Should I use "did you know" or "do you know" to introduce a fact?

Solution 1:

A similar question was asked to the Editor of Merriam-Webster Learner's Dictionary. Serenity Carr, Assistant Editor, answered: "The phrase 'did you know' is used when you are asking someone if they know a fact, and you already know the fact." [...] The phrase 'do you know' is usually used when you are trying to find out information you do not know."

See the full explanation and some examples: http://learnersdictionary.com/qa/When-to-Use-Did-You-Know-Instead-of-Do-You-Know-

Solution 2:

They sentences are used differently.

If I'm talking to someone and I am going to introduce a random topic such as trivia or history, for example: I would say "did you know that XYZ"?

However if I want to find out what someone's level of knowledge on a specific subject is: I would say "do you know"?

I hope that makes sense.

Solution 3:

The two formations are used for specific types of situations.

Do you know what time it is?
Do you know how to tie complex knots?
Do you know how much that costs? (Is it expensive?)

The above are all true inquiries seeking an answer to something the asker does not know.

Did you know that tomatoes are actually a fruit?
Did you know Yoko broke up the Beatles?
Did you know how much that cost? (Because I do...)

All of these are facts that asker knows the answer to. As you rightly pointed out, the construction of a past tense is largely due to the fact that the recipient will know the information as soon as the asker completes the question. However, it is not the only used of "did you know".

Did you know her parents?
Did you know what to do when the car spun out of control?
Did you know how much that cost? (...when you bought it?)

The above are just a past tense version of the previous "do you know". Both people talking probably know the fact now, but the asker wants to determine if the fact was known at a particular moment in the past.

Do you know how long I've been waiting?
Do you know anything about computers at all?
Do you know how much that costs? (Because we totally can't afford it...)

The construction of "do you know" is also often used for the rhetorical.

Did you know that?

Solution 4:

I always thought that "Did you know" was used to introduce trivia or other information a listener is assumed not to know.

Starting with "Do you know" might be used in a similar way, but I think starting with "Do you know" sounds, to an English speaker, like you're asking them for information you assume they have. Starting with "Do you know" may even make them feel like they are being quizzed on the information in question, even if you are not quizzing but offering information to them.

I would go with "Did you know" if I were introducing a fact to someone.