Sept 27 Russian Peasant Multiplication and Ancient Egyptian Multiplication

It was interesting to see the video on Russian peasant multiplication. Numberphile videos never fail to amuse me. I had to scratch my head when trying to relate it to the ancient Egyptian multiplication method. The aforementioned method uses doubling, binary, and sums based on the multiplicands as shown in class. It's an efficient method that is more intuitive for students to understand how to multiply large numbers together. The Russian peasant multiplication method uses a different algorithm but is similar to the ancient Egyptians. For example:   

With the two examples above, the left side uses the Russian peasant method and the right side uses the ancient Egyptian method. I realized that the number of times I half each round for Russian is the same number of times I double each round for Egyptian. There was a consistency there. I also saw that writing [the left] multiplicand in binary, the rows with 1 for Egyptian corresponded with odd numbers for Russian, and the rows with 0 corresponded with even numbers. Therefore the rows with even numbers in the Russian peasant method are not used. The rows with 1/odd are highlighted in teal, and the rows with 0/even are highlighted in red. In essence, with a chosen multiplicand, one method is doubling starting from 1 and reaching the largest power of 2 that is less than or equal to that multiplicand, and the other method is starting from the multiplicand and halving (ignoring the remainder if odd) until 1 is reached.