
I n   I g h t a r i a   T w o   D i m e n s i o n a l    L a n d ..
 
.. everything can move only in two directions or a mix of these directions.
The sky in Ightaria looks like a horizon line: all the stars project to the same line in 
Ightarian eyes.

Despite this apparent simplicity, this world developed complex forms of Life and 
Geometry. In vast Ightarian landscape, severe waves hide horrible monsters and clever 
creatures, dangerous wormholes and bright planets.

Your task is to find rules governing Ightarian Geometry. What are its Geometric Axioms?
You can begin with small steps. Are there any signs of difference from Euclidean Geometry?
Try to measure distances to stars or build and measure triangles ...

Ightarians call their Land HomeFold. The first time you enter there, you are near the beautiful
Villeya Hill surrounded by fast moving satellite.

Ightarians do not know yet, what their HomeFold Geometry is. This task puzzled us when we
first encountered this Land. In human words, it is a two-dimensional manifold and can be a 
Euclidean plane, but it also can be an arbitrary surface in imaginary or real parent space which 
ancient legends call Altigate.

You are entering into Ightaria as a Guest. Solving the geometry puzzles will promote your levels
and give new tools in your hands. Some of following answers can promote you, but not all of 
them are necessary. Fill out omissions. Don't forget put a: which means that you answering a 
question. Case of letters is unimportant.
 
   a:Euclidean distance to Azoruus is ...
  
Above answer means distance from Starting Point. The distance which is apparent to 
observer when travel just began and if to accept "Euclidean rules of the Space".
Here are the answers:

   a:Universe is Euclidean plane.
   a:Radius of the Universe is ...
 
Above answer means radius of curvature, not the size of the Universe.
You can give this answer in simpler form:

   a:radius is ...

More answers:

   a:Radius of the Universe is infinite
   a:Universe is flat. Curvature Radius is oo.
   a:Universe is Hyperbolic. Distance to seddle point is ...
   a:Curvature is ...
   a:HomeFold is torus. Maximum Radius is ...

  
There are more possible answers, we may return to them later ...

In your posession, there is a powerful Vessel, SCViayager. It is your first tool of 
navigating and research. What you see are the screens of SCViyager computer.
At the center - main window which displays Ightarian's Landscape.

You can learn more about your role if you have access to full story (type t:story to see ... ). 
 
 
 
I n t e r p r e t a t i o n.
 
Although there are two dimensions, you obviously see terrain in HomeFold: hills, valleys, and moving 
objects above the terrain. These are rudimentary elements of undeveloped yet third dimension in
Ightaria. For Human convenience, your Vessel's computer represents this elements as objects
in third dimension although native Ightarians will laugh on you if you say so. From their perception,
there is no third dimension along which they can move, but there is a "sixth sence", Elevation, 
which they feel like Humans feel joy or saddnes from music for example. 

Anyway, the restricted ability to elevate helps human driver to navigate 
and is irrelevant for traveling and measurement of distances and angles.
 
In contrast to Human world, where evolution of Space completed before evolution of the race, 
native Ightarians evolve faster than the Space where they compelled to live and developed 
neuroanatomy which Humans could not imagine. For example, Ightarians feel light differently than
Humans. Human brain apparently recalculates distance to objects by synchronizing signals from two 
eyes or simply by comparing with signals from different objects. In contrary, Ightarians, having 
deficit of light rays from different directions, base their distance feeling on the age of photons.
They detect the difference of age between distant and close photons. Relativistic Dirac equation is 
different in HomeFold.  However, wave equation for logic is the same as for Humans' environment, so
they should be able to understand Ightarian's world. 




M e a s u r e m e n t s

Your Vessel, SCViyager, can perfectly measure angles between local directions and directions
to stars and Hills. Angles measured in HomeFold called Azi. There is no need for complex Human
terminology like "altitude", "lattitude", "longitude". This things do not exist in 
two-dimensional world. 

Your instruments use light rays radiated from objects to measure angles to this objects. 
SCViyager nutvigational system can measure the straight path traveled by vessel. 
You stop the vessel when release arrow keys. Move between two stops called trip by Computer.

The word "perfectly measure" means that general accuracy is about 12 decimal digits, 
1e-12. SCV-computer has accuracy of 12-15 digits.

