It can be done, but it will not be a perfect match. The old wood has character marks, pits, splits and small stains, which took 87 years to acquire.
Helpful tips:
Match the species- red oak or white oak?
Match the grade- is it clear, select, #2 or ??
Match the width- it must match pefectly if it is to be "woven in" meaning not an edge match, instead a butt match.
Match the lengths- if the original floor is all lengths over 3 feet, patching with lots of "shorts" will draw attention.
Good luck. As a last resort, dark stain covers a lot of sins.
Casey (chortle, chortle, I said "butt")

I certainly have to have the floor refinished, right now it's thrashed from spending 30 years beneath shag carpeting! I'm leaning towards tiling the cooking area and maybe doing a wood border across the front of the island to cover the gaps left there, otherwise I need to patch about a ten foot area. I've added a link to a pic of the tile border that will give me the most trouble. Any suggestions on how well this will work? My brother is steadfastly against a tile/wood interface where the tile butts up against the end grain of the wood, is this a valid point? I was just planning on cutting out the curve in the wood floor and then cut the tile to fit and use colored cauk between the two materials (I will make them the same height and the line between them will be very small)

Here is a link that might be useful: curved tile border

Wood needs room to expand and contract due to seasonal changes in humidity and temperatures. While it is certainly possible to do what you are proposing, filling the gap between the tile and wood with caulk is not a good idea. There should be at least a 1/4" to 3/8" gap between the two. That means a transition strip will be needed to cover the gap, one that is connected to the sub floor or the tile thus allowing the wood floor to move.

If that transition strip were made of metal---aluminum or steel, it could be made thin enough to not cause a tripping hazard. If it were made of wood, the thichness will need to be at least a total of 3/4" above the floor surface---tapering it will limit the actual trip hazard, but it will still stick up that 3/4". That 3/4" is basically the same as a threshhold at the bottom of an entry/exit door or often the difference between a carpet and tile floor between a hallway and bedroom---with the transition strip in a doorway. Those locations do not cause the same propensity for a trip since there is a definate change of location---going from one space through a door to another. People have learned to expect a change in the floor height in those conditions.

If the change in the spaces is enough, a 3/4" transition strip between the tile and wood could work fine---it just depends on the situation.

I had new oak matched to my old: the old was exposed in one room and under linoleum and parquet in another; the new was a kitchen floor between the two and a few patches of repair in the old. All were stained a neutral, slightly aged color. It looks pretty close--the floor guys tried to match the wood species and apparently the width of the floorboards hasn't changed in 80 years.

The patched new stuff doesn't stick out at all, but the entirely new floor does look newer. As it's the kitchen, though, we're breaking it in very fast. I don't think the new floor is as hard as the old.

Anyway, a good floor person can do a darn good match. Look into it!

RE: Transition from tile to wood: I have seen an expansion joint from oak parquet to tile hearths done in cork. In fact, the cork expansion joint runs the whole perimeter of the room (18x36ft dining salon) I guess it compresses enough to withstand the expansion, yet the color is the same as the surrounding oak. I thought it was pretty clever, anyway.
Casey

The Henry Ford museum has miles and miles of cork expansion joints along everything from railroad tracks to marble--I've never seen it in residential but it does look pretty good.

Interestingly enough, I have an old tile hearth set into oak and there's no expansion joint. I guess it just expands elsewhere. It's not a super tight fit.

Yep, I have a tile hearth set in my oak floor without an expansion joint too, that is what gave me the idea to do this. It covers a lot less area though. I'll look into cord but I think I'll use a metal border strip. Thanks.

Here is a link that might be useful: metal border transition

We just had a 50 year old section of floor, 10 year old section of flooring and brand new sanded, stained and refinished and you can not tell the difference. It all looks brand new. It will be interesting to see how it ages over time. But for now it looks great. Even where they feathered in the old and new boards.

Had a similar experience in my old house. If you are willing to sand, possibly restain and finish the old and new floors together, and you do all the things stated previously about matching the size, grade, type of wood, etc., in my experience you will not see a difference.

We are thinking of replacing our carpeted living room and hallways with hard wood. We understand that you need expansion areas in the transition areas. Our entryway is round brick, and elevated about 6 inches above the rest of the floor. How do you transition around the curve without it looking funky? We can't seem to find any round transition pieces. Help!