
Transcendental, you say? The history of a term | Tangente
Did you say "transcendental"?
In Latin, the verb transcendere combines trans, "beyond," with scandere, "to climb"; it therefore literally means "to climb beyond," "to cross" or "to surpass."


In Latin, the verb transcendere combines trans, "beyond," with scandere, "to climb"; it therefore literally means "to climb beyond," "to cross" or "to surpass."


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A number for which, apparently, no definition involves a polynomial with integer coefficients has no reason to be algebraic. But that does not prove it is transcendental! Despite the many theorems on the subject, a great many numbers continue to resist classification.

Among irrational numbers, transcendental numbers are not roots of any polynomial equation with integer coefficients. They seem to transcend common sense, hence their name. Cantor showed that they make up the overwhelming majority of the real numbers, without identifying a single one!

Almost two thousand years of geometry! That is how long it took, with Descartes, to develop the first tools for studying those mathematical objects we all think we know: curves. How far we have come since the tentative explorations of ancient Greek scholars!

The real numbers include the rational numbers—the quotients of two integers—and the irrational numbers, of which √2 and π are two well-known examples. This gives us one way of classifying the reals. But another classification is possible, based on numbers known as algebraic numbers.
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