Ahead Is The Town of Three Forks, Montana =>
…As Is the Case Of The Three Mathematical Geometries, =>
…..The Narrator Here (At The Town of Three Forks) Chooses Among
…….The Three Roads (Following Three Respective Rivers), and Thus Follows, =>
………The One Road Along The Jefferson River, Which Goes To Rich, Productive, Fruitful Lands! This Is A (Metaphoric Bridge Connection) To The One Most Productive And Useful Geometry, Namely => The Riemann Geometry, Used In The Theory Of Relativity, That Best Describes The World We Live In. “


….“ It had long been sought in vain, he said [Poincaré], to demonstrate the axiom known as Euclid’s fifth postulate and this search was the start of the crisis. Euclid’s postulate of parallels,
….Finally, in the first quarter of the nineteenth century, and almost at the same time, a Hungarian and a Russian—Bolyai and Lobachevski—established irrefutably that a proof of Euclid’s fifth postulate is impossible. …….
….It wasn’t the proof that was alarming. It was its rational byproduct that soon overshadowed it and almost everything else in the field of mathematics. Mathematics, the cornerstone of scientific certainty, was suddenly uncertain. .
….We now had two contradictory visions of unshakable scientific truth, true for all men of all ages, regardless of their individual preferences……..
….This was the basis of the profound crisis that shattered the scientific complacency of the Gilded Age. How do we know which one of these geometries is right? If there is no basis for distinguishing between them, then you have a total mathematics which admits logical contradictions. ……
….And of course once that door was opened one could hardly expect the number of contradictory systems of unshakable scientific truth to be limited to two. A German named Riemann appeared with another unshakable system of geometry which throws overboard not only Euclid’s postulate, but also the first axiom, which states that only one straight line can pass through two points. Again there is no internal contradiction, only an inconsistency with both Lobachevskian and Euclidian geometries.
.. .. According to the Theory of Relativity, Riemann geometry best describes the world we live in.
.... At Three Forks the road cuts into a narrow canyon of whitish-tan rock, past some Lewis and Clark caves. East of Butte we go up a long hard grade, cross the Continental Divide, then go down into a valley. “

In distance is the town of Three Forks, MT. In ZMM Chapter 22, the Narrator takes up his Chautauqua about " .... an alarmingly deep crisis in the foundations of the exact sciences ... ". As he tells us, that mathematicians had found three contradictory major mathematical geometries, of which only ONE of the THREE (“ Riemann Geometry “ ), has fruitful,/practical, application to our world.
…As this Chautauqua ends ...... sure enough ...... exactly on cue ..... the corresponding route of travel arrives at Three Forks of Three Major Rivers plus a Town also named Three Forks, MT..
…. As ZMM Route approaches the town of Three Forks, it crosses several muddy, swampy, channels of the Madison River, before turning South on combined Rt2 & Rt287.
…. As is the case for the Mathematical Geometries, the ZMM Route takes ONE of the THREE forks , the Jefferson River, up into rich, fruitful, productive "valleys".

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…. RIGHT Click & Select New Tab =>To See A Google Satellite View of Southern Montana, Centered On Town of Three Forks, Montana, plus the 3 Roads & 3 Rivers Close By. AFTER This Satellite View Comes Up, Click At Lower Left, To Zoom-In On the Town, AND Look To Northeast to See The Three Rivers At Headwaters State Park.

…. NEXT PHOTO shows => A Scale Model Of the “Landscape Topology of The Area Of The Three Forks Of The Missouri River”, Showing The “Cut” In The High Mountain Ridge, That Force These Rovers Together! Also with this Next Photo Is => A Link To A Satellite View & A Link To A Topo Map View.
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(Photo = 109-0921c ...... ZMM Page = 235 ...... WayPt = 231w 4120)