All Rational Approximations of Pi Are Useless
I think blog.wolfram.com is probably the best company blog I've seen, from a marketing perspective. A large number of the entries are basically of the form "Here is an interesting problem, and here's how I solved it with Wolfram products". They generally let the problem have the spotlight rather than focus on the Wolfram products, so it doesn't feel like you are getting pitched.<p>Here's a related problem, but for e: using each digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 at most once each, and only the operators +, -, x, /, and ^ (exponentiation), and parenthesis for grouping, how close can you get to e? Digits may not be concatenated--for instance, you cannot get a 23 by simply placing the 2 next to the 3.<p>My best, after about 15 minutes of fiddling, were:<p><pre><code>   (3x(4x7+1))/2^5 = 2.71875 ≈ e + 0.000468172
</code></pre>
and<p><pre><code>    2x(9x6-1)/(3x(8+5)) = 2.717948... ≈ e - 0.000333111
</code></pre>
but it turns out you can do FAR better.