dollars equal cents

I find this one on the math bulletin board at CSU, it makes money disappear very fast:

Theorem: 1$ = 1c.

Proof :

We have

1$ = 100c
= (10c)^2
= (.1$)^2
=.01$
= 1c. (qed)

9 Responses to “dollars equal cents”

  1. Toan Says:

    That’s a nice theorem, anh Du.

    By the way, I have a question for you: How a quarter can save you dollars? Answer it fast! he..he..

  2. dxpham Says:

    Toan: this is my try: a quarter can save a dollar in many cases at the vending machine. For example, we want a coke really bad while we only have two quarters in the pocket and the machine wants 75c for a coke.

  3. Toan Says:

    I see. That’s a good example. How many dollars have you saved by this way?

    My answer: go to the Aldi market. I guess you don’t have it at Colorado, do you?

  4. truongtrungtuyen Says:

    Anh Dự: Tại sao 100c=(10c)^2?

  5. dxpham Says:

    @Toan: Right, we need a quarter for a cart at Aldi. I have not seen one at Fort Collins, but there is a singleton store , Sunflower, similar to Aldi.
    @Tuyen: Chỗ đó thật khó giải thích🙂. Nhờ nó mà mình có cái chứng minh.

  6. LD Says:

    Too busy lately to check this blog but it seems (to me!) not much is going on. It’s a shame.😦

    If you want a more rigorous version of this then Banach-Tarski paradox is the one. Mathematically, you can be extremely rich or poor by just having a piece of gold. There is a nice exposition on this paradox by Ian Stuart in a 80’s Naturalist issue (as far as I remember).

    Du’s proof is good for people who hate math and cannot pass College Algebra. Well, that’s how we popularize our stuff, right?🙂

  7. LD Says:

    Sorry! Stuart’s article cannot be on Naturalist but Intelligencer. I am not so sure again. Go Google!

  8. dxpham Says:

    No, I can’t take the copyright of that proof🙂. It involves (10c)^2 = 100c^2 = mc^2=e (take m=100) …. too sophisticated.

    Maybe anh Dung mean the Phd minor thesis of Francis Edward Su at Harvard in 1990:
    http://www.math.hmc.edu/~su/papers.dir/banachtarski.pdf

  9. LD Says:

    @Du: No I meant Ian Stuart at Warwick! I read his article long ago in order to explain the paradox to my daughter (I failed!). His article is for laymen and he did a good job (I didn’t).😦

    I believe that it’s hard to make Math (the real one) relevant to this real world. Either I’d try to cheat (myself) or be happy with my own world. Ask yourself: Is this world quantum or continuous? I hope that you will be happy and successful with your answer. I thought I was!


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