I am trying to compactify Minkowski space, but all I manage
to get is kinds of clovers or squares, while what I'm after
is circles (i.e. the locus of points whose *proper* distance
from the origin is constant).

See <https://www.desmos.com/calculator/b2bl9jiwo8>

Note that I would like to keep it in terms of (y,x) coords,
as that naturally maps to the (t,x) of space-time.

Can anyone suggest scaling formulas (or fix the diagram)?

-Julio

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Op 09/06/2025 om 13:39 schreef Julio Di Egidio:

I am trying to compactify Minkowski space, but all I manage
to get is kinds of clovers or squares, while what I'm after
is circles (i.e. the locus of points whose *proper* distance
from the origin is constant).

See <https://www.desmos.com/calculator/b2bl9jiwo8>

Note that I would like to keep it in terms of (y,x) coords,
as that naturally maps to the (t,x) of space-time.

Can anyone suggest scaling formulas (or fix the diagram)?

-Julio

https://en.wikipedia.org/wiki/Motor_variable#Compactification

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On 09/06/2025 13:39, Julio Di Egidio wrote:

I am trying to compactify Minkowski space, but all I manage
to get is kinds of clovers or squares, while what I'm after
is circles (i.e. the locus of points whose *proper* distance
from the origin is constant).

See <https://www.desmos.com/calculator/b2bl9jiwo8>

Note that I would like to keep it in terms of (y,x) coords,
as that naturally maps to the (t,x) of space-time.

Can anyone suggest scaling formulas (or fix the diagram)?

Never mind, here it is, at least the upper portion: <https://www.desmos.com/calculator/3j9sqkymsf>

The scaling is the obvious one component-wise. Drawing
full diagrams in Desmos makes things quite more complicated,
indeed I have not actually computed `f_e` as that require
the inverse scaling...

-Julio

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