Celestial navigation uses math that assumes the Earth is round. It does not work for a flat surface.
Actually, there is no math necessary:
https://sextantbook.wordpress.com/2014/04/03/how-celestial-navigation-works-in-easy-steps-1/
You may well think celestial navigation is a dark science that calls for a lot of complex mathematics. In a way that’s perfectly true because it took the work of many brilliant mathematicians to perfect the techniques mariners use to fix their position on the open sea.
But to practice the art of celestial navigation today you really don’t need much mathematical skill. In fact you only have to be able to add and subtract – and maybe not even that now that we all have access to computers.
To explain the basic principles of celestial navigation let’s start with a crucial concept – the ‘geographical position’ of a heavenly body.
At any given moment every heavenly body is vertically above a precisely defined spot on the surface of the Earth. So if you imagine a straight line drawn from the centre of the Earth to a star, someone standing where that line passes through the surface of the Earth would see that star directly overhead – or in their zenith. That person will then be standing at the star’s geographical position (GP). Its GP can be defined by its latitude (degrees north or south of the equator) and its longitude (degrees east or west of the Greenwich meridian, a line joining the North and South Geographical Poles that happens to pass through the observatory at Greenwich).
Now if the Earth did not rotate about its axis all the stars (though not the sun, moon or planets) would appear to stand still in the sky. That would of course also mean that their GPs were fixed. So a very simple way of navigating would be to identify the star whose GP was closest to your goal and then sail (or walk, or fly – or whatever) until that particular star was overhead.
You may say that won’t work because the Earth actually does turn. But wait. There are two special places on the Earth’s surface that actually do remain stationary in relation to the sky immediately above them: the North and South Geographical Poles. So if you want to find your way to either Pole you only need to identify the star whose GP is closest to it and travel until it’s overhead.
There is math needed at night when determining position. I have used celestial navigation on more than one occasion. I can tell you to get anything beyond just determining latitude or direction of travel requires math that assumes a round Earth.
Read your link again. You display a lack of reading comprehension regularly. This is not the first time I have seen you link something that does not support what you claim.
"So if you want to find your way to either Pole you only need to identify the star whose GP is closest to it and travel until it’s overhead."
Which means you can follow the North Star and be heading north. No math involved, but you can not determine your position.
"The height of Polaris is in fact equivalent to the observer’s latitude."
Which means you can determine your latitude and that is it. You can not get your position without using some math and observing at least one other or more stars.
The only time you can use celestial navigation without the math to get some place is when that place happens to line up with a certain latitude. You can not determine your position along a line of latitude or longitude without those calculations assuming a round Earth.
Like wave propagation you are talking about something I have used and have experience with.
Edit: Wanted to add look up the difference between fix and line of position.