Hello. This part of the Geodesy lesson is devoted to units, units of measurement that we use in topography and geodesy. The main units used in land-surveying and geodesy are units of angle and units of distance. These geometrical quantities allow us to determine positions in space. Length: throughout history, there have been many definitions of length; length has no absolute reference. It is defined relative to common objects, such as foot, thumb, etc. With respect to Earth, one could define the first definition of the meter. It corresponds to 1/4 of the length of the meridian, that is 10 millions meters, therefore 1/4 of this distance allowed us to define the meter. Then, one defined a more specific meter, and more precise, using a definition with respect to time. Time is defined by periodic movement, at the atomic level which has a very high stability. This provides a definition of the meter, which has been used since 1983. The second dimension we are interested in are angles. For angles, we have various units, and the first that comes to mind, is the degree. We know that a full turn of a circle is 360Âº, 1Âº is divided into 60 minutes and 1 minutes is divided into 60 seconds. This cutting system is called a sexagesimal system. These units are primarily used in navigation, and are found on geographical maps. We will stop for a moment to focus on the usage of degrees relative to the dimensions of Earth. How did we first define a marine mile, or nautical mile? I will let you reflect on that. The nautical mile is actually the generated path at the surface of Earth by an angle measured at the center of 1 minute So 1 minute corresponds to a path at the surface of Earth, which is 1 nautical mile. To calculate this, we will take this angle at the center, so it's 1/60 Âº that we can convert to radian, that is, 1/60 times Ï€/180 so it gives us an angle in radians of Ï€/10 800. And I will multiply this now by the radius of Earth, which is equal to 6 400 km. So, one mile is equal to (Ï€ times 6400) over 10 800 which is equal to 1,85 km. The second angular unit, that we will discuss is the radian. Radian is primarily used in mathematics, especially in trigonometry. I recall here the definition of radian, for this I draw a circle whose radius is 1. 1 radian will generate an arc with a unit length of 1. One rotation around the circle corresponds to 2 Ï€, and the conversion from 1 radian to degrees is equal to 180Âº/Ï€, in this case 57Âº and 18 minutes. The third angular unit that is certainly new to you, is the gon. The gon is found in geodesy and surveying. It can be defined by cutting of a meridian, which I recall is about 40 000 km into 400 parts. So 1 gon, is about 100km. The gon is expressed as following, I give you here an example with 23 gon, 18 57. The first 2 digits here are the minutes, the following 2 digits are the seconds. We are here in a centesimal system. Conversions: conversions are useful moving from one unit to another First, we will look at the conversion of degrees, minutes, seconds and centesimal degrees. I use here an example expressed in degrees, minutes, seconds, for example 36Âº 4 minutes and 57 seconds, I can calculate the following conversion, with 36Âº + 4 minutes/60 + 57 seconds over 3600 which is equal to 36,0825Âº. For angles expressed in gons, we have already seen that if I have an angle, for example, of 27,4372. I would direct the minutes here, and then the seconds, since we are in a centesimal system. An important thing in surveying, is to find the relationship between and angular value and the arc it can intercept at a certain distance. Here is an example of a milligon, so one thousandth of a gon, so a small angle here of 0,001 gon, and a distance, here, of 100 meters. I will intercept with an arc of 1,6 mm. It is important to know this relation between a small measured angle and an intercepting arc. It is important in the use of theodolites, so topometric instruments. Other conversions that are of interest, is the conversion from degrees to radians, and degrees to gon. Here is a small example to illustrate these conversions, with an angle of 30Âº that we want to express in radians, it will be (30Âº times Ï€) over 180Âº, which will give us a value of 0,524 radians. If I take my 30Âº and I want to convert it into gon I simply connect 30Âº times 10/9, which is equal to 33,333 gon.