The Halls of Mandos

[Aiwendil]

Oh! Supplementary! Two angles that equal more than a 90° angle!

Actually, if I recall correctly, supplementary angles are two that add up to exactly 180 degrees. Complementary angles add up to exactly 90.

I know it was said that "The Fates of Men and Elves are apart" but I think that surely they would all meet and dwell in peace when Eru remakes the world, right? They go to the Halls of Waiting until then, or at least, the men do. Where else do you find information about Tolkien's equivalent to Heaven?

As Galorme said, no one's really sure what happens to Elves after the end of the world. The matter is much discussed in Morgoth's Ring, particularly in the "Athrabeth Finrod ah Andreth". There Finrod and Athrabeth, a human of Beor's house, argue over which fate is worse: that of humans, who spend only a brief time in the world, or that of Elves, who face the possibility of a final oblivion. Each one sees the other as more fortunate.

One possibility that is suggested is that following the end of the world, there will be a new earth in which the positions of humans and Elves are, in one sense, reversed; humans will be at home in that world, while Elves will "seek elsewhither".