Step 1.
ESRI can convert, transform, re-project thousands of coordinate system,
But do you really need more than one coordinate system?

Step 2.
NO, you do not.
You only need one 3857( projected) - 4326 ( geographic)
This is tyler software gis requirement.
Tyler cloud service EPL processing a few thousands of cities's gis data in US
They require all cities use single one coordinate system 3857
3857(4326) is for world use,
google map, apple map, any online map, mobile map is using 3857
Step 3.
Flex processing several hundreds of police department gis data in single one coordinate system 3857

Step 4.
Because different law enforcement use different coordinate system,
for example, los angeles county will use:
california zone 5
Why you see 2 different coordinate system here ?

Step 5.
projected coordinate system and geographic coordinate system are in pair.
geographic coordinate system is virtual,
it is how you are going to design the coordinate system.
it is sphere, unit is angle in degree.
projected coordinate system is reality,
you can choose a specific method to project sphere on the flat surface,
it is flat surface unit is length, meter or feet

Step 6.
Flex use ESRI's tool to convert from other coordinate system( in my case, it is california zone 5, ) to 3857.

Step 7.
why you need 2 coordinate system in pair ?
projected-3857 ( geographic-4326 )
Because the earth is a sphere, not flat,

You have to use sphere based coordinate system ( which is geographic - 4326)

Step 8.
while you computer screen, your iphone screen is flat, (not sphere)
to display a earth(sphere) on flat screen
you will have to use specific method to project sphere onto flat surface.
projected-3857 is flat, it is the result of you project sphere-4326.

Step 9.
think about if your iphone screen surface is not flat,
it is a sphere, like a base ball.
Assuming new iphone is like a base ball, screen surface is sphere,
then when you display earth world map, you don't have to project to flat,
you can just display earth surface on a sphere ball.
( use 4326 is good enough, no need 3857)

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