How we divide Mars territory

My first topic :slight_smile:
Thank you guys for the forum

So. We need to decide in what way Mars should be divided.

Number of tokens
Isn’t significant now. Imagine we decide to have 21000 tokens.

Mars is a sphere
In the first approximation. Later we can add some ellipsoid factors or something

Similarity of tokens
If Mars was a rectangular plane it would be easy to divide it into rectangular area. But… :slight_smile:
We have to divide a sphere. We decided to make each area rectangular (as it can be on a sphere) and with same area.
I also propose dividing the planet with fixed number of tokens vertically and horizontally.

Like this:

But:

  1. to make areas equal we need different distances between “horizontal” lines
  2. we exclude poles
  3. we can make special tokens with poles - circle areas
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Here is my first serious mathematical model:

It may be not precise, but I tried to make equal areas

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At all:
if we have 21000 tokens, we have 150 vertical parts and 140 horizontal parts. Later I’ll demonstrate

We also have separate tokens for poles

As for token numerating:
in the beta App I assume that token number is 1xxxyyy, like 1033080, where 33 is a number of horizontal division and 80 - of vertical

In the early beta it looks like this (selected is green, there are 100*100 areas here):

Pls assume that it is an early beta. The Mars depiction would be later - it isn’t major for blockchain development

Next step - to solve some surface integrals (I have already, need to recheck and make formulas in the App) and decide, how big do the two pole tokens.

Stay in touch :*

So.

We need to divide the planet.

Mars equatorial radius is 3396.2 km
Mars polar radius is 3376.2 km

Mean radius is 3389.5 km - we take this number.

Mars surface is 144 800 000 sq. km. Let’s check: 4 * pi * 3389.5 ^ 2 = 144371391. Plus-minus 0.3% - seems legit (also precise area isn’t much sufficient on this step)

Firstly we cut off two caps - southern and nothern pole areas. Let them be for 10 degrees both, see a picture from wiki:
image

So our main space is between -80 and 80 latitudes. We may change this numbers later

as I mentioned we need to have 21000 equal areas - it’s 150 * 140.
Let’s divide the planet vertically with 150 lines - and now we shall decide on which latitudes to divide Mars

An area of a cap with latitude phi is:
image
(see the picture above)

So to get a surface area of a ring zone from latitude a to latitude b we need to subtract two caps:

A = A1 - A2

We have minimum angle of 10 deg, and maximum of 90. We need to divide it into 70 parts (other 70 parts will be mirrored)

So we divide it into 70 and get a surface of each ring (which contains 150 parts divided by meridians):

So we can find the latitude of the ring end:

Lets make it more common:

Later I’ll try to make some equations with it

Hm, seems legit:

The script:

const toRad = phi => phi * Math.PI / 180;
const toDeg = phi => phi / Math.PI * 180;

const cos = value => Math.cos(toRad(value));
const acos = value => toDeg(Math.acos(value));

for (let i = 1; i <= 70; i++) {
  const phi = acos(cos(90) + i * (cos(10) - cos(90)) / 70);
  console.log({ i, phi });
}

Uh, so.

We have token numbers like 1-xxx-yyy, where x is vertical placement from 1 to 150 and y is horizontal from 1 to 140.

Will continue later - almost done

Some modelling

Hey @crystalbit I think, you’ve done an awesome job! I love it it :heart_eyes: :heart_eyes: :heart_eyes:

we have changed 1xxxyyy token numbers to just 1-21000 numbers


surface area of each land is 6770 sq. km

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