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Results tagged with ho.history-overview
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user 50073
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
10
votes
Taking a theorem as a definition and proving the original definition as a theorem
Example 1: In some textbooks, the trigonometric functions are defined via geometry. The advantage is that it is simpler to understand, but the disadvantage is that it is difficult to make completely r …
17
votes
Every mathematician has only a few tricks
(1) Double-counting, which can also be described as counting the same thing in two ways. Very useful, and at least as powerful as interchanging summation order.
(2) Induction. When there is a natural …