Noun Phrases Derived from Names

[Terra]

There are multiple patterns one can use to form nouns phrases from names with.

1) name + noun
§Fibonacci Sequence
§Riemann Hypothesis
§Sierpinski Triangle
*Venn Diagram
*Klein Bottle
*Markov Chain
*Galois Group
*Hilbert Space

2) genetive of name + noun
Pascal's Triangle
Russell's Paradox
Cantor's Theorem
Newton's Laws of Motion
Charles' Law
Euler's Formula
Leibniz's Notation
Hibert's Problems (note Hilbert above)
Fermat's Last Theorem

3) adjective form of name + noun
Boolean Logic
Gaussian Elimination
Cartesian Coordinates
Newtonian Physics (note Newton above)
Keynesian Economics
Pythagorean Theorem
Euclidean Geometry
Platonic Love / Solid
Diophantine Equation
Socratic Method
Aristotelian Ethics

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Some words seem to have both patterns in not insignificant numbers:

Term - Google Hits
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Archimedes' Screw - 106,000 (Also, it's worth noting that imd (in Standard American I think actually?), names that end in [s] still take an additional [s] (with an [@] or inbetween) in the genitive. However, despite "Archimedes" being the name of the man, it's still only "Archimedes' Screw", and not "Archimedes's Screw".)
Archimedean Screw - 42,000

Lagrange Point - 288,000
Lagrangian Point - 178,000

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Thus, my question is, is there any pattern to how one chooses which pattern to use to form a phrase with a name? I've been able to gather two things about this.
1) The third pattern (adjective + noun) seems to attract more Greek names than the others.
2) Certain ones (the one's marked with an asterisk) wouldn't make sense if the second pattern was used, since one can have many of them. *"Venn's Diagrams", *"Klein's Bottles", *"Markov's Chains". The genetive seems to bind to the noun after the plural does. However, this doesn't explain why the ones marked with a section sign still don't appear in the genitive.

Edit: Added more examples. Perhaps when I have the time I'll make a proper comparative table of all the forms and the amount of google hits for each.

[Radius Solis]

I can't say much beyond adding to the list the Pythagorean Theorem - another Greek guy for pattern 3 - and that despite hearing and seeing it that way all my life, in a book I've recently read it's called Pythagoras's Theorem instead.

[Chuma]

Most likely the practice changes over time. #3 is probably the oldest, and then I would guess #2 is older than #1. Then the fixed expressions stick around. You might say it's an example of English becoming more isolating, less fusional.

[makvas]

I don't know how applicable this is to the nouns you've listed as example, but my last name (Vedejas) has no obvious genitive *or* adjectival form in English. Maybe this would be a factor for some names; at least "Vennian" and "Riemannic" sound pretty strange.

[faiuwle]

It actually took me a few seconds to remember that Boole was originally someone's name...

On the note of names that end in [z] getting possessives, there's also Charles' Law, which I would also only pronounce with one [z], but the Wikipedia article title spells it as "Charles's"...

ETA: I think the possessive pattern tends to happen mostly with modern names that stand out more to modern people as names.

[Terra]

I don't know how applicable this is to the nouns you've listed as example, but my last name (Vedejas) has no obvious genitive *or* adjectival form in English. Maybe this would be a factor for some names; at least "Vennian" and "Riemannic" sound pretty strange.

You don't like the sound of "Vedejasian Economics"? (especially after it's anglicized?) ... /'vid@"dZeIZIn/ - Oh, the horror!

Also, on Archimedes again, perhaps it's because his name ends in /iz/. Laymen often encounter the word "parentheses" in only its plural form, and improvise when forced to come up with the singular form, often coming up with "parenthese", where the final 'e' is /i/. Perhaps this bleeds over into making " Archimedes' " no sound so bad. And...

Then the fixed expressions stick around.

Indeed, that plays a part in this too, making old patterns that are no longer use, stick around.