Ancient Egyptian Mathematics

 

Description:

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

Added: 11 months ago

Comments (11)

1.   by binary01 11 months ago

   Interesting.

   Reply
2.   by Kyle 11 months ago

   Thank you, that was awesome.

   Reply
3.   by Explainer 11 months ago

   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
4.   by Snappy 11 months ago

   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 11 months ago

     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.

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   •   by zdp 11 months ago

     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.

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5.   by Voxx 11 months ago

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

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6.   by nbn 11 months ago

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

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7.   by hundert 11 months ago

   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 11 months ago

   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 11 months ago

   Well, that was worth digging up.

   Reply