[math-fun] Rationalizing the numerator
Can anyone think of a problem for which the trick is that you should rationalize numerators rather than denominators? Or more generally leave combinations of surds in some nonstandard but tactically helpful form? Jim Propp
Some limit problems, e.g. lim x-->9 (sqrt(x+7) - 4) / (x-9). On Mon, Jan 22, 2018 at 8:11 PM, James Propp <jamespropp@gmail.com> wrote:
Can anyone think of a problem for which the trick is that you should rationalize numerators rather than denominators? Or more generally leave combinations of surds in some nonstandard but tactically helpful form?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Free associating: I like the inductive proof that every rational number p/q can be written as an Egyptian fraction, i.e., a sum of reciprocals — and specifically that the greedy algorithm which subtracts the largest 1/k less than or equal to p/q terminates. This involves a nice induction on the numerator. C
On Jan 22, 2018, at 7:11 PM, James Propp <jamespropp@gmail.com> wrote:
Can anyone think of a problem for which the trick is that you should rationalize numerators rather than denominators? Or more generally leave combinations of surds in some nonstandard but tactically helpful form?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute Why should we be deported? This is very, very hard for a family. What will our fellow citizens think if honest subjects are faced with such a decree — not to mention the great material losses it would incur. I would like to become a Bavarian citizen again. Your most humble and obedient, Friedrich Trump (1905)
participants (3)
-
Cris Moore -
James Buddenhagen -
James Propp