Egyptian Puzzlers

Michael Schneider shows how ancient Egyptians (and others) performed mathematics:

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(via Scotteriology)

With this in mind, you can appreciate the Rhind Mathematical Papyrus and similar documents that contain a series of math puzzles for the edification of ancient Egyptians. The Rhind Papyrus contains a variation on the puzzle of sevens (“A man has seven wives, each wife has seven bags, each bag has seven cats …”), which is still used today to teach exponents.

Of course, in the ancient world there was always another level. Writing itself was a magical act of creation, and puzzle solving may have provided insight into the nature of the universe. The NYT quotes the author of the Rhind Papyrus, who claims that he provides the “correct method of reckoning, for grasping the meaning of things and knowing everything that is, obscurities and all secrets.”

Incidentally, the Rhind Papyrus sets the value of Pi at about 3.16, which is better than the Bible’s value of 3.

  • Craig Horsup

    Knowing how easy this method is, what is the reasoning behind teaching kids times tables?

    • Darwin

      The usual formula of the rote learning basically tries to make kids memorize times tables perfectly. When you say, ‘What’s 6×7?”, you get an immediate answer. This method depends on repetition, rather than an actual understanding of the principles involved.
      I myself think this system is flawed. For example, after learning the tables up to 5, if you asked them what’s 5×11, they’d answer but they said that they didn’t know the answer to 11×5 since they hadn’t memorized the table for 11 yet.
      I myself never managed to learn anything by rote.

  • Kodie

    25′s a really easy number to double and redouble like that.

    • Francesc

      Every number is pretty easy to double, and anyway you only have to know the 2 table.

      But this is a mixed product when one of the numbers is in binary code, you can put both on binary code and, hey, doing products of 0′s and 1′s is always easy, too.

      An other alternative is factorizing both numbers in a cross-table. Let’s say 17 (16+1) and 37 (1+4+32). You construct rows and colummes with the 2 potencies (1,2,4,8,16,32) and every cell is the product of the numbers in the headings. It’s difficult to do 16 x 32? Well, every cell is the precedent cell, doubled (precedent in the column or in the row), so filling them is pretty easy too. You mark those cells with the factors of the numbers you want to multiply (i.e: (16,4), (16,32)…) and then you only have to add all the resultant cells.

      • Kodie

        Yeah, that didn’t make any sense to me. Usually what I do is round up, multiply in my head, subtract the product of the difference; I modified what I was taught. My mother taught me how to do percentages, like how to figure out what the sale price is. I don’t think I do it by rote – I actually know what those numbers are when I’m multiplying 6×7, or 483×28. I learned the rote “tables” but then I was also one of the few kids who understood why we have to do word problems without explicitly being told: this is how you’ll encounter math problems in the world. This is the actual reason you need to know any of this. I think this way it’s easier to do it in your head than the Egyptian way, I think you have to write it down, and no, it’s not as easy to double and redouble a number like 38 just knowing your 2s, much less keep it in order with the column next to it without writing it down.

        I hope this post was the right length.

        • Francesc

          It is :p
          Double and redouble 40 and 2, and then rest XD

          I too round up or down to already known numbers; sometimes I factorize, it is not that hard doing 17*25 = 17*5*5 = 85 * 5 (when you remember 17*5=85 automatically)
          or 17*25= (20*5 – 3*5)*5

          but of course, weren’t we talking about teaching maths to little kids?

          • Kodie

            I don’t know 17×5 is 85 automatically. I figured it out using the basic techniques I learned in 3rd grade multiplication. I have to say my 3rd grade teacher was dynamically special in a way most teachers I had were not, so maybe I learned something most people aren’t taught, or in a way most people don’t have the benefit of being taught. I was also better than math than most of my classmates until I got to 12th grade (calculus), and often selected for advanced subjects in the lower grades while everyone else was still struggling on the level.

            I mean, we never did “tables” past 10s, nothing over 10. 3×10, 10×10. WTF is a 17? We learned the basic mechanics of multiplication, then we moved on. No such thing as a 17s table or a 2s table up to/beyond 38. (Not that we all didn’t know how to count by 2s, but after 10, we weren’t counting what the 2 was multiplied by).

            I don’t know about teaching it to little kids, that was sort of the first commenters point, although I didn’t respond to him or her directly. The Egyptian way might train the mind to think of it a different way, but it doesn’t look like an effective way of… understanding what those numbers mean any more than the way I learned it.

            Here’s a treat from Abbott and Costello, 13×7=28

        • http://itsmyworldcanthasnotyours.blogspot.com WMDKitty

          I lived for the word problems. Those, at least, made SENSE!

      • Olaf

        Doubling in binary is easy, shift all numbers left. :-)

        • Michael

          This is the reason computers multiply this way. Bitshifting is very fast. When multiplying two base ten numbers, base-two factorization is not worth the effort, so more traditional methods of long multiplication are usually faster. But when multiplying two base two numbers, this method is obviously superior.

          • trj

            This is the reason computers multiply this way.

            If they continue multiplying they will soon outnumber us!

            .

            Heh. Sorry.

            • wazza

              I for one welcome our new, mathematically superior overlords.

  • Igor

    The Egyptians and the Chinese, independently, discovered the binary system, the common math language of the computer. Imagine if the Chariots of the Gods had given them microchips!

    (*mind boggling*)

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