Ancient Egyptian Mathematics

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Description:

Michael S. Schneider explains how the Ancient Egyptians (and Chinese) and modern computers multiply and divide.

Comments (16)

  1. Comment  by binary01

    Interesting.

  2. Comment  by Kyle

    Thank you, that was awesome.

  3. Comment  by Explainer

    You’re just scaling the sequence. 25 * [... 16 8 4 2 1] = [... 400 200 100 50 25]. This allows us to translate the problem easily into simple base 10 arithmetic, as per your example: 25 * 17 = 25 * (16 + 1) = 25 + 400 = 425.

    Really, the beauty of binary is that we can only use each number of the sequence at most once. However, the same works with bases > 2, as long as you realize you can use each number of the sequence more than once.

    For example, base 3 has the place sequences [... 27 9 3 1], and the base ten number 17 is given by 122 in base 3 (we’ve used the bottom 2 places twice each: 1*9 + 2*3 + 2*1). So, just as before: 25 * [... 9 3 1] = [... 225 75 25]. Also, just as before: 25 * 17 = 25 * (1*9 + 2*3 + 2*1) = 1*225 + 2*75 + 2*25 = 425

    Clearly, the benefit of binary is ease of doubling and the fact that each place of the sequence is used at most once.

    • Comment  by mistro

      i love this

  4. Comment  by Snappy

    Question:

    How would one get the multiples of 25 in each case without the initial multiplication tables?

    He conveniently writes down 25, 50, 75, 100, 200, 400 … without basis for arriving at their values.

    • Comment  by Shakey

      Snappy, he’s not writing a proof. There is no need to explain how he got the multiples of 25. It’s just assumed that most people can easily produce those numbers without much thought.

    • Comment  by zdp

      Well, if it was on a computer, you can double a number by shifting the bits left by one and putting a 0 in the ones column.

      • Comment  by Anonymous

        25 + 25 = 50
        50 + 50 = 100
        100 + 100 = 200
        200 + 200 = 400

    • Comment  by Matt

      No. He writes down 25 as a multiple of 2, so 25, 50, 100, 200, 400. Basically doubling the value each time as that is what TIMES BY TWO means, hes not “conveniently” arriving at values. If he were to say 15 as a multiple of 2, it would be 15, 30, 60, 120, 240 etc etc.

  5. Comment  by Voxx

    Thank you Mr. Schneider! What a beautiful, elegant method of math. Where can I learn more?

  6. Comment  by nbn

    but…how do u divide 10 by 7…or…8 by 6 … etc. ?????

  7. Comment  by hundert

    u take whats left and divide by what you divided, i get 10by7=1,3/7 and 8by6=1,1/3

  8. Comment  by very deep

    I am amazed I never learned this in school (and I am a master’s degree electrical engineer!!!

  9. Comment  by aardvarkian underground

    Well, that was worth digging up.

  10. Comment  by Nathir

    I wonder if you have to use 25 in the right columns. Would it work with 10? why?

    The way I do math in my head is by approximating to numbers I can easily do, like 6*9 is 6*10-6

  11. Comment  by marin

    I love this method.However, when i try to apply it in my head..i get back to what i know best.. base 10 math. However, i do use an similar way of doing math when it cames to calculate PC bandwith, IP’s and even storage on Pc’s. CISCO teachers, teach theyr students to think in binary code using the same method that was presented in that movie, (At least, they teched me uing the same method..) but doing it as a game ..
    Anyway, i love this method of doing math.

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Added: February 26th, 2009 at 9:01 am

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Category: Science & Technology

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