Sexagesimal system

The sexagesimal system is a Numbering system using the bases 60. In particular used to measure the Time or the Angle S (in Trigonometry) and to specify geographical coordinates .

Contrary to the majority of the other numerical systems, the sexagesimal system is not so much used in data processing or formal logic, but is practical for the measurement of the angles and the geographical coordinates. The standard unit of sexagesimal is the degree (360 degrees), then the minute (60 minutes = 1 degree) then the second (60 seconds = 1 minute). The modern use of sexagesimal is rather close to that of the measurement of the time, in which 24 hours ago in one day, 60 minutes in one hour and 60 seconds in one minute. The modern measurement of time corresponds in a way round to the duration of rotation of the ground (days) and of its revolution (year). The decimals which are smaller than the second are measured with the Decimal system.

History

The first to use the sexagesimal system seem to have been the Sumériens with the OJ then to III by the Babylonian which invented the Babylonian Numération. It was used much by the Greek astronomers and geographers, such Ptolémée or Théon of Alexandria, which leaves us a method to calculate the square roots of numbers written in the sexagesimal system. Thereafter it was used also by the Arab during the dynasty of the Omeyyades and by European mathematicians like Fibonacci.

Fractions

The sexagesimal system with the advantage of having many whole dividers (1,2,3,4,5,6,10,12,15,20,30,60) which facilitate the calculation of the fractions. 60 is more the divisible small number by 1,2,3,4 and 5.

The sexagesimal system is enough practical to represent fractions: 1/2 = 0.30 1/3 = 0.20 1/4 = 0.15 1/5 = 0.12 1/6 = 0.10 1/8 = 0.07:30 1/9 = 0.06:40 1/10 = 0.06 1/12 = 0.05 1/15 = 0.04 1/20 = 0.03 1/30 = 0.02 1/40 = 0.01:30 1/1: 00 = 0.01 (1/60 into decimal)

To convert the sexagesimal degrees into decimal degrees

The geographical coordinates are often given in sexagesimal degrees, i.e., in degrees, minutes and seconds. However, the computers prefer the decimal system and it is necessary to convert the sexagesimal degrees into decimal degrees.

Example. That is to say a latitude of 45° 53 ' 36" (45 degrees, 53 minutes and 36 seconds). Expressed in decimal degrees, the latitude will be equal to: latitude = 45 + (53/60) + (36/3600) = 45.89

General formulation: latitude (decimal degrees) = degrees + (minutes/60) + (seconds/3600)

To convert the decimal degrees into sexagesimal degrees

Example: that is to say a longitude of 121,135°

the number before the comma indicates the degrees => 121°
Multiplier the number after the comma by 60 => 0,135 * 60 = 8,1
the number before the comma becomes the minute (8 ')
Multiplier the number after the comma by 60 => 0,1 * 60 = 6
the result corresponds to the seconds (6").
Our longitude will be of 121° 8 ' 6"

Version spreadsheet (to be validated):

For the latitude (K2 points on the value in decimal degree):

=concatenate (int (ABS (K2)); " ° " ; int (60* (ABS (K2) - int (ABS (K2)))); " '

" ; int (60* (60* (ABS (K2) - int (ABS (K2)))- int (60* (ABS (K2) - int (ABS (K2)))))); " \ " " ; yew (K2<0; " S" ; " N"))

For longitude (L2 points on the value in decimal degree):

=concatenate (int (ABS (L2)); " ° " ; int (60* (ABS (L2) - int (ABS (L2)))); " '

" ; int (60* (60* (ABS (L2) - int (ABS (L2)))- int (60* (ABS (L2) - int (ABS (L2)))))); " \ " " ; yew (L2<0; " W" ; " E"))

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