I came across this number when determining a certain resistance value for a filter circuit.

Turns out it has a name.

Previously ignored:

[Feb 2020] https://news.ycombinator.com/item?id=25242530

[Nov 2020] https://news.ycombinator.com/item?id=22284104

Suppose we have some resistor R that is in a circuit (e.g. circuit board). Suppose we can solder something to its terminals in parallel, but we may not open the circuit: we may neither replace the resistor, nor insert anything in series with it.)

R determines a filter cut-off frequency f. If we attach another R in parallel, we make the total resistance 1/2 R, which doubles the frequency to 2f.

What parallel value can we add that will change to the frequency that is geometrically between those two, namely √2f ~ 1.41f?

For that, the resistance has to drop to R/√2 or around 0.707R. Obviously, the parallel resistance must be substantially higher than R, which we know cuts the resistance in half.

When you do the little bit of algebra, it turns out that the parallel value needed is (1 + √2)R: the Silver Ratio times R.