Editing Birthday problem (section)

===Square approximation===
A good [[rule of thumb]] which can be used for [[mental calculation]] is the relation

:<math>p(n,d) \approx \frac{n^2}{2d}</math>

which can also be written as

:<math>n \approx \sqrt { 2d \times p(n)}</math>

which works well for probabilities less than or equal to {{sfrac|1|2}}. In these equations, {{mvar|d}} is the number of days in a year.

For instance, to estimate the number of people required for a {{sfrac|1|2}} chance of a shared birthday, we get

:<math>n \approx \sqrt{ 2 \times 365 \times \tfrac12} = \sqrt{365} \approx 19</math>

Which is not too far from the correct answer of 23.