Checkmate, Randall Patrick Munroe

And I never believed my Grade 12 math teacher that calculus would be useful later on in life. Turns out it’s great for screwing with phone companies. Oh well. You’re still a dick Mr. Calder.

Verizon payment


  1. Jaquie M.

    I love this!

  2. Google is the best search engine

  3. Dameon

    So what is the amount he was going for?

    .002 + 23.14^sqrt(-1) + .99999999999999… = ~.002

  4. Arne Lovius

    beautiful :-)

  5. Jason

    This is out of control. I love it! Way to go (the memo is my favorite part). Just listened to the call on youtube… and I thought I had horror stories with phone companies on the phone. Good night! This should be aired on tevevision.. you need to get on some kind of scarborough or o’reilly or something!

  6. Brandon

    Would have been funny if it added up to a real number. Or did I miss something?

  7. CalcMajor

    noob mathematicians ;-p the total is essentially 0.

    e^([pi]i) = -1
    just like ln(-1)=[pi]i

    i, indicates an imaginary number which has a few different calculations than real numbers. You can do it by hand, or just say ‘screw it’ and use a TI-83 or equivalent.

    ∑1/2^n = 1

    Even though beginners will translate it as .999… that number is a fallacious number, and is thus translated as 1. (Just like 2/3 is equal to .666…, 3/3 = .999… AND 1)

    And finally, when dealing with money, anything less than a cent, can NOT be rounded up to a cent. It is in fact rounded down.

    Plan and simple, he gave them a check for nothing… and is refusing to pay his bill.

  8. shane

    Hey everyone,

    The “i” imaginary number is factored out. e^ix = cos(x) + i*sin(x) (Euler’s Law); since sin(pi) = 0, the “i” is factored out — and cos(pi) = -1. Then the series shown does not equal “1”, but rather pi^2/6 (it’s a power series expansion). What you’re left with is:

    0.002 – (pi^2)/6,

    or roughly -$1.64. Which tells me that Mr. Munroe must have had a credit of $1.64 on his account… :-)


  9. Hey Nerds.

    I think you’re missing the point. Stop doing math and enjoy the joke.

  10. Ward

    Shane, you got the power series wrong. Expanded, it’s:
    which converges to 1. Mr. Munroe appears to be paying his good friends at Verizon 2/10ths of a cent.

  11. pat

    I think this check is somehow linked to this episode from YouTube:

    Verizon does not know the difference between .002 cents and .002 dollars.

  12. Lew

    That check is made out incorrectly. The numerical part on the right side is acceptable, but the “Dollar Line” is totally unacceptable because that line is supposed to be written in word form, and not a repeat of the numerical value. Verizon should have refused to accept it and maintained a balance due on the account. HOWEVER, the whole idea is terrific!

  13. someone smack Lew, he must work for a bank.

  14. Phaedrus51

    This is the funniest thing I’ve seen all week. Hats off to Mr. Munroe, and stick to your guns.

  15. Oscar

    Lew, in the US of A, the fractions of $ can be written as er… fractions. That’s numerically. So writing
    0.002 $ is just the same as nought&.2/100$ which makes it acceptable. The series and the complex exponential are… higher order terms which can be safely neglected ;-)

  16. I-Love-It

    The summation evaluates to 1. The exp(i*pi) evaluates to -1 (actually to -1 plus undefined). So the total is 0.002 dollars, or 2 cents. He put in his “2 cents worth” AND it was the infamous number Verizon could not understand as well.


  17. i-love i-love-it


    Your math skills are amazing.

    Please explain how .002 dollars is 2 cents.

    Thats the only part i don’t get.

  18. I-Love-It

    Actually, my math skills are not amazing. $0.002 is not two cents of course–it is 0.2 cents. My bad on that part.

  19. Brad

    The only problem is you payed 39 cents to mail a worthless check to your phone company. Later you’ll pay late fees on top of that. I’m sure that a few people are impressed by your copy and past of a couple of famous mathematical terms that equal -1 and 1, but I am not. Also you gave out your full name, your bank, and your signature to the free world. You might end up with your account drained if some hacker type gets hold of that info. Well, maybe you’ll get a date out of it from some math geek groupie.

  20. Anti-Brad

    Brad is a n00b. ANYONE’s account can be stolen. “Some hacker type”? What kind of nonsensical generalization is that? Not all hackers are bad people. In fact, you can get the information you stated anywhere else on anyone! Obviously you’ve got an intelligence complex. Mr. “Copy and Past” You sicken me, effing n00b.

  21. Bill

    Randall you R DA MAN… that was funny. Well done. As for the NERDS doing all the calculation below? Get a life and smile a bit !!!!

  22. JC

    Randall, I love your object lesson, but it’s not much point in blanking out your routing transit field in the MICR line of the check if you’re going to leave it visible under the check number. Just my opinion, I could be wrong.

