The Number of Hours of Daylight Throughout the Year by Latitude

I did a plot of the number of hours of daylight as a function of the number of days since the winter solstice with steps in latitude of 10° and obtained the following curves.


Above the arctic circle the number of hours of daylight is 24 hours a day for a period of time depending on the latitude. The derived formula indicates that this is indeed the land of the midnight sun. The formula also indicates that at the poles there is either one very long day or one very long night since the Sun either stays above the horizon for one half of the year or below it for the rest of the year.