In this edition of ‘Adventures’ we study a few miscellaneous problems.

In the accompanying article on Tangrams, a claim was made that it is not possible to find integers a and b which make any of the following equalities true: √6 = a+b√2, √7 = a+b√2, √12 = a+b√2, and so on. However, the proofs may not be obvious.
We present once again a miscellaneous collection of nice problems, followed by their solutions. We state the problems first so you have a chance to try them out on your own.

..and other rational approximations to π

In this article, the writer will explain a method to find rational approximations for and other irrational numbers. The key idea here is to use a calculator to find what is called a continued fraction for an irrational number.

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