As a kid, I was fascinated by the concept of irrational numbers.
And I really liked geometry and trigonometry in highschool (nerd alert). And the 45 45 90 triangle (from a circle of radius 1) yielding a side of sqrt(2)/2 was kind of cool to me.
sqrt(2)/2) lies between 0 and 1, which appeases my sense of scale. I mean, if you pick 4,234,753 as a favorite number, it's hard to get a feel for how big or small that number is. But sqrt(2)/2 - that's something most people can get their mind around. 71% is easy 😉.
Some people like the famous special numbers, like e or π, but that's just jumping on the bandwagon. Even sqrt(2) has it's own Wikipedia entry. Are there any other websites dedicated to just sqrt(2)/2) ? Thought so.