Ancient Egyptian Mathematics

Comments (16)

1.   by binary01

   Interesting.

   Reply
2.   by Kyle

   Thank you, that was awesome.

   Reply
3.   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.

   Reply
   •   by mistro

     i love this

     Reply
4.   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.

   Reply
   •   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.

     Reply
   •   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.

     Reply
     •   by Anonymous

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

       Reply
   •   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.

     Reply
5.   by Voxx

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

   Reply
6.   by nbn

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

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7.   by hundert

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

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8.   by very deep

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

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9.   by aardvarkian underground

   Well, that was worth digging up.

   Reply
10.   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

    Reply
11.   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.

    Reply