Good math bed-time stories for children? What are some good references/books/articles from which to derive some good bed-time math stories to pique a child's interest in math? I am fascinated by math (used to hate it as a kid) and want my kids to be curious about it and fond of playing with the subject.
I was thinking a good way would be to talk about the history/origins of various concepts ideas in math and present them as a "once upon a time" stories and then let them explore the ideas. As a kid I felt a story of "why" behind the what would've been motivating for me to explore the ideas in the field instead of shun them away.
What would be some good math 'stories' to tell them all the way from counting to advanced math (for when they grow older)? I don't mind reading existing books and spin a story on the topics by myself :) Any references to use in particular? Age range 3 to 18 :)
 A: Lewis Carroll (of Alice in Wonderland fame, as mentioned) wrote a book called "Pillow Problems" (now usually paired with "A Tangled Tale") about mathematical puzzles that Carroll considered solvable by just mulling them over in one's head before drifting off to sleep.
Of course, what Carroll could successfully mull in his head will be well beyond kids at the lower end ---even the higher end--- of your specified age range. (Personally, I often found myself having to whip out pencil and paper to work out solutions when I came across this book in college.) There's also the issue that the problems are described in 19th century phraseology, which can be a bit stilted. A Tangled Tale is more story-like, but its puzzles are also challenging. 
Project Gutenberg has A Tangled Tale as a free download. (Hmmm ... Also The Game of Logic, which I have not read but seems interesting.) I don't see Pillow Problems, though, but you can find print versions for sale at your favorite online book vendor.
A: Some recommended children's books - these are actual storybooks, with pictures and the like, and while they have math, they aren't math books for children, they are children's books about math (not a distinction without a difference) that tell actual mathematics stories:
For younger kids (4-6)


*

*The Boy Who Loved Math

*On a Beam Of Light

*On Beyond a Million

*Mr. Archimedes' Bath
For older kids (7 and up)


*

*Sir Cumference and the Off-The-Charts Desserts (tons in this series, all great)

*That's a Possibility!

*A Very Improbable Story

*Multiplying Menace series
And all of the Achilles and Tortoise stories in Godel, Escher, and Bach are pretty funny even for kids (although a lot of them have  material related to the words themselves (crostics, etc.), so "telling" them means you miss some of the material.) 
A: Shanameh, the Persian Epic of Kings, contains a mathematically relevant story: http://en.wikipedia.org/wiki/Wheat_and_chessboard_problem
In it, the inventor of the game of chess is called to meet the king, who offers to let the inventor choose a reward. The inventor knows that he cannot ask for too great a reward, because doing so will anger the king and rob him of any reward. Therefore he frames his request in the following way: he wants one grain of wheat on the first square of the chessboard, two grains of wheat on the second square, four grains on the third, eight grains on the fourth, all the way up to the 64th square.
The king accepts, puzzled that the inventor would ask for so little, and tells his treasurer to figure out the amount of wheat the inventor is due. A week later, he asks the treasurer how much the inventor received. To his surprise, the treasurer has not even finished calculating the amount of wheat, and he tells the king that the entire wealth of the kingdom would not suffice to give the inventor his reward.
The story ends in a variety of ways; in one, the inventor becomes the new king in a rare mathematical proletarian revolution.
Short when we hear it, since we know how fast exponentials grow, but if you couple this with the exercise of trying to calculate how much wheat the inventor should receive then this should be a fun bedtime story/opportunity to learn a little math for a child.
EDIT: There is also a great volume of anecdotes from mathematics history that could serve as bedtime reading, though you'd have to adapt them to a good format for putting children to sleep. A lot of my early interest in mathematics stemmed from such stories; most vividly, I recall the story of how Pythagoras (allegedly) ordered his disciple Hippasos thrown off a boat for proving the irrationality of $\sqrt{2}$.
A: There is a well known story about Karl Friedrich Gauss when he was in
elementary school.  His teacher got mad at the class and told them to
add the numbers 1 to 100 and give him the answer by the end of the 
class. About 30 seconds later Gauss gave him the answer.  
The other kids were adding the numbers like this:
 1 + 2 + 3 + . . . . + 99 + 100 = ?

But Gauss rearranged the numbers to add them like this:
 (1 + 100) + (2 + 99) + (3 + 98) + . . . . + (50 + 51) = ?

