math in the news: issue 49

17

Upload: media4math

Post on 05-Dec-2014

515 views

Category:

Education


0 download

DESCRIPTION

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

TRANSCRIPT

Page 1: Math in the News: Issue 49
Page 2: Math in the News: Issue 49

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.

Page 3: Math in the News: Issue 49

Daylight Savings

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

Page 4: Math in the News: Issue 49

Daylight Savings

This table shows the number of hours of daylight throughout the year.

Date Number of Hours of Daylight/Day

1-Jan 1216-Jan 121-Feb 12

16-Feb 121-Mar 12

16-Mar 121-Apr 12

16-Apr 121-May 12

16-May 121-Jun 12

16-Jun 121-Jul 12

16-Jul 121-Aug 12

16-Aug 121-Sep 12

16-Sep 121-Oct 12

16-Oct 121-Nov 12

16-Nov 121-Dec 12

16-Dec 12

Page 5: Math in the News: Issue 49

Daylight Savings

This is a graph of the data.

Page 6: Math in the News: Issue 49

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.

Page 7: Math in the News: Issue 49

Daylight Savings

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

Page 8: Math in the News: Issue 49

Daylight Savings

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

Page 9: Math in the News: Issue 49

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.

Date Number of Hours of Daylight/Day

1-Jan 9.2116-Jan 9.461-Feb 9.92

16-Feb 10.481-Mar 11.02

16-Mar 11.681-Apr 12.41

16-Apr 13.071-May 13.68

16-May 14.211-Jun 14.63

16-Jun 14.821-Jul 14.81

16-Jul 14.581-Aug 14.13

16-Aug 13.591-Sep 12.92

16-Sep 12.251-Oct 11.58

16-Oct 10.921-Nov 10.27

16-Nov 9.751-Dec 9.37

16-Dec 9.17

Page 10: Math in the News: Issue 49

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.

Page 11: Math in the News: Issue 49

Daylight Savings

This table shows the number of hours of daylight for regions located at 60°N latitude.

Date Number of Hours of Daylight/Day

1-Jan 5.6616-Jan 6.351-Feb 7.51

16-Feb 8.781-Mar 9.96

16-Mar 11.351-Apr 12.84

16-Apr 14.221-May 15.57

16-May 16.811-Jun 17.88

16-Jun 18.431-Jul 18.38

16-Jul 17.741-Aug 16.62

16-Aug 15.361-Sep 13.91

16-Sep 12.521-Oct 11.13

16-Oct 9.741-Nov 8.31

16-Nov 7.091-Dec 6.1

16-Dec 5.56

Page 12: Math in the News: Issue 49

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.

Page 13: Math in the News: Issue 49

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.

Page 14: Math in the News: Issue 49

Daylight Savings

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

Page 15: Math in the News: Issue 49

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.

Page 16: Math in the News: Issue 49

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.

Page 17: Math in the News: Issue 49

Daylight Savings

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