  23. Looks like Shane mistook Σ(1/2n) for Σ(1/n2).

  24. I put some <sup> tags in there, and they got stripped. Fellow nerds will guess where.

  25. Randall Munroe, I wish I’d had this when Verizon tried to screw me over. I reported them to the BBB and after that we came to an understanding about what I REALLY owed them. You are a genius!!!

  26. Richard

    I-Love-it has the math right (combining both his posts ;)

  27. sharon

    Pure genius.

  28. Phred

    To all those who disparaged the people who did/could do the math calculations: Is that the typical reaction of someone with intellectual deficiencies? Berate those who didn’t go to school with heads up their arses?

  29. RPM

    $536.49 roughly

  30. Math is Important

    The Math is correct it totals 2 tenths of a cent. And this is important to fully understand what he was saying. If you thought it was just to be confusing you missed the fact that it is referring to the “Verizon is bad at math” incident.

  31. C. Jo

    I also got about $536.50

  32. Eric

    $76.29 to be exact… Where did you guys learn your math?
    It’s not about the math – It’s about the funny factor!

  33. Neil (Engineer)

    It is 0.2 cents or 0.002 dollars as per my calculations… $76.29 is wrong and so is the ridiculous $536.50… I doubt the joke is on verizon if he’s giving them that much money…

    It makes a lot of sense if it is 0.2 cents because verizon didn’t know the difference between 0.2 cents and 0.2 dollars.

    e^i*pi = -1
    and the sum as n approaches infinity is 1

    so both cancel out and you get 0.002 dollars.

    just my 0.2 cents :)

  34. DaleB

    The value of the check is for $0.002
    …2/10 of a cent.

    Why ?

    e^(i^pi) = -1
    the infinite sume = =1

    These 2 terms cancel,
    leaving just the term $0.002.
    People are misinterpreting the exponential
    thinking that the i = sqrt(-1) is a 2.

  35. DaleB

    Note: Typo is previous posting…

    The correct form is: e^(i*pi) = -1

    The value of the check is for $0.002
    …2/10 of a cent.

    Why ?

    e^(i*pi) = -1
    the infinite sume = =1

    These 2 terms cancel,
    leaving just the term $0.002.
    People are misinterpreting the exponential
    thinking that the i = sqrt(-1) is a 2.

  36. Brad Fidel

    Why do you guys keep multiplying by Pi?

    It’s TWO * Pi.

    See the 2?

    e = 2.7182819
    2Pi = 6.2831852

    2.7182819 ^ 6.2831852 = 535.4916867

    Now add .002 ++DOLLARS++. (He’s making a check out in dollars, you all get that, yeah?)

    .002 dollars = $76.

    We now have a check for $611.4916867.

    You all have the rest correct, $1.

    The check is made out for $612.49.

  37. hagbard

    Hey Brad Fidel,

    I’ll give you .002 dollars, if you’ll give me $76.00

  38. John Overfield


  39. The Courtesan

    “Brad Fidel” is an idiot. Do the math. It’s already been explained by “Neil (Engineer)” and “DaleB.” e raised to the power of i times pi is an irrational number (-1). add that to .002 and the the infinite sum, you get 0.002

    There. Also, why do people keep ragging on others who can “do the math”? Are you just jealous of them?

  40. The Courtesan

    Oh, “John Overfield”. The joke was not “THE GUY IS SMART ENOUGH TO WRITE THE CHECK IN THAT MANNER.” It was, in fact, a statement to Verizon on how bad they are at math and how it is evident in their billing department. It had nothing to do with him proving his intelligence. Randall Munroe is a genius; all xkcd fans acknowledge that.

  41. The Courtesan

    Correction. I meant to say that pi was the irrational number while i was the complex number.

  42. Math Whiz

    This is a check for 0.2 cents.

    $0.002 + (-1) + 1 = $0.002

    Look it up, bitches. There’s a story behind it. Randall Munroe is the creator of web comic xkcd. He sent this check to VZ after reading about George Vaccaro’s struggle with the company. Read about it here:

    Randall Munroe, however, used the incorrect amount on this check. His amount agrees with VZ’s position (0.2 cents) rather than George Vaccaro’s position (0.002 cents). Randall can be funny, but ultimately his math is not as funny or as cool as he thought. :-p

  43. Sarah

    Randall, Your IQ matches that of a ( I cant even think of something so low). Your language and thought process it about as low as it can get. Would you call your mom or allow someone to call your sister or if you have mamaged to get one, your wife to be called Bitch. You are low class.

  44. Phrank

    hilarious….I worked for Verizon and our customer relations were not always great. Good for this guy not taking the big old corporate bully routine and hitting back. I wondr if this check cleared? Hmmm

  45. Will

    I believe the scale would be in dollars, so I got 20 cents for the value of the check.

  46. Sheldon Cooper

    That looks like e to the tau x pi to me, which would make it a check for more than $373 million dollars. Very generous. Tau, btw, is 2 x pi, so it would be approximately 2.718281828 to the 19.7392088, or $373,791,533.20-ish, plus the $0.002. plus the sequence ($1)

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