What's the Name of That Book??? discussion

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The Boy Who Reversed Himself
SOLVED: Children's/YA
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SOLVED. child is a caretaker of a world in basement [s]
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"There was a book written with this same philosophical concept called Flatworld. The protagonist was A. Square, in a 2D world, shown the wonders of Spaceworld by a nameless sphere.
There being no kids involved in this story, I'm doubtful it's the same story."
Then 15 min. later he wrote:
"I just found out that somebody wrote a "sequel" to Flatland (not Flatworld, sorry) a little more than a hundred years later called Flatterland. Its protagonist is Vikki Line, a teenager who finds her Square ancestor's writing about Spaceworld.
But it's a 2d female kid protagonist, not a 3d male kid protagonist, so it still doesn't fit."
That's all I could come up with.*shrug*


I'm starting to think I might have read Flatland or Sphereland as a kid and ended up daydreaming a story about these concepts instead of paying attention to what the book was actually about. I had an almost consuming imaginary life as a kid =)


Back in the present day, she has a crush on some boy who is distant and dreamy, not at all like the awkward neighbor. I think the dimensions may be in a closet or under a stair case. I remember something about 2-d, and at some point, octogans. Is this what you remember??



I know that is a little off of what ya'll are mentioning but I know I mess up details after so long so I thought I'd give it a shot.
edit: The goodreads description is tiny. Here is an amazon one:
Once again, Sleator treats us to the best that YA science fiction can offer: averageand sometimes not-so-averageteenagers facing the physical and mathematical absurdities of our universe. Laura's determination to get into medical school has cast her as a brain and, thus, untouchable. She has a crush on Pete, the football captainand weird things are happening on a daily basis, ever since Omar, the creepy boy next door, moved in. Laura makes Omar confess his secrets: he's training to become the guardian of the Second Dimension, while he's exploring the Fifth. Laura invites Pete on a journey to the Fifth Dimensionbut her game becomes a nightmare when she and Pete are captured, and the whole existence of the world depends on Omar's ability to rescue them. After the seriousness of Singularity, Sleator has returned to some of the humor of Interstellar Pig. A welcome offering from a versatile writer.
Copyright 1986 Reed Business Information, Inc.

Thanks!


47- or 48-piece estate, also having the portal to another world in the basement, but more magical/wizardy.
Sarah, I notice your request is marked Solved. Just to confirm, what is title and author of your book?
A recent post reminded me of a book I read as a kid and haven't been able to find since.
I remember the main character being a kid who discovers a portal to another world in his basement, except that world is two-dimensional. It turns out that each world has a portal up to the next dimension as well as down one, but most people don't know about them. I don't remember if he was able to go to the 2-D world or just look through and talk with some of the inhabitants. He kinda becomes the caretaker of that world, and I think there might have been some conflict where he had to "save" that world or something.
I read this as a kid, probably in the early 80s. It was definitely a kid's book. Someone once suggested a non-kid's book from the early 20th century, but that wasn't it.
Help?