Can you find a use for this?

Or what I did when I could not get back to sleep.

If you take two numbers x and y, two obvious things to do with them are to add and subtract them giving x+y and x-y. If the original numbers were far apart then the new pair will be close together and vice versa. For example if x=10 and y=1 then you get 11 and 9. Adding and subtracting these two numbers gives 20 and 2, double the starting values, which will be the general case and means that the numbers have the same ratio as the starting pair.

This got me to wondering if there was a ratio of x to y which would give the same ratio for x-y and x+y. If we take x=1 and y=r then we get r/1 = (1-r)/(1+r). This gives r=sqrt(2) – 1, which I dub LostInParadise’s constant.

It seems to me that there should be some signficance to the constant, though I can’t think of what it could be. Have you got any ideas?