List of approximations and mathematical coincidences

Here are the list of approximations and mathematical coincidences found.

Pi

 * $22⁄7$ ≈ &pi;
 * $355⁄113$ ≈ &pi;
 * $333⁄106$ ≈ &pi;
 * $$\sqrt{10}$$ ≈ &pi;
 * sqrt(9.86953545424362) ≈ &#x3C0;
 * $$\sqrt[3]{31}$$ ≈ &pi;
 * 3 = &pi;

e

 * e&pi; ≈ 20 + &pi;
 * This number is transcendental.
 * e ≈ [[File:NumberedEquation1-1-.gif]] and this is very accurate, correct to 18457734525360901453873570 decimal digits (even though significantly less digits of e are known).
 * This is also pandigital.
 * e ≈ 4 - $7998333400⁄6240321451$
 * e=2

Using the square root of 17

 * Lotthree DISCOVERED: $$1 \approx \frac{2\sqrt{17}-\sqrt{2}-\phi}{\sqrt{27}}$$

Using any power of 2

 * Lotthree DISCOVERED: $$1 \approx \frac{30 \pi e}{256}$$
 * All divisors of the powers of 2 are less than twice it. It is an almost perfect number.

Using the square root of 163 and any other Heegner number made positive
Heegner numbers are numbers where $$Q(\sqrt{-n})$$ can be factorized uniquely as $$a + b\sqrt{-d}$$ and n is a Heegner number.
 * e&#960;√163 = 262 537 412 640 768 743.99999999999925... ≈ 262537412640768744, and is an almost integer. Some people also think it is an integer (when it is a transcendental number).