Sugar in water effect on specific gravity?

So i've been a little stressed about this SG stuff so i'm putting something to make u think or at least to get more info

I needed to find more info about this bc I use the International Metric System and I wanted to know how to get this data using a formula or something so i started to research a lot...

*I was studying about SG and is really called Relative Density bc it's relative to the thing you are using to solubilize or "the solvent" which in this case is water* - So after this said i'm going to continue

The Relative Density is: Solution Density(1.xxx) / Water Density (at 20ºC is about .9982)

The relative density tell us about how is the density of a solution taking account that one is denser than other, easy right? well a lot of literature there complicates this shid a lot

The density of water is .9982 gr/cm3 and pure sucrose is 1.59 gr/cm3, so you will never surpass the 1.59 in your SG if this is made of pure sucrose. Relative Density tell us what is the relation between 2 different densities

So i'm making some math and correct me if i'm wrong:

Density: mass/vol Density of a solution water + pure sucrose = (mass water + mass sucrose)/(vol water + vol sucrose) Example of a calculation based on pounds/galon

(3778.2 gr + 454 gr)/(3785 cm3 + 285.53 cm3)= 1.0395... Relative density: 1.0397/.9982 = 1.0415

So let me ask, ¿¿¿where do people is getting that a pound (454gr) of pure sucrose in a gal (3.785 lt) is 1.045???

I've been checking my calculations with pages like this and im getting pretty close with this formula than the one it's used by everyone

https://www.engineeringtoolbox.com/density-aqueous-solution-organic-sugar-alcohol-concentration-d_1954.html

https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780471790990.oth1

https://www.homebrewtalk.com/threads/1-kg-water-8-g-sugar-1-003-gravity.357672/

*Take in account that starch density is 1.5 gr/cm3 so maybe there is something going on between transformed starches and not 100%transformed by the enzymes

The only way to get the 1.045 SG that everyone uses is that the sugar had 1.67 gr/cm3

To add up on Denny's answer, the density of a solution of sugar and water is (quasi)linear in the range we use in homebrewing (e.g. between 1 and 1.2). (see graph below [0] where concentration in wt% is equivalent to degree Plato)

Using this graph, you could make a sugar solution with known density by adding sugar into water. E.g. a 5°Plato (5 wt%) solution would roughly be 5g of sugar in 95g of water.

[0] https://www.engineeringtoolbox.com/density-aqueous-solution-organic-sugar-alcohol-concentration-d_1954.html

Sugar has about 45 ppg. That's gravity points per pound per gallon. So, one lb. of sugar in one gal. of water will give you a specific gravity of about 1.045. That is the known scale. 2 lb. in 1 gal. gives you 1.090, etc.