Basel_P

 Been vacuuming around the appartment and mulling Euler's solution to

the Basel problem. Mathematicians at the time wanted to know what

the series of the the sum of squares converged to precisely. Euler proposed

(pi^2)/6, and was well appreciated for his answer.

                                                         

Really!! Absolute convergence to a divergent constant... If one morning

my normal 50 kilos weight on the scale has become 50.1, that is divergence. Pi keeps

adding decimals to its values, keeps getting bigger the more one considers

it.

Asked Chatgpt to explain this whole thing to me:

                                                                            

                                                                        *     *     *

On reflection, perhaps I am being silly about pi being divergent. It is a computed

 

constant, and the fact that it can have many decimals only means  that I can ask for

the precision I want. My weight can be 50.12974; I am just not measuring all that with

this bathroom scale!!

Indeed, up to the time of Descartes, mathematicians worked with chords on a circle

to indicate a 2-D plane using the original hypothenuse proff from Antiquity as a model.

Thus, as well, the interest in series.