How does the function Around[] work?

Questions
1

From the Wolfram Blog (Computing Exact Uncertainties—Physical Constants in the Current and in the New SI):

The arithmetic model of Around[] follows the GUM (Guide to the Expression of Uncertainty in Measurement)—not to be confused with Leibniz’s Plus-Minus-calculus.

I do not get what this has to do with the Plus-Minus-Calculus, perhaps the author meant interval arithmetic? Anyway,

Around[1.2, 0.1]^2

leads to 1.44\pm0.24 although [1.2-0.1,1.2+0.1]^2=[1.45-0.24,1.45+0.24], so why do I get the value 1.44 instead of 1.45?

2

At
https://reference.wolfram.com/language/ref/Around.html
under ‘Properties & Relations’ there is just the same operation you are asking about:

Around[10, 1]^2

According to this: (x+y)^2=x^2+2xy+y^2,

computing (1.2+0.1)^2=1.2^2+21.20.1+0.1^2

Let 0.1=delta, then
( 1.2 + 0.1 )^2= 1.2^2 + 2 * 1.2 * delta + delta^2

Around makes a first order series approximation, i.e. the highest delta power is 1, and you can check that 2 * 1.2 * 0.1=0.24, no 0.1^2 added to it.

I Hope this helps.
[1]: http://Around%20Documentation

3

https://mathematica.stackexchange.com/questions/195400/around-usage-results
might also help