In this issue of Math in the News we explore daylight savings time and standard time mathematically.

2. Daylight Savings
No matter what its orientation, only half the Earth gets sunlight at any given
time. But the amount of sunlight, in terms of the length of the day, depends
on your latitude.

3. Daylight Savings
The equator, which is along the great circle relative to the sun, has a
constant amount of sunlight throughout the year.

4. Date Number of Hours of
Daylight/Day
1-Jan 12
16-Jan 12
1-Feb 12
16-Feb 12
1-Mar 12
16-Mar 12
1-Apr 12
16-Apr 12
1-May 12
16-May 12
1-Jun 12
16-Jun 12
1-Jul 12
16-Jul 12
1-Aug 12
16-Aug 12
1-Sep 12
16-Sep 12
1-Oct 12
16-Oct 12
1-Nov 12
16-Nov 12
1-Dec 12
16-Dec 12
Daylight Savings
This table shows the number of hours of daylight throughout the year.

5. Daylight Savings
This is a graph of the data.

6. Daylight Savings
The situation is different for different latitudes. This is because the Earth’s
axis is at a 23° angle relative to the plane of the ecliptic.

7. Daylight Savings
During spring and summer, the 23° tilt of the Earth is oriented toward the
sun.

8. Daylight Savings
During fall and winter, the 23° tilt of the Earth is oriented away from the
sun.

9. Date Number of Hours of
Daylight/Day
1-Jan 9.21
16-Jan 9.46
1-Feb 9.92
16-Feb 10.48
1-Mar 11.02
16-Mar 11.68
1-Apr 12.41
16-Apr 13.07
1-May 13.68
16-May 14.21
1-Jun 14.63
16-Jun 14.82
1-Jul 14.81
16-Jul 14.58
1-Aug 14.13
16-Aug 13.59
1-Sep 12.92
16-Sep 12.25
1-Oct 11.58
16-Oct 10.92
1-Nov 10.27
16-Nov 9.75
1-Dec 9.37
16-Dec 9.17
Daylight Savings
As a result, depending on your latitude, the amount of daylight varies
throughout the year. This table shows the number of hours of daylight for
regions located at 40°N latitude.

10. Daylight Savings
This is a graph of the data. Note that it is the graph of a periodic function. A
graph of several years worth of data would also show a sine curve.

11. Date Number of Hours of
Daylight/Day
1-Jan 5.66
16-Jan 6.35
1-Feb 7.51
16-Feb 8.78
1-Mar 9.96
16-Mar 11.35
1-Apr 12.84
16-Apr 14.22
1-May 15.57
16-May 16.81
1-Jun 17.88
16-Jun 18.43
1-Jul 18.38
16-Jul 17.74
1-Aug 16.62
16-Aug 15.36
1-Sep 13.91
16-Sep 12.52
1-Oct 11.13
16-Oct 9.74
1-Nov 8.31
16-Nov 7.09
1-Dec 6.1
16-Dec 5.56
Daylight Savings
This table shows the number of hours of daylight for regions located at
60°N latitude.

12. Daylight Savings
This is a graph of the data. This is also a sine curve, but notice that it has a
higher amplitude than the 40°N data.

13. Daylight Savings
This graph shows the three data sets for the equator, 40°N, and 60°N. The
farther away from the equator the more variance there is in the length of
daylight throughout the year.

14. Daylight Savings
When there are12 hours of daylight, then sunrise and sunset occur at
times that don’t cause any inconvenience.

15. Daylight Savings
But as the number of hours of daylight shrink, then, without daylight
savings time, sunrise could occur later in the morning. This would cause
an inconvenience, since going to school or work would happen in the dark.

16. Daylight Savings
Daylight savings time is meant to compensate for the decreased number of
hours of daylight. This way, going to school or work in the morning doesn’t
happen in the dark.

17. Daylight Savings
But as spring returns and the number of hours of daylight increase, then
during this period, daylight savings time isn’t necessary.