It's a very well-written article, and you've approached it from a great angle too.
Here are a few stylistic suggestions to consider, but really they're so trivial that I'm reluctant to suggest them:
1. How about writing "billion" and "trillion" instead of B and T? You're presumably writing for a non-technical audience.
2. I would put a comma before "and for good reason".
3. Some of your readers won't know what a Krugerrand is. You could replace the phrase "break that tenth ounce Krugerrand into nine pieces and mail one to you" by "break their gold coin into tiny pieces and mail one piece to you".
4. I would replace the comma by a colon after "two ways to get bitcoins".
5. I would add "and there's" before "no backdoor access".
6. It's difficult for people to assimilate new concepts, but consistent wording helps. You could replace "you give one address to the payer" by "you give a payment address to the payer", and you could replace "pasting the recipient's address" by "pasting the recipient's payment address". This matches your use of "payment address" earlier in the paragraph. Actually I prefer the term "receiving address", because some readers might assume that "payment" refers to an outgoing payment.
7. Replace "hard limit" by "fixed limit". The term "hard limit" is heavily used in computing, but to the lay reader the word "hard" is synonymous with "difficult".
These things are all very minor, and it wouldn't be a problem to publish your article without any of these changes.
There is, however, one part of your article which I don't think is clear to someone who doesn't already understand Bitcoin:
Payments appear immediately, but will not be confirmed until someone includes them in a valid solution
Earlier in the article, you implied that the solution was bitcoin ("Bitcoin is a more modern solution"). You did also refer to "the reward for solving a problem", but didn't explain what kind of problem you're referring to. World hunger, for example? You did explain this by saying "computers solving a math problem who's solution validates transactions and prevents double spending", but that's not clearly tied to the other references.
Perhaps you could rework those parts to refer to the familiar concept of "transaction processing" instead of "solving math problems". Something like "Bitcoins are not dug out of the ground, they are generated by computers processing Bitcoin transactions in a way that is computationally difficult but which validates transactions and prevents double spending".
That's not an optimum wording either, so feel free to ignore this whole post. After all, the perfect is the enemy of the good.