**Map Projection**

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Our title of the project is "projection", which represent by Johnny.Lu73379018 and Grant.Tong73382012. Ok, first of all. let me explain what is map projection. Map projections are kind of systematic transformations that allow us to view the area of land very clarity on a flat map. According to mathematically speaking, map projections are transformations of geographic co-ordinates (latitude, longitude) into the Cartesian (x, y) co-ordinate space of the map. Some map projections can be constructed geometrically. Here is the beauty of map projection, because all map projections can be represented by mathematical equations that convert geographic co-ordinates into map co-ordinates; however, this is also the hard part for us to calculate the co-ordinates. Therefore , we are just gonna focus on 3 main category projection we have used most in our life.

**1. Mercator Projection**

Making a limpid terrestrial globe inside the limpid cylinder, put the light source inside the terrestrial globe, then the projection of the rectangle, which intersected by longitude and latitude is the first graph we draw in first link. However, since the distance between longitude and latitude in high latitude area is much wider, so the area of projection of the land in high latitude area will much bigger than the real area. we will explain this point by some graphics below in the second link. Also, we will provide some information of calculations in the third link.

¡@Link one -demonstrations of projection

Link two -map projected

Link three - calculation

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**2.Lambert Projection**

Making a limpid terrestrial globe inside the limpid coin, put the light source inside the terrestrial globe, then the projection of the rectangles and triangles, which intersected by longitude and latitude is the first graph we draw in first link. Also the area of projection of the land in high latitude area will much bigger than the real area. we will explain this point by some graphics below in the second link. Also, we will provide some information of calculations in the third link. Therefore, we can conclude that Lambert projection of land approach the real area of land in the middle latitude area. we usually use this projection in a topographic chart, aviation chart in the middle latitude area.

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Link one -demonstrations of projection

Link two -map projected

Link three- calculation

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3. **Azimuthal Equidistant Projection & Azimuthal
Equal area Projection**

**a) Azimuthal Equidistant Projection**

**Category:** mathematical projection.

**Step1**: Use a paper to cut the north pole
or south pole of terrestrial globe.

**step2**: Use the point of tangency as a
center to draw the woof, so every woofs got the same arc of concentric circle,
which radius is equal

the distance of every woofs to the point of tangency.

**step3** : Use the point of tangency as a
center to draw the meridian, then every meridian is the radioactive rays, which
intercept the center.

**Feature: **United Nation use this way of
projection

**
**every woof get the same distance

**b)Azimuthal Equal area Projection**

Category: Mathematical projection, equal-area projection

**Step1**: Use a paper to cut the
north pole or south pole of terrestrial globe.

**step2**: Use the point of
tangency as a center to draw the woof, so every woofs got the same arc of
concentric circle, which radius is

1= 2r sin ((90¢X¡Ð Ø)/2)

**step3** : Use the point of
tangency as a center to draw the meridian, then every meridian is the
radioactive rays, which intercept the center.

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**Represent by Johnny.Lu
and Grant.Tong**

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