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Geometer is a prestige class in Complete Arcane that gains a special class feature at level 2:

A geometer uses a unique system for recording the details of a spell that drastically reduces the expense of maintaining spellbooks. Every spell he learns from now on requires only a single page in his spellbook. It still takes 24 hours to scribe a spell into a spellbook and materials costing 100 gp per page

This means that a Geometer only needs one page per spell, regardles of spell level when writing a spell in a spellbook. Without this feature you normally need to write one page per spell level.

Eidetic Spellcaster is an Alternative Class Feature for Wizards that replaces the Scribe Scroll Feat (can be seen here):

You do not need a spellbook, either to record spells you know or to prepare known spells. You can learn spells normally, either through gaining levels in wizard or learning from other spellbooks, and you must pay all the normal costs for learning new spells (used instead in special incenses rather than inks), but you do not need to put them into a spellbook

This means that you remember spellbook pages and do not neet to write them. However the cost remains the same, you just do not need a spellbook.

Question: Since you can commit spellbook pages to memory instead of writing them to a spellbook, and you only need one page to store any spell, does this mean that you can save money in special incenses when adding a spell to your repertoire? i.e. special incenses only need to cost as much as writing one spellbook page instead of one per spell level

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Maybe

Unfortunately, Complete Arcane does not give us enough information here.

Your spells do “require only a single page”

Officially, eidetic spellcaster doesn’t say anything about how many “pages” a spell takes, just that you pay “per page,” and then book of geometry changes the number of pages each spell takes. Since eidetic spellcaster needs to determine the number of pages from outside of itself (as it doesn’t state the number), and it doesn’t specify that you’re stuck with the base rules (which would be an ambiguous question of specific versus general), and it doesn't prevent other effects from changing that number, there simply are no real grounds within the rules to argue that the two don’t work together. An eidetic geometer’s spells all require just one page...

...whatever that means.

But does it matter?

There is one very awkward issue here:

It still takes 24 hours to scribe a spell into a spellbook and materials costing 100 gp per page

(Geometer prestige class, book of geometry class feature, Complete Arcane pg. 40)

What “per page”? Didn’t this very class feature change the number of pages to always be 1? Does this sentence “still” refer to the original number of pages involved, rather than the new singular page?

If so, this feature only allows you to fit more spells in a single spellbook, rather than allowing you to reduce costs. Since eidetic spellcasters don’t have limits on the number of spells they can have in their “spellbook” to begin with, this feature would do nothing for them if that’s the case.

Anyway, you should ask the DM

Taking a step back from the rules per se, this question basically comes down to, what exactly is a geometer doing differently? If the diagram they use consumes exactly the same amount of ink, just fits on a smaller area, that implies a diagram of similar—if not greater—complexity versus a traditional spellcasters’ scribing. That might imply that it’s just as difficult to memorize, and thus requires the same amount of incense—so it doesn’t help an eidetic spellcaster at all. On the other hand, if a geometer is able to encode data in the diagram in a way that uses less ink—the same amount another spellcaster would use on a single page, rather than the number of pages the spell would otherwise require—that might imply that the geometer’s knowledge of geometry enables them to get the full details of the spell from less written—or memorized—information, that there are efficiencies in the diagram beyond just space that may well carry over to the mental work an eidetic spellcaster does.

Complete Arcane just does not give us enough information to say. Even leaving eidetic spellcaster out of the equation, it’s not clear whether or not book of geometry saves you ink and money or not. Even if it does, the nature of those savings don’t clearly apply to an eidetic spellcaster’s process. After all, it is “book of geometry” and so on.

In other words, this is a situation where a ruling is required—where you need to ask the DM. I heartily recommend that DMs allow it—it’s costly (a feat and a couple of class levels is a lot to devote to this) and not terribly strong (the money spent scribing spells is notable but not enormous—and more conveniently mitigated with a Boccob’s blessed book)—but it can’t just be assumed.

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    \$\begingroup\$ You might also add that the relative power of taking a feat to simply shave off some gold is not very powerful compared to other feat choices most characters using a spellbook might otherwise have. It's not part of the question, but probably would be considered by the table's DM. \$\endgroup\$ Feb 24 at 8:29
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    \$\begingroup\$ Eidetic Spellcaster and the Geometer Prestige Class really are two quite contradictory concepts. This is also shown in the fact that you lose Scribe Scroll if you take the Eidetic Spellcaster ACF— but the Geometer Prestige Class (the "master of written magic") has Scribe Scroll as a prerequisite. So you would have to get Scribe Scroll from another source... \$\endgroup\$
    – Peregrin
    Feb 24 at 14:27
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    \$\begingroup\$ @Peregrin True, but who’s to say that a very unusual geometer—one who is an eidetic spellcaster—can’t “write out” everything in their head? It’s not like the geometer is using special inks or paper, or specifically interacting with the physical object in some way. They’re just drawing a fancy diagram. Really, unbound scroll (Dragonmarked) is much more of an actual contradiction. And the rules back that up—since unbound scroll works with scrolls rather than spellbooks, eidetic spellcaster doesn’t help. \$\endgroup\$
    – KRyan
    Feb 24 at 16:56
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    \$\begingroup\$ @annoyingimp That’s... an unfortunately good point. Ugh. Not clearly worded at all. I’ll note that potential problem. \$\endgroup\$
    – KRyan
    Feb 25 at 18:29
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    \$\begingroup\$ @Calabacin That’s a possible interpretation, but the key thing is that it’s not the only possible, valid interpretation. Which means that it’s not really your opinion that matters so much as the consensus around the table. \$\endgroup\$
    – KRyan
    Mar 11 at 13:06

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