sticking to the terms of Meno’s paradox and say that the boy either knew or didn’t know, then he must have known but forgotten, just as the legend said. Right, Meno admits. I wouldn’t swear to all of the legend, Socrates says, but I’m sure it’s got grains of truth. Now that Meno is satisfied that learning is possible, the conversation reverts to the original question of virtue and how it might be taught. Socrates and Meno begin discussing who the teachers of virtue might be.

The youth says yes. Do you know how to double its area? Socrates asks. Of course, is the reply. You double the length of the sides. Obviously! That’s wrong, of course, but Socrates doesn’t let on. A good teacher, he gets the student to spot his own mistake. When he extends the square, doubling the length of each side, the youth sees his error immediately – the new big square contains four squares of the original size, not two. Try again, Socrates says. The boy proposes one and a half times the length of the first side.

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