If you notice every pair of numbers adds up to 101.  There are 50 
pairs of numbers, so the answer is 50*101 = 5050.  Of course Gauss 
came up with the answer about 20 times faster than the other kids.
In general to find the sum of all the numbers from 1 to N:
 1 + 2 + 3 + 4 + . . . . + N = (1 + N)*(N/2)

That is "1 plus N quantity times N divided by 2."
A: You're asking about mathematical content, but part of the romance of mathematics is in its characters; pre-modern mathematicians in particular were colorful characters, entering public competitions of mathematical prowess, dying in duels, etc. Telling some of these stories, even without going into the mathematics itself, could do a lot to counter the image of mathematics, and those who practice it, as staid and boring.
My memory of sources is rusty, but the story of factoring third degree polynomials (public competitions and all), and the later demonstration that it's impossible for high degrees, should make for a good story-- and doubtless has already. How about the story of Fermat's last theorem? And there's another mathematician (the name escapes me) who committed to paper all he could, the night before he died in a duel. Recent mathematics discoveries are also rich sources of drama: Einstein's theories leading all the way to the atomic bomb, Diffie-Helman encryption, etc. Feynman's autobiography makes fun reading, too. 
Maybe this was a bit short of specifics, but the general idea is: You don't necessarily need to convey the mathematical principles in order to nurture interest in math. So consider biographies, and the stories around the discoveries. 
A: E.A. Abbott, Flatland: a Romance of Many Dimensions.
A: You could always tell the story of the Princess and the Frog.

Credit: http://www.smbc-comics.com/
A: The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger is a fun survey of elementary number theory. It's structured similarly to the series of children's books 'Diary of a Wimpy Kid.'
If I remember correctly, the storylines from each of its chapters are pretty close to independent.
A: Russell and Whitehead's Principia Mathematica... Very useful for putting your children (or anyone, really) to bed!
On a more serious note, Conway's Book of numbers is nicely illustrated, and great for kids (and old kids). Not a story book, but definitely worth looking into.
A: I've not read the book Bedtime Math featured on bedtimemath.org, but it's from a brainchild with a background in astrophysics who memorized perfect squares as a child. The site exposes three levels of math challenges: wee ones, little kids, and big kids. It may be worth a look.
A: The aforementioned Norton Juster also wrote the children's book, The Dot And The Line,which famously was adapted by legendary animator Chuck Jones for MGM and narrated beautifully by Robert Morley. I suspect the cartoon is how my generation experienced the story for the first time. It's set in a planar world where a scholarly,upper crust straight line has an unbearable crush on a dot, who unfortunately for the line, falls for a chaotic squiggle with no brains or character. (Girls always fall for the bad boys,don't they? I don't think even they know why most of the time......) How the line ultimately learns the potential of geometry and uses it to win her heart is well worth relating to your kids. 
A: The book $1,2, 3. .. ,\infty$ by George Gamow has lots of interesting stories. I am sure there is atleast one suitable for any age people. For example, The story of invention of Chess is very nice and the solution to the problem at the end is also very interesting which is not very much technical.
A: The Cat in Numberland by Ivar Ekeland is a truly wonderful children's book -- it offers an exposition of the Hilbert hotel within a charming story about the cat who lives there.  
Another excellent choice is Richard Evan Schwartz's You Can Count on Monsters, a 200-page treatise on primality and factoring intended for parents to read to preschoolers.
A: The Phantom Tollbooth, by Norton Juster, has several nice mathematical bits, including an exploration of infinity, a Dodecahedron, and a character who is the 0.58 of a child from an "average" family.
A: Lewis Carroll, Alice's Adventures in Wonderland.
A: I recommend the videos by Vi Hart on YouTube :)
A: "The Man Who Counted" by Malba Tahan would be my suggestion but not sure what exactly ages are your children ... Perhaps it suits better pre-adolescents, not sure.
A: You might try $\epsilon$-Red Riding Hood and the Big Bad Bolzano-Weierstrass Theorem.
A: Going a bit outside the question. What about either http://www.last.fm/music/Matthew+Matics or https://en.wikipedia.org/wiki/Count_von_Count depending on the age of your kids.
A: You might not believe this one: Dear God this is Anna by Fynn. Is is more physics oriented.
